Philosophia Scientiæ, 16-2 | 2012, « Modal Matters » [En Ligne], Mis En Ligne Le 01 Octobre 2012, Consulté Le 04 Décembre 2020
![Philosophia Scientiæ, 16-2 | 2012, « Modal Matters » [En Ligne], Mis En Ligne Le 01 Octobre 2012, Consulté Le 04 Décembre 2020](http://data.docslib.org/img/5104899/philosophia-scienti%c3%a6-16-2-2012-%c2%ab-modal-matters-%c2%bb-en-ligne-mis-en-ligne-le-01-octobre-2012-consult%c3%a9-le-04-d%c3%a9cembre-2020.jpg)
Philosophia Scientiæ Travaux d'histoire et de philosophie des sciences
16-2 | 2012 Modal Matters
Filipe Drapeau Contim et Sébastien Motta (dir.)
Édition électronique URL : http://journals.openedition.org/philosophiascientiae/729 DOI : 10.4000/philosophiascientiae.729 ISSN : 1775-4283
Éditeur Éditions Kimé
Édition imprimée Date de publication : 1 octobre 2012 ISBN : 978-2-84174-592-0 ISSN : 1281-2463
Référence électronique Filipe Drapeau Contim et Sébastien Motta (dir.), Philosophia Scientiæ, 16-2 | 2012, « Modal Matters » [En ligne], mis en ligne le 01 octobre 2012, consulté le 04 décembre 2020. URL : http:// journals.openedition.org/philosophiascientiae/729 ; DOI : https://doi.org/10.4000/ philosophiascientiae.729
Ce document a été généré automatiquement le 4 décembre 2020.
Tous droits réservés 1
SOMMAIRE
Modal Matters
On Modal Knowledge Filipe Drapeau Vieira Contim et Sébastien Motta
Conceptual Truths, Strong Possibilities and Our Knowledge of Metaphysical Necessities Christian Nimtz
A Two-Dimensional Semantics for Epistemic Modals Dan Quattrone
Modal Integration Scott A. Shalkowski
Peacocke’s Epiphany: A Possible Problem for Semantic Approaches to Metaphysical Necessity Jon Barton
What is Absolute Necessity? Bob Hale
Essentialist Blindness Would Not Preclude Counterfactual Knowledge Sònia Roca-Royes
Représentations de soi et modalités Manuel Rebuschi
Varia
Sources et nature de la philosophie de la physique d’Henri Poincaré Joâo Principe
Philosophia Scientiæ, 16-2 | 2012 2
Modal Matters
Philosophia Scientiæ, 16-2 | 2012 3
On Modal Knowledge
Filipe Drapeau Vieira Contim and Sébastien Motta
We would like to thank the persons and institutions without whom this volume would not have been possible. Many thanks in particular are due to Manuel Rebuschi, the managing editor of Philosophia Scientix for having accepted this special issue in his journal and to Sandrine Avril for her remarkable editorial work. Funds allocated by the University of Rennes 1 as part of the "defis scientifiques emergents" program for the years 2010 and 2011 financed a large part in this project. The Archives Henri Poincare (University of Nancy 2) were also of great assistance. Special thanks are due to Anand Vaidya for his substantial help and his friendly encouragements, and to Maud Le Garzic and Philippa Richmond for reading and commenting on preliminary drafts of this paper. Finally, we are very grateful to all those who contributed, through their reviews, to selecting and improving the papers submitted for this issue: Alexandra Arapinis, Bjorn Brodowski, Daniel Cohnitz, Fabrice Correia, Christopher Daly, Julien Dutant, Paul Egre, Marcello Oreste Fiocco, Heimir Geirsson, Adrian Heathcote, Dominic Gregory, Jussi Haukioja, Robert J. Howell, Carrie Ichikawa Jenkins, Pierre Joray, Boris Kment, Franck Lihoreau, Pascal Ludwig, Olivier Massin, Peter Murphy, Brian Rabern, David Robb, Andrea Sauchelli, Anand Vaidya, Clas Weber and Richard Woodward.
1 The present volume is the result of a research project, Ontologie et epistemologie des modalites, supported during 2010-2012 by the universities of Rennes 1, Nantes, Paris IV and Nancy 2. Most of the papers collected here were presented and discussed in the course of an international workshop on modality held at the Maison des Sciences de l’Homme de Lorraine in Nancy, from the 1st to the 3 rd December of 2010. Two main themes stood out.
2 The first was the application of possible worlds semantics to fictional and propositional attitude statements. It is illustrated here by Manuel Rebuschi’s paper "Representations de soi et modalites". Rebuschi starts from those puzzling cases in which reflexive pronouns do not seem to co-refer with their antecedent, notably in reports of someone considering a representation of herself: photograph, statue, mirror, etc. Rebuschi suggests treating these as "modal windows" that represent how an individual would be in other possible circumstances. Rebuschi then offers a semantics in which reflexive pronouns can be interpreted according to modal windows. This accounts for the
Philosophia Scientiæ, 16-2 | 2012 4
specificity of de se attitudes while maintaining the co-reference link between anaphoras and their antecedents.
3 The second theme was modal epistemology. Almost all the papers gathered here deal more or less directly with the vexed question: how can we acquire knowledge of necessities and possibilities? Even though works on modal epistemology have flourished over the past two decades, syntheses on the subject are still scarce.1 This is what our introduction will provide, along with an overview of each paper of the volume.
4 After a quick survey of the different forms that modal knowledge endorses (§ 1), we outline the main difficulty encountered by modal epistemology and probably the simplest theory conceived to remedy it: the analytic theory of necessity (§ 2). We then show how Kripke’s theses on the necessary a posteriori and the contingent a priori put the problem back on the table (§ 3). Next, two attempts to accommodate the analytic account of modal knowledge to Kripke’s results are presented: Alan Sidelle’s conventionalism and Jackson-Chalmers’ brand of two-dimensionalism (§4). The more specific question concerning how to integrate possible worlds style metaphysics into modal epistemology is then addressed. This is followed by a discussion of David Lewis argument to the best explanation and Christopher Peacocke’s principled account of possibility as two possible answers to the integration challenge (§ 5). Finally, we examine a recent proposal made by Christopher Hill and Timothy Williamson. Their aim is to give knowledge of metaphysical modality a certain respectability by showing that it can be derived from knowledge of ordinary counterfactuals (§ 6). We will defend the counterfactual approach against a potential charge of circularity (§ 7).
1 Varieties of modal knowledge
Modal epistemology is a recent branch of epistemology that purports to explain our knowledge of possibilities and necessities, in the alethic sense of modality. As stated, this task presupposes two things. First, that modal truths are at least knowable, if not known. This assumption is nonetheless cancellable to the extent that modal knowledge-claims do not have the robustness of perceptual knowledge-claims or even mathematical knowledge-claims. Thus, if we fail to explain modal knowledge, modal skepticism is still an open option. Second, modal realism is assumed. Modal realism here means that modal statements and beliefs are true or false in virtue of objective features of reality. From [Hume 1992] to [Blackburn 1987], various forms of non- cognitivism have challenged this claim.2 On such views, a statement such as "Socrates is necessarily a person" is not designed to describe a modal fact but to express anorm (to use "Socrates" as a person-noun) or a cognitive state (our incapacity to imagine Socrates as a cat or as a stone). Albeit coherent, non-cognitivism should be considered as a position of last resort insofar as it would lead one to say that ordinary speakers are massively wrong about the truth-value aptness of their modal assertions. Importantly, modal realism so intended is not committed to saying that reality has irreducible modal features. It is indeed compatible with semantic accounts of modality on which linguistic conventions are the ultimate truth-makers of modal statements.
5 In everyday life, modalizing is a pervasive cognitive activity that takes many forms. It manifests itself in ascriptions of capacities and dispositions. It occurs in practical deliberations when possible courses of action are considered. It takes place more
Philosophia Scientiæ, 16-2 | 2012 5
prominently in counterfactual reasoning. Assessing statements of the form "if p were (had been) the case, q would (have) occur(red)" plays a crucial role in our capacities to discover causes,3 to impute responsibilities, to ascribe dispositions or to categorize objects.4 Curiously, ordinary modal knowledge has been quite neglected by epistemologists, their attention being instead focused on modal assertions made in philosophical contexts.
6 Many philosophical statements aim to describe the nature, the identity or the dependence relations between objects, events or properties. Even though these claims have no modal content, they do have modal consequences, mostly expressed in terms of necessity, and the way to test them is to imagine unactual but possible counterexamples. The recent blossoming of modal epistemology is to a large extent indebted to the revival of thought-experiments, in particular in metaphysics of mind. We are, in this respect, witnessing some kind of revival of what happened in the seventeenth century when Descartes dualist "proof" sparked off debates on the reliability of conceivability arguments. The impetus today is the famous argument that [Kripke 1980] sets forth against type physicalism. Type physicalists hold that phenomenal properties, for instance a painful sensation (P), are identical to brain properties, say such and such cortico-thalamic oscillation (C). Yet, it is an instance of the necessity of identity principle that (C = P) only if □(C = P).5 Arguing that C could conceivably have occurred without P, and vice versa, Kripke concludes by modus tollens that type physicalism is false. Since then, Kripke’s conceivability argument has had plenty of descendants: conceivability of zombies, mad pain, Swampman, inverted spectrum, and so on. Interestingly, most of these thought-experiments result in possibility rather than in necessity claims. They are used negatively, to rebut identity or dependence theses, or else to undermine the alleged necessary and sufficient conditions defining a certain concept (knowledge, person, responsibility, etc.). They are often devised by dualists, as shown by the debates around the mind-body problem or material constitution. Their significance in philosophical reasoning reminds us how much modal epistemology is an integral part of the epistemology of philosophy.
7 We have distinguished between two forms of modal knowledge, ordinary and philosophical. It is methodologically best to keep them apart, at least to begin with, since problems raised by the one are not inevitably those raised by the other. Some authors, such as [Van Inwagen 1998] and [Wilkes 1988], thus profess skepticism toward the second and not toward the first. The main difference lies in the fact that ordinary counterfactuals describe possibilities that only differ slightly from the way things actually are; intuitively, they are close possibilities. Correlatively, ordinary necessities are always relative to a set of actual facts held as fixed. In contrast, philosophers claim to describe absolute possibilities and necessities: not only, for instance, what I could have been, given my physical constitution or given what actual technology allows me to do, but what I could have been simpliciter. The philosophical term of art for these absolute modalities is metaphysical possibility and necessity. Since philosophers claim to reason on the most inclusive sphere of possibilities, most of the constraints imposed upon ordinary modality are removed, thus opening the door to remote possibilities in which technology or physical laws differ radically from those prevailing in the actual world. We are asked, for instance, to imagine what would happen to us if we were subjected to a split-brain transplant [Parfit 1984], something that is technologically, and also probably biologically, impossible. Philosophical assertions also claim to deliver
Philosophia Scientiæ, 16-2 | 2012 6
the strongest necessities, for metaphysical necessities imply other necessities but not the other way around. Even thought-experiments of the most speculative parts of physics cannot claim to reach such necessities, for such imaginary scenarios comply with natural laws, traditionally held to be metaphysically contingent by philosophy.6
2 Necessity, apriority and analyticity
Let us concentrate for the time being on problems common to both kinds of modal knowledge. The traditional challenge for modal epistemology is this: perceptive experience constitutes the main source of knowledge; however, it only gives us access to what is the case, and not to what is necessarily the case or what could have been the case. So, how do we come to gain knowledge ofmodal facts? Given that necessities and unactual possibilities are lacking in perceptive contents, only two options remain. The first is to embrace radical empiricism: it denies the reality of modality so that the question of modal knowledge cannot arise. The second option is initiated by [Kant 1965]. Restating his trust in modality and admitting that it cannot be known empirically, Kant concludes that it must be known apriori. Modal knowledge is then less a problem than the starting point of an argument designed to prove the existence of a priori knowledge, in particular the apriority of mathematics. Kant’s argument rests on the following implication: (1) If □p, it is then true a priori that □p (if □p is knowable at all)7 Kant however relies on a stronger principle,8 one that allows him to conclude from the necessity of mathematical truths to their apriority (and not only to the apriority of their necessitation): (2) If □p, it is then true a priori that p (if p is knowable at all) This strategy only postpones the problem. To claim that modal knowledge is a sub- domain of a priori knowledge tells us nothing about its source, insofar as a priori justification is defined negatively: one is justified a priori to believe that p iff empirical evidence does not play any role in the justification of one’s belief. Defined thus, a priori knowledge appears no less mysterious than modal knowledge.
8 An appealing solution is to reduce modal knowledge to a kind of semantic knowledge. The most straightforward way to do this is to adopt the analytic theory of necessity (AN), in the footsteps of the logical empiricists [Carnap 1956], [Ayer 1971]. AN is, first and foremost, a theory concerned with the source of necessity. It explains that a sentence S is necessarily true by the fact that S is analytically true, that is, true purely in virtue of the meaning of its component expressions. It is critical to note that the italicized phrase has no immediate epistemological import. It does not convey that meaning provides knowledge of S’s truth, but that it is the truth-maker of S. In the terms of [Boghossian 1997], we are faced here with the metaphysical concept of analyticity, and it is easy to show how metaphysical analyticity can be a source of necessity. Take e.g., an instance p of the first axiom of Lukasiewicz’s propositional logic, (Ф→(Ψ—Ф)). According to the metaphysical concept of analyticity, p is true purely in virtue of the meaning of the constant "→". Since meaning is sufficient to make p true, then, keeping p s meaning constant, p would be true no matter what else was the case. Yet, "being true no matter what" captures precisely the pre-theoretical sense of absolute necessity, the one reflected in the phrase "true in all possible worlds" whose use is common practice nowadays. Conclusion: p is necessarily true; p s analyticity explains its necessity.
Philosophia Scientiæ, 16-2 | 2012 7
9 The route from AN to modal epistemology is then straightforward. One only has to add the thesis according to which meaning is transparent to competent speakers. It amounts to saying that if S is true by meaning alone, then, just by grasping S, a reflective speaker can know that S is true by meaning alone.
10 To get from here to S being necessarily true, the speaker only has to replicate the explanation given above. So, it is semantic knowledge that gives us access to modal truths. Moreover, AN readily explains how such knowledge is a priori. Metaphysical analyticity is indeed convertible in epistemic analyticity (but not the other way around), 9 which leads naturally to the analytical theory of a priori. According to the latter view, S is true a priori iff the mere grasp of S’s meaning suffices for being justified in holding S true. This makes modal knowledge respectable not only as modal knowledge but also as a priori knowledge.
11 It follows from this ambitious theory of analyticity that modal categories (necessary/ contingent) and epistemic categories (a priori/empirical) are reduced to a single pair of semantic categories (analytic/synthetic). This reduction has a cost however: it does not allow de re modal claims suchas " Socrates is necessarily a person" or "No one could have biological parents other than those one actually has". [Quine 1947], [Quine 1953] showed indeed that attributing a property that is "analytically true" of an object is meaningless.10 "Too bad for essence!" might say those who think that the notion is unintelligible.
12 Another consequence of AN, rarely noticed, is that it "modalizes" a priori knowledge, making it a kind of modal knowledge. In such an account, one cannot know a priori that p unless one has prior knowledge that p is true by meaning alone. More precisely, it is the fact that p is known to be true by meaning alone "no matter what" that explains how one can know it a priori to be true of the actual world, whatever it turns out to be. Since necessity reduces to analyticity, this amounts to saying that one must know a priori that up in order to know a priori that p. Necessity is not injected afterwards to what is known a priori: all a priori truths are known sub specie necessitate. On this point, AN is rejoined by rationalist conceptions of a priori knowledge on which a rational a priori insight that p is true consists in apprehending p as necessary [BonJour 1998]. To the extent that all a priori knowledge involves knowledge of a necessity, AN implies the converse of Kant’s principle (2) seen above: (3) If it is true a priori that p, then □p As we will see in the next section, this is the touchstone of the analytic theory of necessity.
3 The Kripkean turn
The renewal of modal epistemology is greatly indebted to Kripke’s innovative theses on modality. [Kripke 1980]’s main aim is to emancipate modal categories from epistemic and semantic categories. To this end, Kripke brings to light two kinds of statements: necessary but empirical truths and a priori albeit contingent truths. In this section, we will examine first the consequences they have vis-a-vis the analytic theory of necessity, and then their consequences for conceivability-based accounts of modal knowledge. Consider the following statements:
Philosophia Scientiæ, 16-2 | 2012 8
(a) Socrates is a human being.
(b) This table is made out of wood.
(c) Isaac Newton is the biological child of Hannah Ayscough.
(d) Gold has the atomic number 79.
13 (a)-(d) are necessarily true since they attribute essential properties concerning fundamental kind, material composition, origin or microphysical structure to rigidly designated objects.11 Nevertheless, none of them can be known a priori: we need empirical evidence to know that they are true. Such empirical necessities provide a case against modal theories committed to Kantian principles (1) and (2), in particular against AN. Let us consider an a posteriori necessary truth p.If p can only be known empirically, then p cannot be known just by grasping its meaning. As metaphysical analyticity requires epistemic analyticity, a fortiori, p cannot be true by virtue of its meaning. Yet p is necessarily true. Therefore, it follows that p’s necessity does not take its source from meaning or linguistic conventions.
14 This result, however, is not enough to show that the concept of truth by meaning alone is incoherent or denotationless for it remains compatible with the fact that some statements, typically logical and conceptual truths, owe their truth to their meaning. What it does show, at least, is that AN as an ambitious theory of necessity is false. Cases of empirical necessities do seem to show that necessity may take its source from the very nature of things. Correlatively, the new term of metaphysical necessity ousts the use of logical necessity (broadly taken to cover logical as well as conceptual truths) in order to refer to absolute necessity. This new term captures better than its predecessor the idea that necessity may stem from the nature of things and not from meaning alone. Now, in breaking up with analyticity, Kripke not only takes us back to our original problem, that is, explaining modal knowledge, he also makes the problem more mysterious: how can there be empirical essences if experience can only tell us how things are and not how they must be?
15 The emancipation of necessity from apriority does not stop here. Kripke wants us to push it further, up to the denial of the converse implication (3), from apriority to necessity. One counterexample is:12 (e) Neptune perturbs the orbit of Uranus (e) is true a priori albeit contingent. Suppose that, as did the French astronomer Urbain Le Verrier, we fix the reference of the rigid name "Neptune" by the definite description "the planet, whatever it is, that is responsible for the deviations in Uranus’ orbit". This reference-fixing condition then puts us in a position to know a priori that (e) is true. However, it remains contingent that Neptune perturbs Uranus orbit: had the history of our solar system been different, Neptune could have found itself too far from Uranus to interfere with its path.
16 That this kind of counterexample is fatal to AN, insofar as AN is committed to (3), is all too rarely observed. The lesson one can draw is twofold. First, epistemic analyticity is independent from metaphysical analyticity. Just by grasping (e), one can know a priori that (e) is true. However, the contingency of (e) indicates that it owes its truth to extra- linguistic facts, not to meaning alone. Second, a priori knowledge does not involve
Philosophia Scientiæ, 16-2 | 2012 9
modal knowledge, a priori truths are not known sub specie necessitate. This rebuts not only AN but also rationalist theories of a priori knowledge. Indeed, it is one thing to explain how one knows apriori that p, it is quite another to explain how one knows a priori that up, since a priori truths can be necessary as well as contingent. Epistemic analyticity may help to explain a priori non-modal knowledge but it is far from obvious that it can have as much success with a priori modal knowledge. We have thus landed on an old problem: how do we come to know the necessity of logical and conceptual truths? At the epistemological level, the necessity of these a priori truths is no less mysterious than empirical necessity.
17 We have seen that, by bringing down the analytic theory of necessity, the divorce between necessity and apriority raises old, as well as new, problems for modal epistemology. One feels its repercussions beyond the analytic theory since it also threatens conceivability-based accounts of modal knowledge.
18 Here lies the difficulty: take an empirical necessity, such as "gold has the atomic number 79". It is conceivable that gold has a different atomic number— think for example about all the alternative hypotheses that were contemplated before experiment showed us what gold’s atomic number was. By this, it is meant that one can imagine a situation in which gold has a different atomic number, without facing logical or conceptual inconsistencies. Nonetheless, gold could not have had an atomic number other than 79: if an element had possessed a different atomic number, it would not have been gold. This gap between conceivability and possibility is a matter of concern for it is a common view, since Descartes at least, that conceivability is a reliable guide to possibility.
19 For those who subscribe to conceivability-based accounts of modal knowledge, conceivability is even the only road to possibility.
20 Whereas the analytic theory of necessity puts the emphasis on knowledge of necessity, conceivability accounts start from knowledge of possibility. The key idea is that possibilities are known by conceivability intuitions, though there are disagreements concerning the strength of the inferential link that leads from conceivability to possibility.13 It may be strict implication or fallible justification depending on whether the notion of conceivability is more or less cognitively idealized, the difficulty being to strike a happy medium: a too loose notion of conceivability would not provide a reliable criterion of possibility; a notion too idealized would be useless and would only replace the question "how do we know that p is possible?" with the question "how do we know that p is conceivable?". Still, most supporters of the conceivability method accept the (CP) thesis: (CP) If a subject S can imagine a situation under a description which (i) makes p true (ii) is sufficiently detailed and (iii) does not contain any logical or conceptual inconsistencies, then S is justified in believing that it is possible that p. (CP) leaves room for modal errors. They typically occur when an inconsistency goes unnoticed due to an insufficiently detailed description. To detect them can take time. Consider, for example, how long it took to realize that the universal class was in fact impossible since it contradicted Cantor’s theorem. Note however the crucial point that such errors challenge neither the reliability of the conceivability method, nor its a priori character, inasmuch as they can always be corrected through a better reasoning, in a purely a priori way.
Philosophia Scientiæ, 16-2 | 2012 10
21 This traditional picture is swept away by Kripkean cases of empirical necessities. Indeed, for any empirical impossibility p, the conceivability method will generate a "false positive", i.e., a case where p is conceivable without being possible. Worse: the gap between conceivability and possibility can never be fulfilled, not even by ideal cognizers. A subject with unlimited time and reasoning capacities is as incapable as we are to detect a priori an inconsistency when conceiving p. It is as if our concepts were blind to impossibilities, at least the empirical ones. Even though this gap does not generate "false negatives" (i.e., cases of inconceivability without impossibility) and so does not directly affect necessity claims, it does cast a doubt on all possibility claims. This has, it would seem, disastrous consequences for armchair style philosophy since many of its distinction or independence theses are based on possibility claims.
4 Reconciling necessity and apriority
While they have contributed to rehabilitate the notion of essence that has fallen into disfavor since Quine’s critics, Kripkean a posteriori necessities have sparked off a vigorous reaction from the supporters of the traditional link between modality and apriority. Their main strategy consists not in questioning the existence of a posteriori necessary truths, but in offering a deflationist reading of them, both at an epistemological and a metaphysical level. The philosophical significance of Kripkean necessities, so they say, has been greatly exaggerated: these question neither the fundamentally a priori character of modal knowledge, nor its reduction to a sort of semantic knowledge. They are also compatible, it is argued, with the idea that necessity has its source in meaning. In a certain way, it is all about elaborating a sophisticated version of the old analytic theory of necessity, one that is able to incorporate Kripke’s results and then render them harmless.
22 Paradoxically, Kripke himself suggested the main line for this strategy. [Kripke 1971] claims that empirical knowledge of a necessity stems from knowledge of two kinds of premises: on one hand, one (or many) empirical and non-modal premise(s), responsible for the empirical character of this knowledge; and, on the other hand, one (or many) modal and a priori known premise(s), responsible for its modal content. In order to illustrate this division of epistemic labor, consider the following a posteriori truth:
(4) □ (water is made of H2 O molecules) According to Kripke’s proposal, empirical knowledge of (4) can be factorized into empirical non-modal knowledge of (5) and a priori modal knowledge of (6):
(5) Water is made of H2O molecules
(6) Water is made of H2O molecules → □ (water is made of H2O molecules). If it is contested that (6) is known a priori, the factoring can be pushed further until the step where necessity is injected corresponds to an a priori knowledge. Abstracting from the particular subject and predicate, one could claim thus that the de re necessity occurring in (6) is ultimately derived from the general individuation principle (7) that is known a priori: (7) (K is a chemical kind and S is a microphysical structure) → ((K has S) -□ (K has S))
23 The crucial point is that all essentialist conditionals used as ultimate premises in the derivation of empirical necessities are a priori known. If Kripke’s conjecture is right, this reconciles knowledge of essence with a priority. Kripkean necessities thus lose
Philosophia Scientiæ, 16-2 | 2012 11
much of their puzzling appearance. One can indeed assert that there are a posteriori necessary truths while conforming to Hume-Kant’s dictum according to which experience tells us only what is, and not what must be.
24 There is still, however, an unelucidated point here: how do we get to know a priori (7) or (6) in the first place? Kripke is rather allusive in this respect and simply says that essentialist conditionals can be known "by a priori philosophical analysis" [Kripke 1971, 153]. This opens the door to refined versions of the analytic theory of necessity. A noteworthy example is given by Alan Sidelle’s conventionalist account of necessity [Sidelle 1989]. Sidelle holds that what makes de re general principles such as (7) true are not extra-linguistic modal facts, but the rich semantic structure of natural kind terms. It is thus argued that the meaning of natural kind terms encodes a complex convention concerning how to apply them in the description of counterfactual situations. One can formulate it as follows: If most of the samples that fix "K"’s reference satisfy a property P which is responsible for their observable features, then "K" applies to x in a counterfactual situation w iff x satisfies P in w.14 This leaves room for experience since schematic letters figure blanks that can only be filled by empirical inquiry. However, once the values of the parameters have been specified, necessity is generated by a purely semantic rule that determines the counterfactual extension of the terms as a function of their actual extension. An essentialist conditional such as (K is P) → □( K is P)(where "K" and "P’"s range are restricted to relevant kinds and properties) is then nothing more than a semantic rule put in the material mode. Likewise, modal knowledge is no longer mysterious, being based on tacit knowledge of rules governing the application of terms in counterfactual reasoning.
25 If Sidelle is right, necessity takes its source in meaning. However, and this is where Sidelle’s theory diverges from the old analytic theory of necessity, this does not mean that all necessary statements are true by meaning alone. For instance, even if (5) owes its necessity to semantic rules, it is still made true by extra-linguistic facts, namely that
most of the samples by which the reference of "water" is fixed, are made of H2O molecules. This is what accounts for the empirical profile of (5). In this way, all cases of a posteriori necessity can be integrated into the analytic conception of necessity. This also shows a deeper difference between the old and the new analytic theory of necessity. In the old theory, the necessity of a statement (e.g., it being made true by meaning alone) explains why it is actually true. The new theory reverses the order of explanation: the actual truth of (5), combined with conventions, explains why (5) is true of necessity. Insofar as a posteriori necessities are concerned, necessity is not something from which truth derives; it is something that our conventions add on top of truth.
26 Although it reconciles knowledge of essence (in its general form) with apriority and analyticity, Sidelle’s theory does not fill the gap between conceivability and possibility generated by a posteriori necessities. This is precisely the challenge that [Jackson 1998], [Chalmers 1996], and [Chalmers 2002] are claiming to meet. According to them, the divorce between necessity and apriority is only a superficial linguistic phenomenon that does not constitute a real threat for conceivability approaches of modal knowledge; the golden triangle that linked modal, epistemic and semantic categories
Philosophia Scientiæ, 16-2 | 2012 12
before Kripke can be restored thanks to the powerful machinery of two-dimensional semantics.
27 Two-dimensional semantics covers a family of semantic theories whose common point is to evaluate statements and their components, not relative to a single index, as in standard modal semantics, but relative to a pair of indices, the first one normally used as a context of interpretation, and the second as a circumstance of evaluation. This double dependence of semantic values on indices enables two sorts of intensions to be defined, from which emerges a finer-grained theory of meaning. The strong two- dimensionalism advocated by Chalmers and Jackson stands out by its metaphysical and epistemological ambitions. Their declared purpose is to re-establish the equivalence between necessity and apriority undermined by Kripke.
28 The central idea is that there are two ways of considering a possible world w when evaluating a statement S. First, we may assess S’ s truth-value relatively to w considered as counterfactual. This is the standard procedure since Kripke: we keep the actual world fixed, and w is considered as a way the world could have been but is not. The "secondary intension" or "2-intension" associated with S is then defined as a function from possible worlds taken as counterfactual to truth-values. Second, we may evaluate S relatively to w considered as counter-actual. This is the novelty: we suspend our knowledge of how the actual world is and we consider w as a way the actual world may turn out to be, for all we know a priori. The "primary intension" or "1-intension" associated with S is then defined as a function from possible worlds taken as actual to truth-values. The whole interest of the two-dimensionalist apparatus lies in those cases in which 1-intension and 2-intension do not coincide.
29 Take, for instance, the statement (5) seen above and a possible world w1 in which the Earth verifies the Twin-Earth scenario imagined by Putnam: the surface of the Earth is 70% covered in a liquid that has all the macroscopic features of water (it quenches thirst, is colorless, tasteless, findable in the seas, the lakes and the oceans, and so on— in short, the waterish stuff), but it consists of molecules of XYZ. Let us then grant that the term "water" has its reference fixed by a complex descriptive condition, e.g., being the waterish stuff, which any speaker tacitly knows by being competent in her use of the term "water". Since "water" is rigid and its reference-fixing condition picks up
H2Ointhe actual world, "water is H2O" is true relatively to all possible worlds taken as counterfactual, including w1: considered as counterfactual, w1 can be described as a
world in which water—alias H2O—is replaced by some other superficially similar liquid. The2-intensionof (5) is thus necessary. This is what accounts for the fact that it is metaphysically necessary that water is H2O. However, (5) is false relatively to some possible worlds considered as actual, especially w1: if w1 turns out to be our actuality, then the XYZ-liquid satisfies the reference-fixing condition of "water" and (5) is then false. Considered as actual, w1 must this time be described as a world in which water is XYZ. Since the truth-value of (5) varies depending on the way the actual world might turn out to be, the 1-intension of (5) is contingent. This accounts for the empirical character of (5).
30 This example shows that the discrepancy between apriority and necessity noticed at the level of secondary modality disappears at the deeper level of primary modality. Jackson and Chalmers extend this conclusion to all cases of Kripkean a posteriori necessities: albeit 2-necessary, they are all 1-contingent, in accordance with their empirical character. Likewise, all a priori contingent statements are 2-contingent but 1-
Philosophia Scientiæ, 16-2 | 2012 13
necessary, in accordance with their apriority. Thus, the Kantian equivalence between necessary and apriority can be re-established at the level of 1-modality. This is the core thesis of Chalmers’s two-dimensionalism: Core Thesis: for any sentence S, S is a priori iff S has a necessary 1-intension. [Chalmers 2004, 165] This amounts to saying that we have a priori access to possibility when modality is taken inits primary sense. Readfrom right to left, the equivalence excludes "strong necessities", namely cases where a hypothesis H cannot be excluded by a priori reasoning in spite of the fact that all 1-possible worlds verify ~H. Granted that there is no such counterexample, the link between conceivability and possibility can thus be restored. Let us say that S is 1-conceivable when it is possible in principle to imagine in great detail a situation considered as actual that verifies S, such that no contradiction is revealed, even on idealized a priori reflection [Chalmers 2002, 153]. It is one thing to say that one can 1-conceive a situation that verifies S, it is another to say that there is a true 1-possible world that verifies S. Yet the Core Thesis warrants that there is no deceitful 1-conceivability or illusion of 1-possibility, when the notion of conceivability is sufficiently idealized. This is the main line of the new brand of Modal Rationalism championed by Chalmers: Modal Rationalism: For any sentence S, S is 1-conceivable only if S is 1-possible. [Chalmers 2002, 194] The critical point is that the conceivability method keeps its a priori character, for 1- conceivability rests on a priori reasoning and mastery of 1-intensions, to which competent speakers have a priori access. More importantly, 1-conceivability may be used as a reliable guide to metaphysical possibility in those cases in which it can be established a priori that 1-possibility implies 2-possibility. It happens for any sentence whose 1-intension and 2-intension coincide (again, something to which a competent speaker has a priori access).
31 Lack of space prevents us from discussing in detail the abundant literature that Chalmers and Jackson’s two-dimensionalisms have generated. Many criticisms came from the supporters of a posteriori physicalism who dispute the inference from conceivability to possibility in Chalmers zombie dualist argument.15 The neo- descriptivist interpretation that Chalmers and Jackson give of primary intensions also gave rise to vigorous reactions from philosophers of language within the tradition of Direct Reference Theory [Soames 2005].
32 The present volume includes two papers from the two-dimensionalist trend.
33 In "Conceptual Truths, Strong Possibilities and our Knowledge of Metaphysical Necessities", Christian Nimtz undertakes to show that knowledge of conceptual truths can provide a priori knowledge of metaphysical necessities. His argument proceeds thus: first, he champions the idea of conceptual truth against the recent objections that [Williamson 2007] addressed to epistemic analyticity. Then, Nimtz uses two- dimensionalist tools in order to show that there is a reliable epistemic route that leads from epistemic analyticity to a priori knowledge of metaphysical necessities (2- necessities in Chalmers terminology). This route incorporates two steps. (i) First, from the fact that p is a conceptual truth, one infers that p is 1-necessary. (ii) Second, from the fact that p is 1-necessary, one infers that p is 2-necessary. Step (ii) is the critical one. Its legitimacy is indeed questioned by all cases of contingent a priori in which 1- necessity coexists with 2-contingency. Nimtz’s answer is that it does not undermine the reliability of this inference insofar as we can know a priori what those cases where it
Philosophia Scientiæ, 16-2 | 2012 14
fails are. Indeed, all cases of contingent a priori occur in the presence of an actuality- dependent term, that is, a term whose counterfactual extension is determined by its actual extension. And, precisely, a competent speaker can know a priori which terms are actuality-dependent. Step (i) remains, which corresponds to the Core Thesis read from left to right. (i) would be defeated only if there existed "strong possibilities", that is to say converse cases of the "strong necessities" seen above, in which p is not conceivably false for all we know a priori, though there is a true possible world considered as actual that falsifies p. Arguing that there isn’ t any such plausible counterexample, Nimtz concludes that step (i) is safe and that it can thus be the starting point of our knowledge of metaphysical necessities.
34 In "A Two-Dimensional Semantics for Epistemic Modals", Dan Quattrone concentrates on a thorny difficulty posed by cases of empirical necessities for the semantics of epistemic modals. Standard truth-conditions of statements of the form "it may/might
be the case that p" (in symbols ◊ep) are given by quantifying over a restricted set of
possible worlds: ◊ep is true iff there is a possible world consistent with our knowledge in
which p is true. Consequently, ◊ep cannot be true unless p is metaphysically possible.
Now, take any a posteriori necessity, for instance "water is H2O", and suppose we assert "◊e(water is XYZ)" while there is no available empirical evidence that water is not XYZ. Intuitively, the epistemic modal is true. However it has to be false under the standard
account: since "water is H2O" is true by metaphysical necessity, there is no possible world in which water is XYZ, and a fortiori no such possible world consistent with our knowledge. In short, we don t have enough possible worlds to represent all the hypotheses left open by our current knowledge. Quattrone sets himself the task of reformulating epistemic modals truth-conditions leaning upon the conceptual resources provided by Stalnaker’s two-dimensionalism [Stalnaker 1978].
35 First, each sentence S is associated with a metaproposition that represents how the proposition expressed by S varies depending on the world in which S is produced. Next, epistemic modals’ truth-conditions are given by "diagonalizing" the metaproposition:
◊eS is true iff there is a possible world w such that the value of S’s metaproposition in w is true at w. Since "water is XYZ" expresses a true proposition when produced in a
"waterish-XYZ" possible world, this accounts for the intuitive truth of ◊e (water is XYZ). An interesting and quite puzzling feature of Quattrone’s account is that the ◊e operator behaves like a "Monster" [Kaplan 1989], that is, like an operator capable of shifting the
context of utterance. Sentences embedded in ◊e seem indeed to be interpreted from a world different from the world of utterance. Quattrone replies that it does not affect the plausibility of his account inasmuch as there are recognized cases of monstrous operators in natural languages. Finally, Quattrone shows how his two-dimensionalist treatment of epistemic modals differs from Chalmers and why his should be preferred.
5 The Integration Challenge
The problem we are now facing is much more general in its scope than the previous one. The Integration Challenge put forward by [Peacocke 1999] concerns not only the modal domain but also the philosophy of mathematics, of time, of mind, and metaphysics of properties. In its modal version, it starts from the acknowledgment that the demands for modal epistemology and those for modal metaphysics seem to push in opposite directions. A gain for the former constitutes a cost for the latter, and vice
Philosophia Scientiæ, 16-2 | 2012 15
versa. Theories that ground modality in possible worlds are prima facie appealing as they match directly with our best account of truth-conditions for modal statements, i.e., possible worlds semantics. Thus the same feature that makes them ontologically recommendable seems also to induce insuperable difficulties in epistemology for we have no idea on how to access possible worlds. Conversely, by adopting an analytic theory of necessity, we dispel the aura of mystery surrounding modal knowledge since it reduces to a sort of semantic knowledge. Yet, this advantage has a metaphysical cost, analytic theories being illadapted to account for the modal strength of logical or mathematical principles—how can we make necessity out of contingent conventions? The challenge is thus to make modal ontology and modal epistemology coherent with each other. We would like to have a satisfactory account of what makes modal statements true and how we know them to be true.
36 The difficulty is made especially acute in that most of the metaphysical modal theories that flourished in the 1970s and 1980s have developed in the wake of possible worlds semantics, without paying attention to epistemology. From such semantics, we have inherited the now deeply entrenched habit of giving truth-conditions for modal statements by quantifying over possible worlds. Possible worlds have, in fact, become almost indispensable nowadays: used in the meta-language of modal logic, they make sense of iterated modalities and provide an illuminating account of the validity of modal inferences; their expressive power seems even superior to that of modal operators. Similarly, a lot of theses in philosophy of mind, such as physicalism, mind- body supervenience and externalism, would be hardly intelligible without the possible- worlds idiom, not to mention philosophy of language, whose main theses and concepts are often put directly in terms of possible worlds (think for instance about the rigidity thesis or the distinction between intension and character).
37 For a lot of metaphysicians, the theoretical utility of possible worlds is a good enough reason to consider them otherwise than as mere heuristics. They argue that quantification over possible worlds must be taken at face value, thus embracing possible worlds realism, be it extreme [Lewis 1986] or actualist [Adams 1974], [Plantinga 1976], [Stalnaker 1976]. Possible worlds realism often goes hand in hand with a stronger thesis according to which possible worlds are the ultimate truth-makers of modal statements. In such a view, the truth-maker of "Socrates could have been killed at the battle of Potidaea" is not Socrates himself, his nature (the fact that it does not preclude Socrates being killed), nor one of his dispositional properties (being possibly killed). It must be founded in the very existence of a possible world in which Socrates, or one of his counterparts, is killed at Potidaea.
38 Albeit ontologically appealing, such views seem to make the problem of modal knowledge intractable. In Lewis strong realism, possible worlds are maximal mereological sums of spatiotemporally related concrete parts. Ex hypothesi, each world is causally isolated from all others, and this is particularly true of our world. Yet a possible constraint that weighs on knowledge is that it must rest on a causal link, even indirect, with its object, especially when it deals, as is the case here, with concreta. Now, if possible worlds have no causal influence on our cognitive lives, how can we ever come to know of them? Moreover, if modal statements have inaccessible truth-makers, how can we be justified in believing that they are true? Lewis retorts that all modal truths are necessary and that a causal relation is not required in order to know
Philosophia Scientiæ, 16-2 | 2012 16
necessary facts.16 However, this reply blatantly conflicts with cases of empirical necessities.17
39 Our epistemological concern does not dissipate if we fall back on a more moderate form of possible worlds realism. Suppose that we endorse an actualist view in which possible worlds are maximally consistent sets of propositions. Propositions are no longer defined, as in Lewis’ account, as functions from possible worlds to truth-values; they are now more fundamental abstract intensional entities out of which possible worlds are made. If so, we fall into one of the instances of the problem Benacerraf formulated concerning the epistemology of mathematics [Benacerraf 1973]: abstract entities such as numbers, sets or propositions, being causally inert, do not have any impact on our cognitive lives, making our capacity to know them utterly mysterious.
40 In this volume, two attempts to take up the Integration Challenge in possible worlds style metaphysics will be discussed: David Lewis explanationist strategy and Christopher Peacocke’s principle-based theory of modality.
41 Lewis’ point of departure is this: to the extent that causally isolated possibilia pose the same epistemological problem as mathematicalia, they call for the same solution [Lewis 1986, 190]. What paves the way to numbers is not causality but their theoretical utility: if our current best theory of reality involves mathematics and if it requires quantifying over abstract objects such as numbers or sets, then we are justified in believing that numbers or sets exist. Thus, their existence can be known by an inference to the best explanation (IBE).18 Note that, according to Lewis, theoretical utility does not merely give reasons to use numbers or sets: it justifies the belief that mathematical realism is true. This epistemic warrant conferred by explanatory virtues is what one is to expect if one takes IBE seriously as a knowledge-conducive method.
42 Lewis then applies the same line of argument to explain how we can know that modal realism (in its strong Lewisian form) is true. Strong modal realism outperforms its rivals regarding explanation—or so Lewis argues. First and foremost, it allows a reduction of modality, something actualist realism about possible worlds is unable to do given that it uses possibility as a primitive concept. Armed with the counterpart relation, Lewisian realism solves in an elegant manner some vexing puzzles, such as the paradox of material constitution or the modal versions of sorites paradoxes. Mostly, it offers a highly systematic account of intensional and epistemic notions, such as properties, propositions, knowledge and so on. All this provides the premises needed to conclude, by IBE, that strong modal realism is true.
43 Most modal philosophers think that something is amiss with Lewis argument as its conclusion is simply unbelievable. One way to resist his explanationist strategy would be to dispute his right to use IBE inasmuch as every explanation lies on a causal relation, and causal relations are precisely absent in the case of Lewisian worlds. However, this objection collapses when it is pointed out that there are many non-causal explanations, including in the sciences.19 More annoyingly, one may challenge the alleged explanatory superiority of strong modal realism,20 or more drastically, reject the idea of IBE altogether [Van Fraassen 1989]. In "Modal Integration", Scott Shalkowski follows another line of criticism, first put forward in [Shalkowski 2010]. His purpose is to show that, even if IBE is a legitimate inference in scientific and ordinary contexts, it cannot provide warrant in metaphysical contexts, especially not in modal metaphysics. The core objection is to say that there are no grounds for thinking that IBE is reliable in such contexts as there are no independent ways to determine if IBE
Philosophia Scientiæ, 16-2 | 2012 17
leads us to the truth. Shalkowski defends his "independence" objection against a recent attempt to rehabilitate the use of IBE in metaphysics by means of a reliabilist epistemology.
44 Let us now turn to Peacocke’s principle-based account of modality, probably the most thorough attempt to reconcile possible worlds style metaphysics with epistemology. The crucial link between the two is through the Principles of Possibility, to which Peacocke assigns a dual-purpose. At the metaphysical level, these principles are what makes some worlds possible, namely those that conform to these principles. At the epistemological level, these principles are tacitly known by the very fact that one possesses the concept
45 The overall metaphysics in which such principles operate is actualist: possible worlds are not huge concreta but sets of (Fregean) propositions. Contrary to what the term might suggest, Principles of Possibility do not impose constraints directly on possibility but on the more fundamental notion of admissibility, said of assignments. An assignment allocates to each atomic concept its appropriate extension: objects for singular concepts, functions from n objects to truth-values for n-place predicative concepts, and so on. To each assignment corresponds its specification, which is the set of propositions true under this assignment. Hence, possible worlds are nothing but specifications of a certain kind, e.g., those that are genuine possibility (interestingly, this framework admits impossible worlds). We now come to the delicate point met by every actualist theory of possible worlds: what does the possibility of worlds—that is, of specifications in Peacocke’s terms—consist in? Here comes the key notion of admissible assignment: A specification is a genuine possibility iff there is some admissible assignment which counts all its members as true. [Peacocke 1999, 126] Albeit indefinable explicitly, the concept of admissibility is implicitly defined by a set of Principles of Possibility, each formulating a necessary condition for falling in its extension—their conjunction being sufficient for admissibility.21 Two types of principles are distinguished. The first takes the form of a unique general principle concerning concepts, the Unified Modal Extension Principle (MEP): Unified Modal Extension Principle. An assignment s is admissible only if: for any concept C, the semantic value of C according to s is the result of applying the same rule as is applied in the determination of the actual semantic value of C. [Peacocke 1999, 136] As an illustration of MEP, an assignment would be counted as inadmissible if the concept of < bachelor> were not allotted the intersection of the extensions of
46 The second type of principle consist so falist of "Constitutive Principles", not claimed by Peacocke to be exhaustive. Constitutive Principles are metaphysically more loaded than MEP. They capture constraints that are not concerned with the nature of concepts but with the nature of objects, properties and relations. For instance, if a is a person who actually originated in the particular sperm b and egg cell c, then there will be a constitutive principle responsible for the essential character of a s origin: An assignment is inadmissible if it both counts the proposition a exists true and counts the proposition a develops from b and c as false. [Peacocke 1999, 146] Next, Peacocke gives the truth-conditions for modalized thoughts:
Philosophia Scientiæ, 16-2 | 2012 18
Characterization of Necessity (Possibility): A proposition is necessary (possible) iff it is true according to all (some) admissible assignments. [Peacocke 1999, 150] Combined with the theory of modal concepts possession, this principled account of modality provides a straightforward explanation of how we can know de dicto (by MEP) and de re modal truths (by Constitutive Principles). The gap between knowledge of modals and their truth-makers is easily filled once one realizes that modal judgments are drawn from tacit knowledge of those very principles responsible for their truth.
47 Peacocke’s account gave rise to a number of criticisms, notably the recurrent charge of circularity. The complaint is that the concept of admissibility must involve an irreducible notion of possibility to account for modal truths [Sullivan 1998], [Rosen 2002]. Even if Peacocke, contrary to Lewis, does not seek to give a reductionist analysis of modality, this circle nevertheless constitutes a threat to his epistemology as it requires a priori knowledge of which assignments are "possible" in a sense not accounted for by the theory.
48 Another objection is the charge of incompleteness. Modal knowledge, Peacocke says, is grounded on tacit knowledge of constitutive truths; but how did we come to know constitutive truths in the first place? For instance, how do we know that biological origin is constitutive of persons? This does not as such raise a circularity worry since Peacocke has it that constitutive truths are not modal in content, rather they have to do with the identity of a thing, what makes it the thing it is. Yet, the feeling remains that Peacocke’s modal epistemology would not honor its agenda if it did not elucidate constitutive knowledge, in which modal knowledge originates [Heathcote 2001], [Wright 2002], [Roca-Royes 2010].
49 At first sight, the challenge is easily met insofar as Principles of Possibility implicitly define the concept
50 Certainly, but this does not dissipate our concern since it does not exclude the following pessimistic scenario: suppose that our concept of absolute possibility operates exactly as described by Peacocke but that, as a matter of fact, principles that govern its use fail to capture the nature of things, either by default, or by excess. By default: there are constraints in the nature of things to which no principle corresponds. By excess: there are principles governing
Philosophia Scientiæ, 16-2 | 2012 19
so to speak, "tuned" to the nature of things. Evidence for this external correspondence is what Peacocke cannot provide from the inside of his self-enclosed theory of modality.
51 In "Peacocke’s Epiphany", Jon Barton examines another, but related, difficulty discussed in [Peacocke 1999] and [Wright 2002]. The trouble here is that, if truth in all possible assignments does not merely coincide with necessity but captures its target property, it has to be shown, by the means of Peacocke’s theory, that Characterization of Necessity (Chzn) seen above is not merely true, but necessarily so. Barton shows that the theory cannot provide the intended result. More precisely, he holds that, contrary to what [Peacocke 1999] suggests, the self-recursive application of MEP cannot establish the necessity of Chzn, or even its truth. At best, the necessity of Chzn must be accepted as a brute fact, knowledge of which has no explanation in Peacocke’s theory.
6 Counterfactual accounts of modal knowledge
The problem of integration is as much a problem for philosophical modal knowledge as for ordinary modal knowledge. In this section, we will address a problem affecting the former and present the strategy that seems the most promising to solve it: counterfactual approaches.
52 In the first section, we saw that philosophical modal knowledge differed significantly from ordinary modal knowledge by its object, i.e., modality taken in an absolute sense. It is thus very tempting to allocate to this special knowledge a sui generis faculty whose goal is to detect metaphysical possibilities and necessities. Even though it has long predominated in the rationalist tradition, the hypothesis of such a specialized faculty is unfortunately implausible since it makes no sense from an evolutionary point of view. As [Williamson 2007, 136] reminds us, humans evolved under no pressure to do philosophy. Certainly, the existence of a capacity for ordinary counterfactuals can receive an evolutionary explanation insofar as it gives us a lot of advantages (like detecting causes, imputing actions, attributing dispositions…) that can explain why it was selected throughout our evolutionary history. Yet, knowledge of metaphysical possibilities and necessities seems to have played no role at all in the survival of our species. What is advantageous from the point of view of our survival is the capacity to conceive close possibilities that can easily obtain, such as the possibility of a source of water or the presence of a predator, rather than speculative possibilities such as the inverted spectrum or philosophical zombies.
53 The hypothesis of a "sense" of metaphysical modality being ruled out, two options remain: either we adopt skepticism toward philosophical modal knowledge or we show that this knowledge is anchored in ordinary modalizing. It is this last option that is favored by the champions of the counterfactual approach of modal knowledge [Hill 2006], [Williamson 2007]. According to them, philosophical modal knowledge does not rest on cognitive mechanisms isolated from those that allow us to know ordinary counterfactuals: it is only a by-product of the capacity of thinking about counterfactuals. This means that the epistemology of metaphysical modals is subsumed under the epistemology of counterfactuals.
54 One can distinguish four steps in the implementation of this project. The first is to link metaphysical modality to subjunctive conditionals. This is permitted by the following equivalence:22
Philosophia Scientiæ, 16-2 | 2012 20
(E) □Ф iff ¬Ф□→⊥
◊Ф iff (Ф□→⊥)
According to (E), the fact that Ф is metaphysically necessary is logically equivalent to the fact that an inconsistence follows from the counterfactual supposition that Ф is false.
55 The next step is to give the counterfactual idiom an explanatory priority over metaphysical modality, in the sense that the former can explain some properties of the latter. In "What is Absolute Necessity?", Bob Hale thus holds that counterfactual modality explains in what sense metaphysical modality is absolute, as opposed to relative modalities such as "technologically possible" or "biologically possible". Most modal theories explain the contrast between absolute and relative necessities by means of the distinction between unrestricted and restricted universal quantification over possible worlds. Thus, it is absolutely necessary that 24 = 16 because this statement is true relatively to all possible worlds without restriction. Whereas, if we say that the speed of an object with a mass cannot exceed c, this physical impossibility is only relative since only the subset of those worlds in which laws of physics hold is considered.
56 Hale rejects this traditional line of explanation. The main defect of the quantificational approach is to make of metaphysical necessity a relative notion, which seems highly counterintuitive. Indeed, as all logical necessities are metaphysical necessities but not the other way around, such a view commits us to say that metaphysical necessities only hold in a restricted sphere of possibilities, namely those metaphysically possible worlds that form a subset of the maximal set of logically possible worlds. Rejecting the quantificational approach and other candidates, Hale defines the absoluteness of metaphysical necessity by means of the counterfactual idiom. In his view, Ф is absolutely necessary because Ф would obtain no matter what else was the case; in symbols:
57 (∀Ψ)(Ψ□→Ψ) This formula is provably equivalent to the one occurring in (E) seen above. In a sense, then, Hale keeps something from the quantificational approach since absolute necessity is characterized by an unrestricted quantification over propositions (or, alternatively, over statements). Relative necessities, such as those expressed when we say "I could not come on time to this appointment" or "objects with a mass cannot travel faster than the speed of light" are explained by the fact that, when they are submitted to the counterfactual test, the antecedent is filled by a restricted set of propositions, namely those that hold in the contextually relevant possibilities. When combined with an essentialist theory of modality [Hale 2012], this generalized counterfactual analysis of absoluteness has the serious advantage of accounting for the distinction between logical necessities and non-logical metaphysical necessities, without relativizing metaphysical modality or introducing a dualism between logical possibilities and metaphysical possibilities in the whole space of possibilities.
58 An additional step consists in saying that metaphysical modality, and not just one of its properties (viz. absoluteness), is reductively explained by the counter-factual idiom. In such a view, (E) does not only state a logical equivalence, rather it gives the full explanans of metaphysical modality. If one intends moreover to explain how
Philosophia Scientiæ, 16-2 | 2012 21
philosophical modalizing emerged from ordinary counterfactual practice, as is the case here, one must make a further step and claim that the concept of metaphysical modality originated from our capacity to handle counterfactuals (combined with our mastery of the concept of inconsistency).23 From this, it follows that the epistemology of metaphysical modality is a special case of the epistemology of counterfactuals. It suffices that one knows that ¬p □→⊥, to analytically infer that □p.
59 The success of counterfactual accounts depends on the correctness of (E). However (E) seems to be challenged by some counterexamples, in particular in cases of a posteriori necessity. Consider for instance a speaker who knows that gold has the atomic number 79 and who wonders what would have been the case had gold had a different atomic number. The speaker has to imagine scenarios that make true the antecedent of the counterfactual, and develop this assumption so that imagination proceeds as "realistically" as it can [Williamson 2007, 143]. It is notoriously difficult to detail the rules that a speaker must tacitly know in order to evaluate a counterfactual, but the following would be a good approximation: when evaluating a counterfactual "p□→q", (i) add the antecedent p to what is known of the actual world, (ii) minimally revise background knowledge in order to preserve consistency, then (iii) use all available knowledge to check if q follows. Thus, in our example, the speaker must imagine a scenario that verifies "gold has an atomic number other than 79", and then imagine away the fact that gold has the atomic number 79 in order to preserve consistency. From this, the speaker, using her background knowledge, can infer that gold would have shown different thermal and electrical conductivities, ductility, malleability, and so on from those that it actually has. But note the crucial point: it seems that however far the speaker pushes the development of the antecedent, she will never face a logical inconsistency. If the truth-conditions of counterfactuals reflect the methodological rule seen above, then the right hand side of (E) is false. However, the left hand side is true: it is metaphysically necessary that gold has the atomic number 79. Therefore, it seems that the use of counterfactuals cannot provide knowledge of metaphysical necessities, especially those that are not logical or conceptual truths.
60 Williamson is well aware of this difficulty. It originates from the fact that the rule of development of counterfactual assumptions given above is not sufficiently constrained. Condition (ii) must be reinforced in the following way: revise minimally the background knowledge in order to preserve consistency, but never imagine away "constitutive facts" [Williamson 2007,164]. Good candidates for being constitutive facts are facts concerning microphysical structure, origin, kind-membership, material composition, and so on. If Williamson is right, our competence for ordinary counterfactuals presupposes a capacity to discriminate constitutive from non- constitutive facts. Constitutive facts must always be kept fixed when we develop a counterfactual assumption, even at the expense of an inconsistency. This is precisely how we are led to know metaphysical necessities: in the example of gold, condition (i) stipulates adding the assumption that gold has an atomic number other than 79 whereas condition (ii) forbids imagining away the constitutive fact that gold has the atomic number 79. The application of (i) and (ii) creates a contradiction, hence the conclusion that it is metaphysically necessary that gold has the atomic number 79.
61 The constraint stemming from constitutive facts is analogous to Peacocke’s Constitutive Principles and raises the same kind of difficulty. The risk is to make counterfactual accounts circular. Knowledge of counterfactuals can hardly explain
Philosophia Scientiæ, 16-2 | 2012 22
knowledge of metaphysical modality inasmuch as the former presupposes the latter. Let us then go back to our example: in order to infer an inconsistency from the assumption that gold has an atomic number other than 79, the speaker must first know that it is a constitutive fact—that must be kept fixed— that gold has the atomic number 79. To ignore this would lead the speaker to under-detect inconsistencies, and therefore to acknowledge more possibilities concerning gold than there actually are. The speaker must also know which facts concerning gold are not constitutive. Thus, it is not a constitutive fact that 8 500 m3 of gold have been mined throughout human history until now; believing the opposite would lead the speaker to over-generate inconsistencies, and herefore to acknowledge more necessities concerning gold than there actually are. What does knowledge that a fact is constitutive consist in if not in modal knowledge? To say that it is constitutive of gold that it has the atomic number 79 is just another way of saying that this property is part of its essence, and essence is a modal notion. If the speaker was asked to explain herself, she would invoke counterfactual considerations such as "it is constitutive for gold to have the atomic number 79 because if a substance had an atomic number other than 79, it would not be gold" or "it is not a constitutive fact of gold that 8 500 m3 of it have been extracted since we can easily imagine that half as much gold could have been extracted or even not at all". Therefore, either knowledge of constitutive facts rests on counterfactual reasoning, in which case counterfactual accounts of modal knowledge are circular; or knowledge of constitutive facts is admitted as a brute epistemic fact, in which case counterfactual accounts fail too since they do not explain our basic modal knowledge, namely knowledge of constitutive facts. At best such accounts can explain how we expand our modal knowledge thanks to counterfactual reasoning, but they remain silent about its origin.
62 As embarrassing as this negative result is, it does not threaten the evolutionary respectability of philosophical modal knowledge. It keeps intact the core thesis of counterfactual accounts according to which our capacity to hold ordinary counterfactuals somehow involves a capacity to detect metaphysical modality, even if it rests on an unexplained sensitivity to constitutive facts. It is precisely this thesis that is targeted by Sonia Roca-Royes in "Essentialist Blindness Would Not Preclude Counterfactual Knowledge". Roca-Royes wants us to imagine a speaker who knows (tacitly) all the development rules of counterfactual assumptions (i) to (iii) seen above, while ignoring rules concerning constitutive facts. This speaker is, so to speak, affected with essentialist blindness, to the point that she even lacks the concepts required to entertain contents such as "it is essential for a to be P". Will this blindness preclude our speaker from knowing the truth of all the counterfactuals that are useful in everyday life, namely those that contribute to detecting causes, to explaining and predicting events, to imputing responsibility, and so on? Roca-Royes answers that it will not. At most, the blind speaker will be mistaken about some counterfactuals, those whose evaluation crucially relies on sensitivity to constitutive facts, in particular "counterpossibles", i.e., counterfactuals whose antecedent describes a metaphysical impossibility. Consequently, our speaker will ignore metaphysical necessities concerning origin, identity, microphysical structure, and so on. She will also overestimate the number of remote possibilities. But for all the rest, her knowledge of counterfactual truths will be in all respects similar to ours. The lesson drawn by Roca- Royes from the fictitious case of essentialist blindness is that our capacity to handle ordinary counterfactuals does not bring with it a capacity for metaphysical modals. If
Philosophia Scientiæ, 16-2 | 2012 23
the latter can be removed from our conceptual scheme without collateral damage, counterfactual accounts cannot appeal o the evolutionary relevance of counterfactual reasoning in order to explain the emergence of essentialist thought and, a fortiori, the existence of a capacity for metaphysical modal knowledge.
63 If correct, this second objection is devastating for counterfactual accounts. Since it raises cognitive and evolutionary issues, it would be particularly interesting to confront it with results obtained in cognitive sciences. Indeed, some cross-cultural and developmental studies tend to show that a cognitive bias governs inductive generalizations and projections made by pre-schoolers [Gelman 2003]. It concerns natural kinds rather than individual objects. Conditions for kind-membership seem to be spontaneously identified with "hidden" properties that are responsible for clusters of correlated observable features. This poses a challenge to the position defended by Roca-Royes. Indeed, if such an essentialist thought has been selected for the advantages it provides to our inductive practices, it must therefore make a difference in the practice of ordinary counterfactuals, in particular those of the form "if x was/had been a K, x would present/have presented the property P".24 This suggests that our capacity to hold ordinary counterfactuals would be severely impaired if essentialist thoughts were removed from our cognitive architecture. Does this not conflict with the thesis defended by Roca-Royes according to which our capacity to detect essential facts does not constitute a core capacity for counterfactual knowledge? The answer is far from obvious since several points need first to be clarified. One in particular is that we have no direct proof of this unarticulated essentialism. Cognitive scientists postulate it on a tacit level in order to explain the inductive behavior of pre-schoolers. It remains to be shown whether this tacit essentialism has enough in common with philosophical essentialism in order to claim that the second is anchored and can thus be explained by the first. These are difficult questions whose treatment deserves more space than we have here. Putting them aside, therefore, for another occasion, in what follows we will focus on the first objection against counterfactual accounts of modal knowledge.
7 Knowledge of essence
This objection stated that counterfactual accounts are circular since our capacity to hold counterfactuals presupposes knowledge of some basic metaphysical necessities, namely those constitutive truths that must be kept fixed during counterfactual reasoning. We will maintain that this charge cannot hold inasmuch as our knowledge of constitutive truths is in no way a kind of modal knowledge. Even if it delivers our basic modal contents through subjunctive reasoning, neither its object nor its epistemology belongs per se to the modal domain.
64 Let us examine first its object. "It is a constitutive truth about a that Фa "will be hereafter used to capture the old but vivacious pre-modal notion of essence or nature. Except for its factivity, it is intended to mean the same thing as "being $ belongs to the nature of a".25 The crucial point is that this notion of essence is not coined in modal terms. This view, in line with a long tradition running from Aristotle to the present day with e.g., [Fine 1994], [Lowe 2007] and [Hale 2012], considers that the notion of essence or nature is fundamentally characterized in terms not of necessity but of identity. In this sense, a being F is a constitutive fact about a iff a being F makes a what it is. By claiming that a property is a part of the essence of an object when it contributes to
Philosophia Scientiæ, 16-2 | 2012 24
define it, we are assuming that definitions can be about things and not only about words. This seems to us to be no more obscure than the modal conception of essence that dominates contemporary metaphysics today. Those who despise definitions of things are primarily those who despise essentialism in general, be it formulated in terms of necessity or in terms of identity.
65 It is important then to carefully distinguish the concept of essence relevant for constitutive knowledge from the more widespread modal concept of essence, according to which the essence of an object is the set of properties that are necessary conditions for its existence. (8) is neither defined nor explained nor even equivalent to (9): (8) It is a constitutive truth about a that a is F (9) a exists and necessarily, a exists only if a is F. A connection certainly exists between constitutive facts and necessary facts to the extent that (8) implies (9); it is even crucial that such an implication holds if we want to explain how constitutive knowledge generates modal knowledge by interacting with counterfactual reasoning. However, the independence of constitutive facts toward modal facts is (in part) shown by the fact that the converse implication from (9) to (8) does not hold, as [Fine 1994] forcefully emphasized. For instance, it is necessary that, if Kripke exists, Kripke is numerically distinct from de Gaulle since they are actually numerically distinct and distinction is necessary.26 Yet, it is not constitutive of Kripke that he is numerically distinct from de Gaulle. The distinction with the hundreds of billions of persons that have existed or that exist is not a part of his essence. Since constitutive facts about x imply necessary facts about x, but not the other way around, one may be tempted to believe that there will be many more necessary properties than constitutive ones. Albeit true, this claim requires more support than we can give it here, due to lack of space. Let it be sufficient here to say that, as the constitutive concept of essence is more constrained than its modal surrogate, necessary properties are abundant whereas constitutive properties are sparse.
66 One could argue against this proposal to emancipate essence from modality by pointing out that the failure of the implication from (9) to (8) shows at most that the notion of essence is too fine-grained to be captured by conditionals of the form (9), and this is entirely compatible with the fact that essence stays an intrinsically modal notion whose knowledge requires modal methods. Our response to this is that someone can attribute a constitutive property to an object by relying on purely explanatory considerations, without using counterfactual reasoning or thought experiments on remote possibilities. In order to be convinced of this, one only has to turn to science and examine the kind of methods used to isolate constitutive facts. Let us take for example number theory. It is a constitutive fact about 2 that it is the immediate successor of 1 in the N sequence. Mathematicians know that. By saying this, not only do we mean that it is a constitutive fact that 2 is the immediate successor of 1, and that mathematicians know this fact, we are also saying that they know that this is a constitutive fact about 2. In other words, mathematical knowledge brings with it a "frankly inequalitarian attitude" [Quine 1961] that separates constitutive facts about 2 from facts involving properties that, albeit necessary, are not constitutive of 2, suchasthepropertyofbeingthepositivesquarerootof4. How do mathematicians distinguish here between what is constitutive and what is not? By knowing that if the number 2 is defined this way, this property, combined with Peano’s axioms (and with the definitions of the other numbers and operations), explains all the other properties
Philosophia Scientiæ, 16-2 | 2012 25
of 2. Knowing what is constitutive of 2 results from explanatory considerations, and not from answers to modal questions such as "What would have happened if 8 were the immediate successor of 1 in N?" or "can we imagine a world in which 2 is the immediate successor of 5?" In this sense, knowledge of constitutive facts is amodal, in its content as well as in its epistemology.
67 This claim can be generalized, mutatis mutandis, to all empirical sciences such as physics, chemistry or biology. It has often been claimed, since Kripke, that science contents itself with discovering such amodal truths as gold having the atomic number 79, and that it is up to philosophy to say whether such a property is essential to gold, as if science were blind to the special status of this property compared to all the other properties of gold (ductility, thermal conductivity, etc.). If "essential property" is understood as a metaphysically necessary condition for existence, this claim is correct: physicists do not ask themselves whether gold could have had another atomic number, and there is no room for metaphysical modals in physics papers or manuals. On the other hand, if "essential property" is intended to mean a constitutive property that makes gold what it is, the claim is then false: "what is gold?", "what is electricity?" or "what is light?" are scientific questions that require the constitutive properties of gold, electricity or light to be isolated, and the answers to these questions can be found without philosophical modalizing. In the case of gold, we have discovered empirically that having the atomic number 79 is constitutive of gold because this property explains the cluster of observable properties possessed by the samples that fixed the reference of the term "gold". Once again, only explanatory considerations come into play to separate what is constitutive from what is not; modal reasoning does not play any role in this. If, as we maintained above, knowledge of constitutive facts does not presuppose a capacity to know metaphysical modality, we can follow Williamson in assuming the constraint of keeping fixed constitutive facts in counterfactual reasoning, without making counterfactual accounts of modal knowledge circular.
68 To conclude this sketchy defense of counterfactual accounts, we will address a last but important concern. Some might protest that, even if they show no circularity, such accounts deprive counterfactual reasoning of any interesting epistemological role; it becomes, so to speak, a mere registering chamber of what is delivered by our capacity
to know constitutive facts. As soon as we know that water being H2O, that persons having first-person thoughts or that knowledge involving true belief, are constitutive facts, it seems that the role of counter-factual reasoning is limited to reformulating this knowledge in a modal form, putting "it is metaphysically necessary that… " instead of "it is a constitutive fact that...".
69 Modal knowledge then seems redundant vis-à-vis knowledge of constitutive facts. Now, if our capacity for the latter carries all the weight of the epistemic labor, in what sense do counterfactual accounts reveal anything of epistemological interest about metaphysical modal knowledge? Does this not come down to saying that interesting questions are not on the side of modal epistemology but on the side of the epistemology of constitutive knowledge? If this is indeed so, then counterfactual accounts do not advance us much. Much ado about nothing!
70 We reject this pessimistic assessment. Most modal truths are remote consequences, rather than mere reformulations, of constitutive truths, and one of the roles of counterfactual reasoning is precisely to help us discover them.
Philosophia Scientiæ, 16-2 | 2012 26
71 Let us take, for instance, the necessity of distinction: (a≠b) □→ ( a≠b). From our perspective, this is a substantial modal principle: since there is nothing in the nature of an object a that makes it so that it has to be distinct from another object b, it is not platitudinous to claim that two daughter cells could not have formed one and the same cell, or that two sibling species could not have constituted one and the same species, while maintaining their identity. Yet, these modal truths cannot be drawn from the simple reformulation of constitutive truths. Thus, it is probably a constitutive fact about identity that it is a reflexive relation or that it involves indiscernibility. By keeping fixed such constitutive truths in counterfactual reasoning, one can immediately obtain the necessity of self-identity or the necessity of the indiscernibility of identicals, but one can never draw the necessity of distinction. How can we then get this substantial piece of modal knowledge? This is where counterfactual accounts are fruitful, by showing how the interplay of various constitutive truths plunged into counterfactual reasoning may result in new modal truths. In this case, the explanation proceeds as follows. First, from the trivial (a≠b) □ → (a≠b) and from the fact that reflexivity of identity is a constitutive fact that must be kept fixed, we draw (a≠b) □→ ((a≠b)ᐱ(a=a)). Suppose now that actually a=b. From the fact that "a" and "b" are rigid de jure in counterfactual reasoning,27 one can infer that (a≠b) □→((a=b)ᐱ(a=b)),or in other words: (a≠b) □ →⊥. From (E) seen above, it follows that □(a=b). By discharging the supposition, we thus obtain the Necessity of Identity (NI): (a=b) □→ (a=b).Next, it can be shown that the Brower principle (B) ◊□Ф→Ф is a theorem of logic of counterfactuals, asitisequivalent under (E) to ¬(¬(p□→⊥)□→⊥)→p, which follows from axiom schemata and inference rules for counterfactuals. From (B) and by distributing ◊ over (NI), we draw ◊(a=b)→(a=b), which is the necessity of distinction in its contraposited form.
72 This example, chosen amongst many others, shows how reasoning counter-factually on quite trivial constitutive truths can lead to substantial modal truths, such as the necessity of distinction, schemas (B), (S4) and (S5), and many specific modal truths about persons, mental states, and so on; and also—we conjecture—to much more controversial truths such as the necessity of origin. We saw that to achieve this, counterfactual reasoning must be constrained by constitutive truths that are known by other means. In a sense then, counterfactual approaches of modality do not tell us the truth of the matter. The elucidation of the ultimate source of modal knowledge requires them to be supplemented by an epistemology of the constitutive. However, this hardly calls into question their fruitfulness. It just reminds us that answering a "What is X?" question in philosophy, as well as in science, does not rely on modal methods alone. After all, the recourse to reflective equilibrium or inference to the best explanation has resulted in many partial but valuable answers to philosophical questions, without any need whatsoever for modal intuitions.
Philosophia Scientiæ, 16-2 | 2012 27
BIBLIOGRAPHY
ADAMS, ROBERT MERRIHEW 1974 Theories of actuality, Nous, 8, 211-231.
AYER, ALFRED JULES 1971 Language, Truth and Logic, Penguin Books.
BENACERRAF, PAUL 1973 Mathematical truth, Journal of Philosophy, 70(19), 661-679.
BLACKBURN, SIMON 1987 Morals and modals, in Fact, Science and Morality: Essays in Honour of A. J. Ayer’s Language, Truth and Logic,edited by MACDONALD,G. & WRIGHT, C., Oxford: Blackwell, 119-141.
BOGHOSSIAN, PAUL 1997 Analyticity, in A Companion to the Philosophy of Language,edited by HALE,B. & WRIGHT, C., Oxford: Blackwell, 331-368.
BONJOUR, LAURENCE
1998 In Defense of Pure Reason, Cambridge: Cambridge University Press.
BURGESS, JOHN 1997 Quinus ad omni naevo vindicatus, Canadian Journal ofPhilosophy,
CARNAP, RUDOLF 1956 Meaning and Necessity, London: University of Chicago Press.
CHALMERS, DAVID 1996 The Conscious Mind, New York: Oxford University Press. 2002 Does conceivability entail possibility?, in Conceivability and Possibility,edited by GENDLER,T. S. & HAWTHORNE,J., Oxford: Clarendon Press, 145-200. 2004 Epistemic two-dimensional semantics, Philosophical Studies, 118(1-2), 153-226. 2010 The Character of Consciousness, New York: Oxford University Press, chap. The two-dimensional argument against materialism, 141-191.
DIVERS, JOHN 2002 Possible Worlds, London: Routledge.
ELLIS, BRIAN 2001 Scientific Essentialism, Cambridge: Cambridge University Press.
FINE, KIT 1994 Essence and modality: The second philosophical perspectives lecture, Philosophical Perspectives, 8, 1-16.
GEIRSSON, HEIMIR 2005 Conceivability and defeasible modal justification, Philosophical Studies, 122, 279-304.
GELMAN, SUSAN 2003 The Essential Child, Oxford: Oxford University Press.
GENDLER, TAMAR SZABO & HAWTHORNE, JOHNS (EDS.) 2002 Conceivabilityand Possibility, Oxford: Clarendon Press.
Philosophia Scientiæ, 16-2 | 2012 28
HALE, BOB 2012 What is absolute necessity?, Philosophia Scientis, 16(2), 117-148. 2010 Modality. Metaphysics, Logic, and Epistemolgy,Oxford: Oxford University Press.
HEATHCOTE, ADRIAN 2001 Yes, but what is the mother of necessity?, Philosophical Books, 42, 92-100.
HILL, CHRISTOPHER 2006 Modality, modal epistemology, and the metaphysics of consciousness, in The Architecture ofthe Imagination: New Essays on Pretense, Possibility and Fiction,edited by NICHOLS, S., Oxford: Oxford University Press,
HUME, DAVID 1992 A Treatise ofHuman Nature, Amherst: Prometheus Books.
JACKSON, FRANK 1998 From Metaphysics to Ethics. A Defense ofConceptual Analysis,Oxford: Oxford University Press.
KANT, IMMANUEL 1965 Critique of Pure Reason, New York: St. Martin.
KAPLAN, DAVID 1989 Demonstratives, in Themes from Kaplan,edited byALMOG,J., PERRY, J., & WETTSTEIN, H., New York: Oxford University Press, 481-564.
KRIPKE, SAUL 1971 Identity and necessity, in Identity and Individuation,editedby MUNITZ, M., New York: New York University Press, 135-164. 1980 Naming and Necessity, Oxford: Blackwell.
LEWIS, DAVID 1973 Counterfactuals, Oxford and Cambridge: Blackwell Publishers, and Harvard University Press. 1986 On the Plurality of Worlds, Oxford: Blackwell.
LIPTON, PETER 2004 Inference to the Best Explanations, London: Routledge.
LOWE, JONATHAN 2007 La metaphysique comme science de l’essence, in Metaphysique contemporaine,edited by GARCIA,E.& NEF, F., Paris: Vrin, 85-117.
MCLEOD, STEPHEN 2005 Recent work on modal epistemology, Philosophical Books, 46(3), 235-245.
MENZIES, P. 1998 Possibility and conceivability: a response-dependent account of their connections, European Review ofPhilosophy, 3, 255-277.
O’LEARY-HAWTHORNE, JOHN 1996 The epistemology of possible worlds: a guided tour, Philosophical Studies, 84, 183-202.
PARFIT, DEREK 1984 Reasons and Persons, Oxford: Clarendon Press.
PEACOCKE, CHRISTOPHER 1999 Being Known, Oxford: Clarendon Press.
Philosophia Scientiæ, 16-2 | 2012 29
PLANTINGA, ALVIN 1976 Actualism and possible worlds, Theoria, 42, 139-160.
QUINE, WILLARD VAN ORMAN 1947 The problem of interpreting modal logic, Journal ofSymbolic Logic, 12, 43-48. 1953 Three grades of modal involvement, in Proceedings of the Xlth International Congress ofPhilosophy, vol. 14, 65-81. 1961 Reply to professor marcus, Synthese, 13, 323-330.
ROCA-ROYES, SÒNIA 2010 Modal epistemology, modal concepts, and the integration challenge, Dialectica, 64, 335-361.
ROSEN, GIDEON 2002 Peacocke on modality, Philosophy and Phenomenological Research, 64(3), 641-648.
SHALKOWSKI, SCOTT A. 2010 IBE, GMR, and metaphysical projects, in Modality: Metaphysics, Logic, and Epistemology,editedbyHALE,B.&HOFFMAN,A.,Oxford: Oxford UniversityPress, 169-187.
SHOEMAKER, SIDNEY 1984 Causality and properties, in Identity, Cause and Mind,Cambridge: Cambridge University Press, 234-260.
SIDELLE, ALAN 1989 Necessity, Essence and Convention, Ithaca: Cornell University Press.
SOAMES, SCOTT 2005 Reference and Description, Princeton: Princeton University Press.
STALNAKER, ROBERT 1968 A theory of conditionals, in Studies in Logical Theory,Oxford: Blackwell, American Philosophical Quarterly Monograph Series,vol. 2, 98-112. 1976 Possible worlds, Nous, 10, 65-75. 1978 Assertion, in Syntax ans Semantics, New York: New York Academic Press, vol. 9, 315-332.
SULLIVAN, PETER 1998 The "Modal Extension Principle": A question about Peacocke’s approach to modality, Mind, 107(427), 653-660.
VAIDYA, ANAND J. 2007 The epistemology of modality, The Stanford Encyclopedia of Philosophy, edited by E. .N zalta. http://plato.stanford.edu.
VAN FRAASSEN, BAS 1989 Laws and Symmetry, Oxford: Oxford University Press.
VAN INWAGEN, PETER 1998 Modal epistemology, Philosophical Studies, 92, 67-84.
WILKES, KATHLEEN 1988 Real People, Oxford: Oxford University Press.
WILLIAMSON, TIMOTHY 2007 The PhilosophyofPhilosophy, Oxford: Blackwell.
Philosophia Scientiæ, 16-2 | 2012 30
WRIGHT, CRISPIN 2002 On knowing what is necessary: Three limitations of peacocke’s account, Philosophyand Phenomenological Research, 64, 655-662.
YABLO, STEPHEN 1993 Is conceivability a guide to possibility?, Philosophy and Phenomenological Research, 53(1), 1-41.
NOTES
1. Precious syntheses can be found however in [O’Leary-Hawthorne 1996], [Gendler & Hawthorne 2002], [McLeod 2005], [Vaidya 2007] and [Hale & Hoffmann 2010]. 2. Strictly speaking, [Blackburn 1987] does not endorse modal non-cognitivism, but his "quasi- realism" comes close to it. 3. In order to know that an event a caused an event b, a speaker must surely know that b would not have happened had a not happened. 4. Consider for example the following reasoning: "If a had been a K, it would (not) have presented those features that we are actually observing. Hence a is (not) a K". 5. Here and in the following, "it is necessary that p" is symbolized by "□p". 6. Even if it is the dominant view on the modal status of the laws of nature, it is not uncontroversial. [Shoemaker 1984] and [Ellis 2001] argue thus for their metaphysical necessity. Note that even if physical necessity and metaphysical necessity turned out to coincide extensionally, they would still remain notionally distinct. 7. "It is true a priori that p" abbreviates "p is true and knowable a priori". 8. (2) is stronger than (1) for (2) implies (1) but not the other way around in any modal logic including the axiom schema □Ф→□□Ф 9. [Boghossian 1997] thus intends to redeem epistemic analyticity while rejecting its metaphysical concept. 10. Kripke s rigidity thesis is often considered as rebutting Quine s objections against de re modality. As [Burgess 1997] reminds us, this is mistaken. Certainly, if we interpret, as Kripke does, □ as meaning metaphysically necessary, draining any idea of analyticity in it, then attributing non-trivial essential properties is intelligible. Modality thus understood does produce transparent contexts that allow the substitution of co-referential rigid terms and the "quantifying in". However, Quine s objections aim for de re modals when □ means analytically true. In this sense, the idea of non-trivial essential properties remains unintelligible, even after the Kripkean turn. 11. To accommodate the contingent existence of their objects, (a)-(d) are implicitly prefixed by an existential condition. 12. Again, (e) is tacitly prefixed by an existential condition since Neptune’s existence cannot be known a priori. 13. For various elaborations of the notion of conceivability, see in particular [Yablo 1993], [Menzies 1998], [Chalmers 2002], [Geirsson 2005], along with the articles published in [Gendler & Hawthorne 2002]. 14. For practical purposes, this is a simplification of Sidelle’s view. For more details, see in particular chapters 2 and 3 of [Sidelle 1989]. Sidelle’s conventionalism also postulates semantic rules in order to account for de re necessities concerning singular objects, for instance the necessity of origin. 15. For a survey of physicalists objections to the Zombie argument along with Chalmers responses, see [Chalmers 2010].
Philosophia Scientiæ, 16-2 | 2012 31
16. It is usually admitted that metaphysical modality verifies the axiom schemata □Ф→□ □Ф (S4) and ◊Ф →□◊Ф(S5). That’s why Lewis holds that all true statements of the form "□Ф"and "◊Ф " are themselves necessary. 17. Take for instance the non-modal statement "if Hannah Ayscough (HA) and Isaac Newton (IN) exist, IN is the biological child of HA". Assuming that origin is essential, this statement describes a fact which (i) is necessary, albeit knowable only empirically, (ii) concerns concreta. It should be obvious that the necessity of such a fact does not exempt us from needing a causal relation to know it. To accommodate such examples, Lewis has no choice but to embrace a strong form of two-dimensionalism in which all empirical necessities are 1-contingent. 18. This line of reasoning is close to the so-called "indispensability argument" for mathematical realism. Arguments by IBE must nonetheless be carefully distinguished from indispensability arguments, for the indispensability condition is much more demanding than the best explanans condition. 19. For an example of non-causal explanation in science, see in particular [Lipton 2004, 31-32]. 20. The literature on this point is profuse but one can find a valuable discussion in [Divers 2002]. 21. This clause of sufficiency is stated by a second-order principle of possibility, the "Principle of Constrained Recombination" [Peacocke 1999, 149]. 22. "Ф □→ Ψ" abbreviates "if Ф had been the case, Ψ would have been the case". Equivalence (E) appears in [Lewis 1973]. [Stalnaker 1968] prefers: □Ф iff ¬Ф □→ Ф. While both use the □→ operator in order to define □, they have never exploited these definitions for epistemological purposes. As noted by [Williamson 2007, 159] "[…] such definitions seem to have been treated as convenient notational economies, their potential philosophical significance unnoticed." 23. We take this last step to be independent from reductive explanation since A can reductively explain B even if concepts required for entertaining B are not analytically tied to concepts exercised in entertaining A. 24. The thesis according to which essentialist thought is an adaptive capacity must be taken cum grano salis. As Susan Gelman remarks "[...] essentialism is not a single adaptation, but the result of several distinct cognitive biases that emerged for varying purposes. In other words, essentialism per se was not specifically selected, but components of essentialism were." [Gelman 2003, 15]. Let it be also repeated that the fact that a cognitive mechanism has been selected does not in any way prove that it tends to produce true beliefs in wider contexts, particularly in philosophical theorizing. It is well known that folk essentialism brings with it many erroneous beliefs, not only about socially constructed categories, such as race, but also about natural kinds. People thus believe that kind-membership rests invariably on the sharing of intrinsic properties when evolutionary biology considers that biological species are individuated by relational properties, namely their phylogeny. 25. If it is a constitutive truth about a that Фa,then Фa. But, it can be argued, someone can claim that being Ф belongs to the nature of a without committing herself to the existence of a, and so without implying Фa. 26. I.e., (a≠b) □→ ( a≠b),where "a" and "b" are rigid designators. 27. Notice that in counterfactual accounts, the rigidity of referential terms within the scope of ◊ and □ operators is a consequence of their rigidity in □→ contexts.
Philosophia Scientiæ, 16-2 | 2012 32
ABSTRACTS
The role of this introduction is twofold: it presents the papers collected in this volume and offers a synthesis of recent developments of the epistemology of modality.
L’objectif de cette introduction est double : elle présente les articles rassembles dans ce volume et offre une synthèse des développements récents de l’épistemologie des modalités.
AUTHORS
FILIPE DRAPEAU VIEIRA CONTIM Universite de Rennes 1 (France)
SÉBASTIEN MOTTA Centre Atlantique de Philosophie, Nantes (France)
Philosophia Scientiæ, 16-2 | 2012 33
Conceptual Truths, Strong Possibilities and Our Knowledge of Metaphysical Necessities
Christian Nimtz
1 The simple argument introduced
The category of metaphysically necessary statements1—of metaphysical necessities, for short—is widely held to be of particular importance to philosophical inquiry. Following Kripke [Kripke 1980, 34-60], everyone agrees that metaphysical necessity contrasts with the traditional categories of logical, conceptual and nomological necessity in that there are metaphysical necessities that cannot be discovered by apriori reflection, in that there are metaphysical necessities that aren't analytic, and in that metaphysical necessities hold true in all possible worlds simpliciter. Beyond this, there is no consensus on what makes a necessity a metaphysical necessity, or what marks off metaphysical modality in general [Cameron 2009].
1 Metaphysical necessity poses two interlocked puzzles. On the one hand, there is the metaphysical puzzle of what, if anything, grounds metaphysical modality [Cameron 2010], [Hale & Hoffmann 2010, part I]. On the other hand, there is the epistemic puzzle of how we may arrive at knowledge of metaphysical necessities [Vaidya 2011], [Roca- Royes 2011], [McLeod 2005], [Hale & Hoffmann 2010, part II]. I will be dealing with the epistemic puzzle. I argue that our ordinary knowledge of conceptual truths, knowledge we possess since we know what (many of) our terms semantically apply2 to, is a reliable epistemic source of, and hence a reliable route to, knowledge of metaphysical necessities. (I will often shorten 'knowledge of conceptual truths' to 'conceptual knowledge', and unless indicated otherwise, I will take 'modal knowledge' to mean 'metaphysically modal knowledge'.) Here is the argument I put forth. I call it the simple argument for modal knowledge, or just the simple argument:
Philosophia Scientiæ, 16-2 | 2012 34
We possess conceptual knowledge, since we know for (many of) our terms what they (1) semantically apply to.
Any item of conceptual knowledge we so possess either ipso facto is knowledge of a (2) metaphysical necessity. Or the conceptual knowledge we are concerned with is such that we can reliably determine that it does not lead to modal knowledge.
Hence:
The conceptual knowledge we possess since we know what (many of) our terms apply to (3) reliably yields knowledge of metaphysical necessities.
2 That conceptual knowledge yields modal knowledge has been argued before, notably by Peacocke and Bealer. So let me accentuate what is distinctive about the simple argument.
3 Peacocke and Bealer both draw on bold background designs. In his actualist metaphysics of modality, Peacocke postulates implicitly known general principles that at the same time govern modality, and give rise to modal knowledge [Peacocke 1999], [Peacocke 2002]. This scheme has proved controversial both in technical detail [Williamson 2002] and in principle [Rosen 2002]. Bealer enlists an understanding of concepts as sparse ante rem universals with characteristic possession conditions [Bealer 2000, esp. 21ff], [Peacocke 1999, 299f], [Sosa 1998]. On his view, a thinker A determinately possesses some concept C only if, simply put, As rational intuitions track the true nature of the property of being C. Determinate concept possession thereby virtually ensures modal knowledge, but it turns out to be exceedingly demanding. On these standards, few humans (if any) will ever determinately possess a concept. That is why Bealer [Bealer 2000, 12, 23f] merely argues that determinate concept possession is metaphysically possible.
4 The simple argument contrasts sharply with either approach. It rests neither on an ambitious metaphysics of modality, nor on an extravagant theory of concept possession. The argument is designed to be, well, simple. It aims to establish a connection between knowledge of conceptual truths and knowledge of metaphysical necessities drawing on widely shared views of our knowledge of our terms semantic properties, and on ideas about modality that are deeply entrenched in the standard view of modal space.
5 Here is what I will do. I begin by arguing that, since we know how we do and would apply our terms (§ 2) and since, as neo-descriptivists and orthodox Kripkeans agree, considered application often determines semantic properties, we often know what our terms semantically apply to, and thereby possess conceptual knowledge (§ 3). I go on to defuse Williamson's recent charge that there is no conceptual knowledge, since there are no epistemic analyticities (§ 4). Drawing on common ideas about modal space, I then argue that all defeaters to the universal rule that knowledge of conceptual truths is ipso facto knowledge of metaphysical necessities are, as it were, harmless. I conclude that the conceptual knowledge we possess since we know what (many of) our terms apply to does indeed give rise to modal knowledge (§ 5). I close by reviewing my
Philosophia Scientiæ, 16-2 | 2012 35
argument, and by wondering whether there is anything left to do in modal epistemology (§ 6).
2 From considered application to knowledge of notions
The simple argument rests on the epistemological premise that:
(1) We possess conceptual knowledge, since we know for (many of) our terms what they apply to.
This premise combines two claims: (i) we do have knowledge of conceptual truths, and (ii) we do have knowledge of conceptual truth since we know for (many of) our terms what they apply to. Either claim may appear contentious. Yet if we start from mundane facts about how we use language and work our way up to standard semantic theories, we find that there should be sufficient common ground to support both.3
6 Here is a patent truth about the way we use language: To which entities we do and would apply our (classificatory) terms depends on the properties we take those entities to have. For example, I call a liquid 'flammable' because I take it to ignite easily, I call John a 'liar' because I take him to have intentionally presented a falsehood as truth, and I call Venus a 'planet' because I take it that it meets the criteria laid down by the IAU. These characterizations aptly reveal what properties the considered application of my terms is sensitive to. After all, they all sustain the pertinent counterfactuals. It is not just that I do call a liquid 'flammable' if I take it to ignite easily. I also would call a liquid 'flammable' if I were to take it to ignite easily.
7 In order to coin some terminology apt to generalize these observations, let the notion a speaker associates with some term F'4 be the conditions something has to satisfy such that the speaker does and would, on reflection, apply 'F' to it. The notion someone associates with a term F' guides her application of that term. That is simply to say that she does and would apply F'tosomethingif she takes it to satisfy that notion. As revealed above, the notion I associate with 'flammable' is being such that it ignites easily, as this is what guides my considered application of the term. Please note that, as introduced, the notion of a notion' belongs to the theory of language use. Whether it is of relevance to semantics depends on the relevance of language use to semantics. (I will come back to this in the next section.)
8 The observations about language use rehearsed above sustain two general claims about notions. First, UBIQUITY: We quite generally associate notions with our terms guiding how we do and would reflectively apply them. The reason for this is plain to see. Our considered application of (classificatory) terms depends on the properties we take those entities to have. But notions just are the very properties our considered application is sensitive to. Hence, we quite generally associate notions with our terms guiding our considered application.
9 Secondly, ACCESS: We have readily available, yet presumably mostly tacit, non-trivial knowledge of what the notions we associate with our terms are. I call something a planet' because I take it to satisfy the notion I associate with planet'. That of course requires me to have readily available non-trivial knowledge of what this associated notion is, otherwise my considered application could not be sensitive to the conditions
Philosophia Scientiæ, 16-2 | 2012 36
the notion encapsulates. Such an association will quite generally be forged by beliefs and/or dispositions on the part of the subject, and there is no guarantee that the readily available knowledge this yields will be explicit rather than tacit.
10 Still, we have no reason to think that our explicit armchair judgments on what we do and would apply our terms to are customarily unreliable. On the contrary, we quite generally find that our considered use is basically what we consider it to be. It hence is hardly surprising that (almost) everyone in philosophy treats speakers' answers to questions such as "Would you call an easily ignitable liquid 'flammable'?" or "Would you call a woollen bonnet a 'hat'?" as revealing their considered use—given that we allow them to reflect on the question, that we describe or present the relevant items with sufficient care, and that we present contrasting cases. Think of Kripke [Kripke 1980, 82ff] and Putnam [Putnam 1975, 223-227] on the one hand. Think of experimental philosophers on the other hand [Knobe & Nichols 2008]. For all their disagreement, they agree that subjects can reliably tell how they do and would apply their terms in specific possible cases.
11 Our armchair reflection on how we do and would apply our terms is arguably fit to reliably provide partial accounts of the notions we associate with our terms, or so everyone agrees. This consensus carries no assurance that coming up with a comprehensive account of any of our notions will be a simple affair. On the contrary, we typically need to generalize from the considered judgments we find ourselves making with respect to a limited assortment of possible cases. By consequence, our armchair-based accounts of the notions guiding our considered application are typically conjectural, always defeasible, and very often provisional. But we can apparently rest assured that providing explicit, if partial, accounts of the notions guiding the application of terms such as knowledge', 'circle', 'neighbour', 'poisonous', 'uncle', 'I' or 'flammable' is typically not beyond our epistemic ken.
3 From knowledge of notions to conceptual knowledge
I have argued that we associate notions with our terms guiding our considered application, and that we can (at least often and partially) determine what these notions are. These are claims about language use. Thus far, I have made no claims about semantic properties. So let us turn from use to semantics and ask: Do the notions guiding our considered application affect or constrain the semantic properties our terms have? Proponents of traditional descriptivism emphatically think they do [Ayer 1946, chap. 1-3], [Hanfling 2000]. Embracing the slogan that use determines meaning,5 traditional descriptivists hold that the notion we associate with any of our terms straightaway determines what this term semantically applies to. On this picture, 'flammable' or 'gold' as used by us apply to items that ignite easily and to yellowish metal substances, respectively, because these fit the notions we associate with these terms. The analogous holds true for proper names such as Nixon', and indexicals such as I 'or here'.6
12 There is almost universal agreement that the traditional descriptive paradigm is flawed. What is controversial is whether it is beyond repair. Orthodox Kripkeans forcefully maintain that it is [Kripke 1980, 82-87, 118, 124], [Putnam 1975], [Soames 2002]. They point out that proper names such as Nixon' and natural kind terms such as
Philosophia Scientiæ, 16-2 | 2012 37
water' designate rigidly and that Nixon and water thus could very well not have had the very properties we actually identify them by, that we habitually defer in our application of kind and artefact terms to experts in line with Putnam's [Putnam 1975, 227f] famed linguistic division of labour', and that our associated notions quite often contain factual falsehoods such that, strictly speaking, nothing satisfies them. From this they conclude that traditional descriptivism is fundamentally mistaken: The notions we associate with names and natural kind terms are extraneous to their semantics, or so orthodox Kripkeans maintain. What these terms do and would apply to is rather determined by the very items or samples we find at the beginning of the causal-historical chains our use of these terms belongs to [Kripke 1980, 9197]. For example, our term 'gold' applies to something o in some possible world w iff (i) the actual causal-historical chain our use of' gold' belongs to originated with some sample k —maybe the producers of that term just ruled: "That (☞)is gold", pointing to k—and (ii) o is of the same natural kind as k.
13 Neo-descriptivists reject the causal-historical picture just sketched [Jackson 2010], [Jackson 2010, chap. 2], [Jackson 1998, chap. 2], [Lewis 1994], [Chalmers 2004], [Nimtz 2010]. They think that a semantics loyal to the descriptivist idea that our notions essentially fix the semantic properties of our expressions can account for factual errors, deference, and rigid designation. Factual errors are permitted since what a term applies to is fixed by best rather than by perfect fit with the associated notion [Lewis 1997, 358f], [Lewis 1972, 253], [Lewis 1994, 298]. Deference is accounted for by allowing individual notions to comprise explicitly deferential conditions along the lines of gold is the goldish stuff of our acquaintance our experts accept as gold [Jackson 2004, 270-273]. Finally, rigid designation and the counterfactual variation in surface properties that comes with it is accounted for by combining the idea that a term's application in a possible world is determined by a trans-world relation of sameness-of-natural-kind to an actual sample—vide clause (ii) of the Kripkean proposal above—with the claim that this actual sample is determined by our associated notion rather than by historic origin. On neo-descriptivist premises, our term 'gold' applies to something o in some possible world w iff (i) there is a sample k in the actual world such that k best fits the notion we associate with 'gold', and (ii) o is of the same natural kind as k.
14 Neo-decriptivists discern two perspectives we can take on possible worlds [Jackson 1998, 47-51]. We can consider a possible world w as counterfactual. To do so, "one acknowledges that the actual world is fixed, and thinks of a possibility as a way the world might have been but is not" [Chalmers 2004, 159]—i.e., as a possible variation in how things are given that the actual world is how it is. Let me call a world considered
thus a counterfactual or C-world (in symbols: □CS).These worlds capture the metaphysical dimension in modality in that a statement S is metaphysically necessary iff S is true in all C-worlds. Or we can consider a possible world as a possible variation in how things actually are, as "representing a way the actual world might turn out to be" [Chalmers 2004, 159]. Let me call a world considered thus a counter-actual or A-world. Counter- actual worlds are centred, i.e., they have at least a place, a time, and a speaker/thinker highlighted. Taking conceptual truth and conceptual necessity to be the very same thing, A-worlds afford a straightforward way to explain what conceptual truth comes to: A statement S is conceptually necessary iff S holds true in all A-worlds (in symbols:
□AS).
Philosophia Scientiæ, 16-2 | 2012 38
15 Drawing on this modal distinction, neo-descriptivists can provide a quite precise account of how associated notions affect semantic properties, thereby making good on their idea that our notions are what essentially fixes what our terms apply to. Our notions straightforwardly determine what our terms apply to across all counter-actual worlds; a fortiori, they straightforwardly determine the actual extensions our terms have. However things turn out to be,' flammable' applies to what best fits my notion being such that it ignites easily, and 'gold' applies to what best fits my notion being the goldish stuff of our acquaintance our experts accept as gold. Yet what terms such as 'gold' apply to in some counterfactual worlds might well not be what best satisfies the associated notion within that world. As explained above, a term's application across counterfactual worlds will often be determined by what is of the same natural kind as the items or samples the term actually applies to. Of course, this actual extension is always straightforwardly fixed by the associated notion.
16 The pronounced differences in the semantic theories proffered by orthodox Kripkeans and neo-descriptivists7 should not blind us to their substantial agreement. Their dispute concerns specific kinds of expressions, notably proper names such as 'Nixon' and natural kind terms such as 'gold' or 'tiger'—terms whose semantic properties are, according to the typical orthodox Kripkean, fixed causal-historically. Yet both parties agree that our language comprises quite a lot of expressions that, modulo deference, fit the traditional decriptivists' paradigm. Expressions such as 'circle', 'neighbour', 'poisonous', 'uncle' or 'flammable' are cases in point. These do not designate rigidly, and the orthodox Kripkean wouldn't think that their application is determined causal- historically—no orthodox Kripkean is an externalist about uncle'. Orthodox Kripkeans and neo-descriptivists also agree that terms such as I' or the actual winner of the Man Booker Prize 2005' fit the neo-descriptivists account in that they designate rigidly whatever satisfies the associated descriptive condition, a condition that is encapsulated in the notion guiding our considered application of these terms. In the end, then, orthodox Kripkean and neo-descriptivists agree that semantic properties are often determined by associated notions, yet quarrel over the range of expressions actually fitting this model. Given that we can (at least often and partially) determine what the notion we associate with a term is, we hence find that Kripkeans and neo-descriptivists agree that we (at least often and partially) know what our terms apply to.
17 So what we find is that (i) our considered application of our terms is guided by the notions we associate with these expressions across the board, that (ii) armchair reflection on how we do and would apply our terms is arguably fit to reliably provide partial accounts of the notions we associate with our terms, and that (iii) there is a broad consensus that, at least in many cases, our associated notions determine the semantic properties of our terms. More precisely, if the orthodox Kripkean is right, notions determine what our terms semantically apply to in many, yet by no means in all cases, whereas if the neo-descriptivists' analysis holds true, notions determine at least application across counter-actual worlds across the board. But given that we know what our terms apply to, we ipso facto are in a position to have knowledge of conceptual truths. Since I know that 'uncle' applies to male relatives, and that' circle' applies to geometric figures, I know that uncles are male relatives, and that circles are geometric figures.
18 I conclude that we have every reason to believe that we do possess knowledge of conceptual truths, and that we do so since we know for (at least many of) our terms
Philosophia Scientiæ, 16-2 | 2012 39
what they semantically apply to. This fits nicely with our pretheoretical convictions. It seems very hard to deny that my knowledge of what my terms apply to puts me in a position to accurately judge that, say, "You do not know that p if p is false", "Neighbours have neighbours", "Uncles are relatives" or "Hats are coverings of the head" hold true. In fact, any doubt on this matter has a decidedly skeptical feel to it.
4 Against Williamson against epistemic analyticity
Acknowledging conceptual knowledge commits us to acknowledge analytic truths. At minimum, acknowledging conceptual knowledge requires us to acknowledge epistemically analytic truths held to be "such that one can determine their truth-value merely by grasping the meanings of the terms that occur in them" [Grayling 1997, 33], cf. also [Boghossian 1997, 334], [Boghossian 2003]. However, Williamson has recently argued that "no truths are analytic in the epistemological sense" [Williamson 2006, 8].8 So before we can rest assured that we do in fact have conceptual knowledge, I need to review Williamson's case.9
19 Williamson argues that "[f]or even the simplest candidates for analyticity or conceptual truth, understanding is consistent with considered rejection" [Williamson 2006, 32]. Consider Peter, an expert logician who holds the odd view that universal quantification in English is existentially committing in that: "There is at least one F" is a necessary condition for the truth of "Every F is G".10 Peter has also been swayed by a curious conspiracy theory to believe that there are no vixens. Since he holds that the existential commitment of "Every vixen is a vixen" is not fulfilled, Peter neither assents to "Every vixen is a vixen", nor believes the thought it expresses.
20 According to Williamson, Peter nevertheless understands this sentence and grasps the thought it expresses. Peter understands 'vixen' just as we do, taking it to be synonymous to female fox'. He also understands the mode of combination used in "Every vixen is a vixen". More importantly still, Peter understands the English every' occurring in "Every vixen is a vixen". He is a native English speaker with a standard learning history whose conception makes little difference in practice—since Peter classifies what we consider a pragmatic presupposition as a logical inference, we usually do not even notice his deviation. Peter is also not trying to reform our language. He intends his theory to capture the meaning of every' in English, and he agrees to revise his account if he is proven wrong on this. What is peculiar about Peter thus is his logical theory, not his understanding, and as Williamson stresses: Giving an incorrect theory of the meaning of a word is not the same as using the word with an idiosyncratic sense. [Williamson 2006, 12]
21 Williamson concludes that neither "Every vixen is a vixen", nor "Every vixen is a female fox" is epistemically analytic. He maintains that this line of thought smoothly generalizes. Since we can find some 'logical unorthodox' [Williamson 2006, 32] in any single case, there simply are no epistemic analyticities.
22 By way of reply, note first that Peter is acutely aware of how he uses 'every', as well as of the fact that his use differs from ours. In fact, Williamson stipulates that Peter's "refusal to accept ['Every vixen is a vixen'] as true is stable under conscious reflection, exposure to further arguments and the like" [Williamson 2006, 16]. Hence, in clear contrast to the way we use 'every', Peter reflectively employs the terms such that his "Every F is G" entails "There is at least one F". The deliberate and reflected use Peter
Philosophia Scientiæ, 16-2 | 2012 40
makes of 'every' accords, moreover, with his theory. We thus find that the use Peter makes of 'every' fits his own theory, but systematically deviates from how we use that term.
23 This marked difference in considered and theory-guided use gives us every reason to conclude that Peter's "Every F is G" differ in truth-conditions of our "Every F is G". Since everyone agrees that a difference in truth-conditions makes for a difference in thought expressed, we find that 'every' in Peter's mouth does differ in sense from 'every' in our mouths. Pace Williamson, Peter thus attaches an idiosyncratic sense to every', and he does so precisely because his theory accords with him using it in an idiosyncratic fashion. Williamson rightly points out that holding an incorrect theory of a word's meaning is not the same as using the word in an idiosyncratic sense. But he does not appreciate the fact that the former can be a sure sign of the latter if the incorrect theory conforms to, or even shapes the speaker's reflected use. This is precisely what we find in Peter's case. I therefore conclude that Peter does not grasp the thought we express with "Every vixen is a vixen". Hence, we have no reason to believe that not even this simple logical truth amounts to an epistemological analyticity.
24 Williamson tries to preempt this line of thought in two different ways. On the one hand, he emphasizes that every' in Peter's mouth must mean the same as it does in our mouths; after all, we all speak English. On a strict Lewisian individuation of natural languages [Lewis 1975], this does indeed follow. But Williamson employs far more lenient criteria for speaking the same natural language, viz., fluency of communication [Williamson 2006, 11f] and non-deviant first acquisition [Williamson 2006, 13], as he needs to do to bestow prima facie plausibility on his idea that Peter speaks the same language as we do. And on these criteria, sameness of natural language does not guarantee sameness of meaning.
25 This fits well with the natural languages we know. Consider e.g., the term 'hat'. According to the OED, there are two uses of this word. On the former, a hat is almost any covering for the head. On the latter, a hat is a specific kind of headgear that typically has "a more or less horizontal brim all round the hemispherical, conical, or cylindrical part which covers the head". Thus there might well be a community of English speakers whose members exclusively use 'hat' in the former sense, and one whose members exclusively use 'hat' in the latter sense. The overlap in the senses would allow ordinary communication to proceed by and large smoothly. Still, the communities would use 'hat' in different senses. Meaning can thus cut finer than shared natural language.11 Hence, the fact that we all speak English is consistent with the fact that 'every' in Peter's mouth means something different from what it means in our mouths.
26 On the other hand, Williamson thinks that a homophonic rendering of Peter's: "Every vixen is a vixen" is more faithful to his intentions than any non-homophonic reading. After all, Peter's logical theory attempts to capture our shared meaning of 'every'. From this Williamson concludes that Peter associates the sentence: "Every vixen is a vixen" with "the same thought as we do in any relevant sense of 'thought"' [Williamson 2006, 25]. But that inference is flawed. In most contexts, we report homophonically because the differences in truth-conditions do not matter. And in contexts where these differences do matter, we report homophonically because we lack a word expressing Peter's sense of 'every'.12 But when it matters, we flag the differences: "Peter denies that every vixen is a vixen. You see, the way he uses 'every' is
Philosophia Scientiæ, 16-2 | 2012 41
such that such a claim is true only if there are some of these things, and Peter believes that there are no vixens." In writing we can easily devise a new term, and we would not
hesitate to distinguish our 'every1' from Peter's 'every2'. There is nothing paternalistic about this. We have diagnosed a simple difference in use and meaning, and highlight it.
27 Please note that a difference is all we need. We hold that "Every vixen is a vixen" is a conceptual truth in our community because we think it obvious that we use 'every' in
the sense of 'every1'. Peter's challenge might prompt us to reflect about the way we do and would use 'every' in order to determine whether the seemingly innocuous "Every vixen is a vixen" is indeed analytic in our community. But the fact that Peter's challenge prompts us to re-assess our judgment as to how we employ the term across possible situations does not imply that "Every vixen is a vixen" is not a conceptual truth in our community. Even less does it follow that since such a challenge is possible in any single case, there are no epistemic analyticities. This merely implies that our judgements about which statements are conceptual truths are generally defeasible.
28 Yet that is granted anyway. There might always be a queer possible situation we have not thought of—as I have stressed above, our armchair-based accounts of the notions guiding our considered application are typically conjectural, always defeasible and very often provisional. But Peter does not draw our attention to a possible situation contemplation on which is expected to convince us that we, at least sometimes, employ "Every F is G" such that it entails "There are Fs". He maintains that we are wrong about the semantics of 'every' in our mouths although we know perfectly well how we do and would use that term. Please recall that Williamson stipulates that Peter's refusal to accept "Every vixen is a vixen" is stable under reflection, exposure to further arguments, and the like. By parity of reasoning, we can assume that our refusal to give in to Peter's account is likewise stable such that learning more about how we do and would use 'every' won't change our verdict either.
29 I conclude that Williamson hasn't established that there are no epistemic analyticities. A fortiori, he hasn't shown that there is no conceptual knowledge. In the light of the positive case offered in the last section, we can rest assured that we do in fact have conceptual knowledge. The first premise of the simple argument still stands tall, or so I maintain.
5 From conceptual truths to metaphysical necessities, or the argument from strong possibilities
Turning to the second premise of the simple argument, I need to show that
Any item of conceptual knowledge we so possess either ipso facto is knowledge of a (2) metaphysical necessity. Or the conceptual knowledge we are concerned with is such that we can reliably determine that it does not lead to metaphysically modal knowledge.
Here is a quick argument for this premise. We do have knowledge of conceptual truths, or so the first premise of the simple argument assures us. Given the distinctions made in § 3 above, we know that a conceptual truth amounts to a statement that holds true
across all counter-actual or A-worlds (in symbols: □AS). But any such conceptually necessary statement is ipso facto metaphysically necessary in that it holds true across all
Philosophia Scientiæ, 16-2 | 2012 42
counterfactual or C-worlds as well (in symbols: □CS). That is to say, the following principle I dub the 'NN-Rule' holds true:
If statement S is conceptually necessary, S is metaphysically necessary as well (in symbols: (NN) □AS→□CS)
On the NN-rule, then, conceptual necessities are directly convertible into metaphysical necessities. Hence, premise (2) holds true in virtue of its first disjunct holding true: Any item of conceptual knowledge we possess ipso facto is knowledge of a metaphysical necessity.
30 The quick argument clearly is too quick. It presumes that there are no defeaters to the NN-rule. But Kripke [Kripke 1980, 53-56] has shown that we find statements that defeat
it. Consider: "The standard meter is one meter long at t0" Although this statement expresses a conceptual truth, it is metaphysically contingent rather than metaphysically necessary. It thus defeats the NN-rule. But if there are defeaters to the NN-rule, we cannot rely on it to convert some conceptual truth S we have arrived at by conceptual reflection into a metaphysical necessity. For how can we make sure that S does belong to the statements the NN-rule holds true for?
31 So the quick argument won't do. But something very much like it will do, for all exceptions to the NN-rule are identifiable in advance, or so I will argue. That is to say, the NN-rule fails only for statements for which we can know, by armchair semantic consideration, that it fails for them. All defeaters of the NN-rule thus are harmless. If this is true, then we can decide, for any conceptual necessity we find, whether it yields a metaphysical necessity, or whether it is a defeater to the NN-rule. Conceptual reflection thus puts us in a position to safely derive metaphysical necessities from insights gained by conceptual analysis.
32 Please note that distinguishing between counter-actual or A-worlds and counterfactual or C-worlds allows us to distinguish two kinds of truth-conditions, and hence two kinds of contents encapsulating those. On the one hand, there are counter-actual truth- conditions—A-contents, for short. These capture the conceptual dimension in that, as rehearsed above, a statement S is conceptually necessary iff it holds true in all A- worlds. On the other hand, there are the more familiar counterfactual truth-conditions —the C-contents, for short. These capture the metaphysical dimension in that, as already explained, a statement S is metaphysically necessary iff it holds true in all counterfactual or C-worlds. Any defeater of the NN-rule must hence be such that its A- contents are necessary whereas its C-contents aren't. So let us consider what could make a statement's counterfactual and counter-actual truth-conditions differ. Two answers to this are widely discussed.
33 The first idea is this: A statement's counterfactual and counter-actual truth-conditions may differ if the statement contains actuality-dependent terms. Actuality-dependent expressions such as 'here', 'water' or 'one meter' designate rigidly whatever actual extension their A-contents carve out. This might well make that their C-contents deviate from their A-contents. A statement's C-content may hence differ from its A- content because it contains actuality-dependent terms.13 This yields clear defeaters for the NN-rule. Actuality-dependence brings about a posteriori necessities such as "Water
is H2O" with 'water' rigidly designating the substance 'water' actually applies to.
Philosophia Scientiæ, 16-2 | 2012 43
Actuality dependence also brings about a priori contingencies such as "The standard
meter is one meter long at to." The latter combine a necessary A-content with a contingent C-content and hence defeats (NN). Yet these defeaters are harmless. Since we can diagnose actuality-dependence by armchair semantic considerations, statements whose C- and A-contents deviate because they comprise actuality- dependent terms are recognizable from the armchair. Given that we reflect on that matter, and given that we are alert to the possibility that apriority and metaphysical necessity may come apart, we simply won't mistake a priori contingencies such as "The
standard meter is one meter long at to" for metaphysical necessities. 34 Neo-descriptivists hold that actuality-dependence is the only reason for a statement's C- and A-contents to differ, and thus the only source of a posteriori necessities. Quite a few philosophers reject this claim. This brings us to the second idea as to how a statement's counterfactual and counter-actual truth-conditions may come apart. Advocates of so-called strong necessities hold that "God exists", "e=mc2", or the key materialist claim □(PHYS→PHEN)14 state a posteriori necessities, although they do not contain actuality-dependent terms and we judge them to be false in some A-world [Chalmers 2002, 189-192], [Kallestrup 2006]. For any such statement S, it holds true that May, but need not. For many actuality-dependent sentences it holds true that if they are conceptually necessary, they are metaphysically necessary. Consider e.g., 'Water is the actual watery stuff of our acquaintance" or "One meter is the actual length of the &¬ standard meter at □cS □A S. Hence, any strong necessity is putative example of a non- actuality-dependent statement whose A- and C-contents nonetheless differ.
35 Chalmers [Chalmers 2010], [Chalmers 2002, 189-194] argues that there are no strong necessities. He points out that we have no reason to think that the examples given are metaphysically necessary in the first place, that strong necessities presuppose inexplicable brute modal facts, and that their existence would require the space of A- worlds to outrun the space of C-worlds. This fact would violate modal monism on which A- and C-world are the same worlds viewed under different perspectives. But modal monism provides a prima facie highly plausible account of modal space, and it is less opulent than any picture assuming A- and C-worlds to be different entities. So Chalmers concludes that we have good reason to think that there are no strong necessities.
36 Still, many philosophers maintain that things are different when it comes to the phenomenal, and they accept that □(PHYS — PHEN) is a strong necessity. They argue that we have good reasons to uphold physicalism and reject mind-body dualism, and they provide a theory of phenomenal concepts to explain how strong necessities involving those concepts come about [Tye 2003]. I am rather wary of this line of argument,15 and I consider strong necessities to be rather dubious. But let us for the moment acknowledge them. Let us agree that there are as many strong necessities as you like. How does this affect the case to be made here in support of premise (2) of our simple argument?
37 Acknowledging strong necessities does not affect this case at all. For strong necessities do not affect the NN-rule. Actuality-dependence yields defeaters to the NN-rule that are harmless. Strong necessities are far from harmless. We won't learn that some statement expresses a strong necessity by armchair semantic considerations. But strong necessities do not defeat (NN). Put simply, if there are strong necessities, there are more A-worlds than C-worlds: Since a strong necessity S is true in all C-worlds but
Philosophia Scientiæ, 16-2 | 2012 44
false in some A-worlds, these A-worlds cannot be C-worlds. But if there are more A- than C-worlds, arguing from the truth of "God does not exist" or "PHYS &¬ PHEN" in some A-world to their truth in some C-world becomes problematic. Strong necessities thus would defeat the following principle I dub the PP-Rule':
If statement S is conceptually possible, S is metaphysically possible as well (in symbols: ◊ S — (PP) A ◊CS).
38 This would be significant enough. But it would not affect the NN-rule. The NN-rule S entails that ◊cS→◊A holds true. This rule cannot be invalidated by statements falsifying S S. the converse ◊A →◊c
39 So we find that neither of the reasons the current debate contemplates for a statement's C-content to deviate from its A-content yields harmful defeaters for the NN-rule. This was to be expected. Any harmful defeater to (NN) would have to be a non- actuality dependent statement stating a metaphysical contingency that we nevertheless judge to be true in all A-worlds. In other words, any harmful defeater to
(NN) would have to be a strong possibility. Only for strong possibilities S does □AS&¬□CS hold true in spite of the absence of any actuality-dependent terms, which is what we would need for defeater of (NN) that we cannot diagnose by armchair semantic reflection.
40 To my knowledge, no one has ever defended strong possibilities, or produced a single example. What is more, anyone who recognizes metaphysical necessity has good reasons to doubt that there are any strong possibilities.
41 First of all, suppose someone takes "Some grandmothers aren't female" to state a strong possibility. She has to hold that (i) "All grandmothers are female" is conceptually necessary, that (ii) there nevertheless are metaphysically possible worlds with non-female grandmothers, and that (iii) "All grandmothers are female" does not function like "Water is watery", since neither 'grandmother' nor 'female' is actuality- dependent. But taken together, (ii) and (iii) seem to contradict (i). Our speaker seems to hold that there is some possible situation correctly describable as containing non- female grandmothers and to hold that there is no possible situation correctly describable as containing non-female grandmothers whilst agreeing that 'female grandmother' applies to precisely the same objects in both possible situations.
42 Secondly, to hold that there is a statement S such that □AS&¬□CS is to agree that there is
a statement S' such that ¬◊AS'&◊CS'. To accept strong possibilities is thus to accept that some conceptual impossibilities are metaphysically possible. But everyone treats conceptual impossibility as sufficient for metaphysical impossibility. No one who grants that: "There are round squares" or "There are married bachelors" are conceptually impossible (and non-actuality dependent) thinks that we still need to check whether they are metaphysically possible. That is exactly right. If there are Moorean facts about modality, that there cannot be a metaphysically possible world in which a conceptual impossibility holds true is clearly one of them.
43 Finally, if there are strong possibilities, there are more C-worlds than A-worlds: Since a strong possibility S is false in some C-worlds but true in all A-worlds, these C-worlds cannot be A-worlds. So if there are strong possibilities, there are metaphysically
Philosophia Scientiæ, 16-2 | 2012 45
possible worlds that are conceptually impossible. An advocate of strong possibilities thus had to avow that metaphysical necessity outruns conceptual necessity. This would mean to embrace modal dualism. It would also run counter to everything we thought we knew about how conceptual and metaphysical modality are related. Anyone who acknowledges metaphysical modality at all will agree that although modal space may have some unexpected features, it cannot deviate that much from how we think it is.
44 I conclude that there are no strong possibilities. Consequently, there are no harmful defeaters to the NN-rule. Hence, premise (2) of the simple argument holds good. By consequence, the conceptual knowledge we possess reliably yields knowledge of metaphysical necessities.
6 Wrapping up, or modal knowledge and metaphysical ambition
I have argued that there are conceptual truths we know since we know what our terms semantically apply to. Yet any such conceptually true statement S we know either ipso facto provides us with knowledge of a metaphysical necessity. This holds true if S is conceptually necessary and does not comprise any actuality-dependent term. Or S comprises at least one actuality-dependent expression, making its extension across counterfactual worlds dependent on (as a rule) contingent actual fact. Then our knowledge of S does not provide us with knowledge of a metaphysical necessity. But since we can uncover actuality-dependence by armchair semantic reflection, we are in a position to know that S does not ipso facto amount to a metaphysical necessity. Hence, our ordinary knowledge of conceptual truths, knowledge we possess since we know what (many of) our terms semantically apply to, is a reliable epistemic source of, and hence a reliable route to, knowledge of metaphysical necessities.
45 This argument relies neither on an extravagant theory of concept possession, nor on fancy ideas about matters modal. The claim that we do possess conceptual knowledge rests on what appears to be a broad consensus in semantics, viz. that we often do know what our terms semantically apply to, since we know how we do and would apply them. And as for modal part, no one granting that: "You do not know that p if p is false", "Neighbours have neighbours", "Uncles are relatives" or "Hats are coverings of the head" express conceptual necessities goes on to wonder whether these statements may still be false at some metaphysically possible world or other—unless, that is, she suspects a somewhat hidden actuality-dependence. There thus de facto is something like a consensus that conceptual knowledge allows us to uncover metaphysical necessities.
46 Since there is no reason to think that ways to acquire modal knowledge are mutually exclusive, you still might want to explore alternative epistemic routes to modal truth. You might try to gather modal knowledge from conceivability [Yablo 1993], [Chalmers 2002], from our empirically informed ability to pass counterfactual judgment [Williamson 2007, chap. 5], or from inferences to best explanation [Biggs 2011]. But is there any need to do so, now that we know that we can rely on our ordinary conceptual knowledge? That depends on how grand your metaphysical ambitions are. If you are content with metaphysically modal insights such as the ones concerning circles, knowledge, neighbours, uncles and hats paraded above together with a posteriori
necessities such as "Water is H2 O' or "Hesperus = Phosphorus" derived from conceptual truths in tandem with empirical discoveries, you won't feel much pressure to do so. Yet
Philosophia Scientiæ, 16-2 | 2012 46
if you are a staunch believer in more ambitious metaphysical necessities such as, say, the necessity of origin or substance, or if you wish to uncover metaphysical possibilities (that aren't metaphysically necessary), I fear you will want to keep looking16
BIBLIOGRAPHY
AYER, ALFRED 1946 Language, Truth, and Logic, London: Penguin Books.
BALCERAK JACKSON, BRENDAN 2009 Understanding and semantic structure: A reply to Williamson, Proceedings of the Aristotelian Society, 109(1), 338-343.
BEALER, GEORGE 1998 A theory of concepts and concept possession, Philosophical Issues,9, 261-301. 2000 A theory of the A Priori, Pacific Philosophical Quarterly, 81(1), 1-30.
BIGGS, STEPHEN 2011 Abduction and modality, Philosophy and Phenomenological Research, 83, 283-326.
BOGHOSSIAN, PAUL 1997 Analyticity, in A Companion to the Philosophy of Language, edited by HALE,B. & WRIGHT, C., Oxford: Blackwell, 331-368. 2003 Epistemic analyticity: A defence, Grazer Philosophische Studien, 66, 15-35.
CAMERON, ROSS P. 2009 What's metaphysical about metaphysical necessity?, Philosophy and Phenomenological Research, 79(1), 1-16. 2010 The grounds of necessity, Philosophy Compass, 5/4, 348-358.
CHALMERS, DAVID 2002 Does conceivability entail possibility?, in Conceivability and Possibility, edited by GENDLER,T. S. & HAWTHORNE,J., Oxford: Clarendon Press, 145-200. 2004 Epistemic two-dimensional semantics, Philosophical Studies, 118(1-2), 153-226. 2010 The Character of Consciousness, Oxford University Press, chap. The two-dimensional argument against materialism, 141-191.
GRAYLING, ANTHONY C. 1997 An Introduction to Philosophical Logic, Oxford: Blackwell.
HALE, BOB & HOFFMANN, AVIV (EDS.) 2010 Modality. Metaphysics, Logic, and Epistemolgy, Oxford: Oxford University Press.
HANFLING, OSWALD 2000 Philosophy and Ordinary Language. The Bent and Genius of our Tongue, London: Routledge.
HORGAN, TERENCE & TIENSON, JOHN 2001 Deconstructing new wave materialism, in Physicalism and Its Discontents, edited by GILLETT,C. & LOEWER,B., Cambridge: Cambridge University Press, 307-318.
Philosophia Scientiæ, 16-2 | 2012 47
JACKSON, FRANK 1998 From Metaphysics to Ethics. A Defense of Conceptual Analysis, Oxford: Oxford University Press. 2004 Why we need A-intensions, Philosophical Studies, 118(1-2), 257-277. 2007a Reference and description from the descriptivists' corner, Philosophical Books, 48(1), 17-26. 2007b On not forgetting the epistemology of names, Grazer Philosophische Studien, 74, 239-250. 2010 Conceptual analysis for representationalists, Grazer Philosophische Studien, 81, 173-188.
KALLESTRUP, JESPER 2006 Physicalism, conceivability, and strong necessities, Synthese, 15(3), 273-295.
KNOBE, JOSHUA & NICHOLS, SHAUN 2008 Experimental Philosophy, Oxford: Oxford University Press.
KRIPKE, SAUL 1980 Naming and Necessity, Oxford: Blackwell.
LEWIS, DAVID 1972 Psychological and theoretical identifications, in Papers in Metaphysics and Epistemology, Cambridge: Cambridge University Press, 248-261, 1999. 1975 Language and languages, in Philosophical Papers I, Oxford: Oxford University Press, 163-188, 1983. 1986 On the Plurality of Worlds, Oxford: Blackwell. 1994 David Lewis—Reduction of mind, in Papers in Metaphysics and Epistemology, Cambridge: Cambridge University Press, 291-324. 1997 Naming the colours, in Papers in Metaphysics and Epistemology, Cambridge: Cambridge University Press, 332-358.
MCLEOD, STEPHEN 2005 Recent work on modal epistemology, Philosophical Books, 46(3), 235-245.
NIMTZ, CHRISTIAN 2009 Conceptual truth defended, in The A Priori and Its Role in Philosophy, edited by KOMPA,N., NIMTZ,C., &SUHM, C., Paderborn: mentis, 137-155. 2010 Philosophical thought experiments as exercises in conceptual analysis, Grazer Philosophische Studien, 81, 191-216.
PEACOCKE, CHRISTOPHER 1999 Being Known, Oxford: Clarendon Press. 2002 Precis of being known, Philosophy and Phenomenological Research, 64(3), 636-640.
PUTNAM, HILARY 1963 Mind, Language, and Reality. Philosophical Papers, Cambridge: Cambridge University Press, vol. 2, chap. The Analytic and the Synthetic, 33-69, 1975. 1975 The meaning of meaning', in Mind, Language, and Reality. Philosophical Papers, Cambridge: Cambridge University Press, vol. 2, 215-271.
ROCA-ROYES, SÒNIA 2011 Modal knowledge and counterfactual knowledge, Logique et Analyse, 54(216), 537-552.
ROSEN, GIDEON 2002 Peacocke on modality, Philosophy and Phenomenological Research, 64(3), 641-648.
SEGAL, GABRIEL 2000 A Slim Book of Narrow Content, Cambridge (Mass.): MIT Press.
Philosophia Scientiæ, 16-2 | 2012 48
SOAMES, SCOTT 2002 Beyond Rigidity. The Unfinished Semantic Agenda of 'Naming and Necessity', Oxford: Oxford University Press.
SOSA, DAVID 1998 Getting clear on the concept, Philosophical Issues, 9, 317-322. SPICER,FINN 2010 Kripke and the neo-descriptivist, Grazer Philosophische Studien, 81, 215-233.
TYE, MICHAEL 2003 A theory of phenomenal concepts, Royal Institute of Philosophy Supplement, 53, 91-105.
VAIDYA, ANAND J. 2011 The epistemology of modality, The Stanford Encyclopedia of Philosophy, edited by Zalta, E. .N. URL http://plato.stanford.edu.
WILLIAMSON, TIMOTHY 2002 Peacocke's theory of modality, Philosophy and Phenomenological Research, 64(3), 649-654. 2003 Understanding and inference, Aristotelian Society Supplement, 77(1), 249-293. 2006 Conceptual truths, Aristotelian Society Supplement, 80(1), 1-41. 2007 The Philosophy of Philosophy, Oxford: Blackwell.
YABLO, STEPHEN 1993 Is conceivability a guide to possibility?, Philosophy and Phenomenological Research, 53(1), 1-41.
NOTES
1. As I employ the term, a 'statement' is an interpreted sentence. 2. The "semantically" in "semantically applies" is of course redundant. For to say of a term 'F' that it applies to something just is to mark off one of its semantic properties. I put the 'semantically in for emphasis. 3. For the following, see also [Nimtz 2010, 200fff]. With less emphasis on language use, Jackson [Jackson 2007a], [Jackson 2010] presents a similar line. 4. I throughout employ quotation marks in lieu of Quine-quotes. 5. Here is a way to render precise what this slogan amounts to in our context: To hold that use determines meanings is to hold that the reference-determining semantic values of our terms (see [Lewis 1986, 27-55]) supervene on considered application alone. 6. Note that the idea that all terms are definable drawing on a limited stock of somehow basic terms is not part of the descriptivists' position. In fact, traditional descriptivists such as Ayer [Ayer 1946, chap. 3] or Hanfling [Hanfling 2000] clearly reject this idea. 7. See e.g., [Spicer 2010] for a Kripkean rebuttal of neo-descriptivist ideas. 8. Williamson presents the very same case in very much the same words in chapter 4 of his [Williamson 2007]. I stick to the original paper. 9. For a more elaborate development of the case presented here, see [Nimtz 2009]. See also [Balcerak Jackson 2009] for objections to Williamson's line of thought. 10. I focus throughout on one of Williamson's two examples. 11. Discussing the idea that concepts are much more finely individuated than linguistic meanings, Williamson argues that it creates methodological issues such as: to which concept does the phrase 'the concept square' refer to if the word 'square', with its usual meaning in English, is associated with different concepts in the minds of different speakers of English at one time (. . . )? [Williamson 2003, 271f]
Philosophia Scientiæ, 16-2 | 2012 49
But the claim is that meaning can cut finer than shared natural language, not that it must cut finer. 12. See [Segal 2000, 76-83] for an argument along these lines. 13. May, but need not. For many actuality-dependent sentences it holds true that if they are conceptually necessary, they are metaphysically necessary. Consider e.g., 'Water is the actual watery stuff of our acquaintance" or "One meter is the actual length of the standard meter at to." 14. Here 'PHYS' abbreviates a statement that reports all actual (micro-) physical facts and 'PHEN' abbreviates a statement that reports all actual phenomenal facts. 15. See [Horgan & Tienson 2001] for a general argument against these views. 16. I am indebted to two unknown referees for Philosophia Scientix, as well as to Peter Schulte. Their criticism has helped me to substantially improve on the initial draft of this article. I would also like to thank the participants at the 2010 Nancy conference on "Modality—Semantics and Epistemology" where I first presented the material for many valuable comments.
ABSTRACTS
I argue that there is a reliable epistemic route from knowledge of conceptual truths to knowledge of metaphysical necessities. In a first step, I argue that we possess knowledge of conceptual truths since we know what (many of) our terms apply to. I bolster this line of thought with a rebuttal of Williamson's recent argument against epistemic analyticity. In a second step, I argue that our knowledge of conceptual truths allows us to reliably attain knowledge of metaphysical necessities. Either this knowledge straightforwardly yields knowledge of metaphysical necessities. Or it is such that we can by armchair semantic reflection discover that it fails to do so. I conclude that conceptual knowledge provides a safe route to modal knowledge.
Dans mon article, je soutiens qu'il existe une voie epistemique fiable qui mène de la connaissance des verités conceptuelles a celle des nécessites métaphysiques. Dans un premier temps, je montre que nous pouvons prétendre connaitre des vérites conceptuelles dans la mesure ou nous savons à quelles conditions nos termes (ou du moins un grand nombre d'entre eux) s'appliquent. Je défends notamment cette idée face a un argument récent que Williamson adresse a la conception épistémique de l'analyticite. Dans un second temps, je montre que notre connaissance des vérités conceptuelles constitue un moyen fiable de connaitre des nécessités métaphysiques. En effet, de deux choses l'une : ou bien la connaissance conceptuelle conduit directement a la connaissance de nécessités métaphysiques ; ou bien, lorsque ce n'est pas le cas, nous pouvons du moins savoir qu'une telle inférence n'est pas permise, en vertu d une réflexion purement sémantique, « depuis notre fauteuil» (armchair). J'en conclus que la connaissance conceptuelle constitue un moyen sur d'acquérir des connaissances modales.
AUTHOR
CHRISTIAN NIMTZ Bielefeld University (Germany)
Philosophia Scientiæ, 16-2 | 2012 50
A Two-Dimensional Semantics for Epistemic Modals
Dan Quattrone
This is highly counterintuitive. I offer a new account of modality that is capable of representing what I call EPMIs: epistemically possible metaphysical impossibilities.
Sentences like: "Water might not be H2O" and "Hesperus might not be Phosphorus" are examples of EPMIs, and others can be readily found (including many that do not rely on Kripkean considerations about metaphysical possibility). My account explains the existence of EPMIs while retaining the versatility and explanatory power of the standard accounts.
1 A motivational example
Alice and Bob are talking about water. They know that water is the clear liquid typically found in lakes and rivers. They know that (pure) water is clear, tasteless, and odorless.
However, when asked: "Is water H2O?," both of them reply "I don’t know." Alice says: "For all we know, water might be XYZ." Bob agrees. Given what Alice and Bob know, it seems like Alice has said something true. Alice’s statement is an example of an epistemic modal. On the traditional account of epistemic modals, we would say that Alice’s sentence expresses the following proposition: 1 1) ◊E(Water is XYZ).
The question arises: how should we interpret the ◊E operator? Standard accounts of modality treat all modal operators as quantifiers over some space of possible worlds. Metaphysical possibility and necessity are standardly represented by quantifying over 2 all possible worlds. Statements of the form ◊Mp are trueiff thereis some world in which p is true; statements of the form □Mp are true iff p is true in every possible world. Other kinds of possibility—such as epistemic or deontic possibility—have been analyzed by restricting the space of possibility. For instance, on the standard account of epistemic possibility, the ◊E operator quantifies over only those worlds consistent with our knowledge. That is, we look at all possible worlds when we evaluate metaphysical modals, but only some of the worlds (those consistent with what we know) when we
Philosophia Scientiæ, 16-2 | 2012 51
evaluate epistemic modals. The truth conditions for epistemic modals on this kind of view look like this:
• Statements of the form ◊E p are true iff there is some world consistent with our knowledge in which p is true.
• Statements of the form □Ep are true iff p is true at all worlds consistent with our knowledge. But now we have a problem. Assume for the moment that Kripke and Putnam are correct about the semantics for "water" and other natural kind terms, as described in [Kripke 1980] and [Putnam 1996].3 On their view, natural kind terms like "water" are rigid designators—that is, terms which denote the same object or class of objects in any possible world. If "water" is a rigid designator and it denotes H2O in this world, then it denotes H2O everywhere. Kripke and Putnam argue further that the fact that names and natural kind terms function as rigid designators entails that identity statements of the form "water is H2O" express necessary truths, because "water" denotes H2O in all possible worlds, and "H2O is H2O" is a necessary truth. This is the necessity of identity, and if we have necessity of identity and "Water is H2O" is an identity statement, then
"Water is H2O" will express a necessary truth. I will not detail the arguments advanced in favor of semantic externalism or the arguments for necessity of identity. The main reason for this is that I aim to present an account of epistemic possibility that is consistent with semantic externalism and necessity of identity, and as such will not challenge the central claims of the position. For my purposes, then, the arguments can be assumed to stand. Note, though, that while I do not aim to refute semantic externalism, I am not committed to its being true. Moreover, the problem I identify can arise independently; for instance, in [Johnston
1997], Mark Johnston argues that sentences like: "Water is H2O" are not identity statements but nonetheless express necessary truths about material constitution.
Given this assumption, the standard account of epistemic modals says that ◊E (Water is XYZ) is true if there is an accessible (metaphysically) possible world w such that: 1. w is consistent with Alice and Bob’s knowledge 2. in w, water is XYZ. But Kripke and Putnam’s arguments for semantic externalism (and necessity of identity in particular) show that water is necessarily H2O, and hence we will find that there are no worlds in which water is XYZ. If there are no worlds in which water is XYZ, then we will have to conclude that Alice said something false in saying: "For all we know, water might be XYZ." But we want to say that Alice said something true. Intuitively, then, it seems that Alice’s statement expresses an epistemically possible metaphysical impossibility, or an EPMI for short. Standard accounts of modality (such as those given in [Kratzer 1977] and [Portner 2009]) treat epistemic possibility as a restricted sort of metaphysical possibility and hence predict that there will be no EPMIs. But cases like Alice’s suggest this prediction is false. If we want to resolve this problem, it seems clear that we have to say that Alice’s sentence doesn’t just express 1) above. I want to suggest that Alice’s sentence is instead associated with a metaproposition, and that it is this metaproposition which is epistemically possible. Intuitively, a metaproposition is supposed to represent something like a Kaplanian character. Sentences with indexicals can express different propositions in different contexts, and the relation between the indexical and its contribution to the proposition expressed is
Philosophia Scientiæ, 16-2 | 2012 52
captured by the indexical’s character. In the same way, the metaproposition is intended to capture the relation between the world in which a sentence is produced and the proposition it expresses. Formally, metapropositions are functions from a world win which an expression is produced (the worlds of production) to the propositions expressed by that utterance when produced in w. On this account, Alice’s sentence expresses a truth if there is a world w in which she could utter the same sentence and have it express a proposition which would be true when evaluated in w.4 It seems reasonable to suppose that there are such worlds. Twin Earth is one of them; as Putnam describes the scenario, "water" picks out something XYZ when used by a Twin Earth native. If this is correct, the sentence: "Water is XYZ" expresses a different proposition when produced on Twin Earth than it does when produced here. In fact, the proposition it expresses when produced on Twin Earth (roughly, that XYZ is XYZ) is a necessary truth. So if the sentence: "Water is XYZ" is produced on Twin Earth, it expresses a proposition which is true when evaluated in Twin Earth, and hence Alice’s original sentence ("Water might be XYZ") expresses a truth here on the actual world.w
2 The problem with EPMIs
In the preceding section, I used: "Water might be XYZ" as an example of an EPMI. This example relies on certain claims about the semantics of natural kind terms. Kripke and Putnam advance similar claims about the semantics of names, and as a result we can expect the problem of EPMIs to arise for them if Kripke and Putnam are right. Furthermore, we can find examples of EPMIs that do not rely on their (perhaps controversial) semantic claims. One possible example (Johnston’s claim that: "Water is
H2O" expresses a necessary truth about material constitution) was given above; there are others. For example, there are likely to be sentences which are either necessary or impossible and whose truth value is independent of our knowledge. Let us call such sentences unknown non-contingent sentences. Some statements of metaphysical necessity and possibility might be unknown non-contingent sentences. To borrow an example from Quine, consider the sentence: "It is metaphysically possible for something without extension to be colored." If we do not know the truth of this sentence, then it is an unknown non-contingent sentence (assuming the truth of the principles of the modal logic S5). If it’s false, it is presumably an EPMI. Sentences regarding de re necessary properties of objects can also be unknown non- contingent sentences, if we don’t know whether or not the object in question has the property under consideration. For example, suppose that Alice, a painter, is about to display her newest work. No one but Alice has seen the work, which is named "Figure 1." It is known, though, that Figure 1 depicts a plane figure—in fact, it either depicts a square or a circle. We do not know whether Figure 1 is a square or a circle. If Figure 1 is a square, it is necessarily four-sided.5 And so "Figure 1 is four-sided" is an unknown non-contingent sentence. Suppose there is at least one unknown non-contingent sentence. If that sentence is true, then it is metaphysically necessary but it might well be epistemically contingent. If it is false, then it is metaphysically impossible but it might well be epistemically contingent, in which case it could be an EPMI. In either
Philosophia Scientiæ, 16-2 | 2012 53
case, the problem I have outlined in this section for most extant accounts of epistemic modality arises. Once we have examples of EPMIs in hand, it is fairly easy to see why traditional accounts of epistemic modality cannot adequately account for them. On the traditional account, epistemic possibility is taken to be a restricted sort of metaphysical possibility. That is, if something is metaphysically impossible, it must be epistemically impossible as well. This is because the traditional account takes metaphysical impossibility to be falsehood in all possible worlds and takes epistemic possibility to be truth in some possible world consistent with some knowledge base. If there are no worlds in which a given statement s is true, then we will not find any worlds consistent with any given knowledge base in which s is true. To resolve this problem, we have to have an account of epistemic modality that takes epistemic possibility to be something other than a restricted sort of metaphysical possibility. The metapropositional account that I offer does just that.
3 The metapropositional account
Many semantic theories index truth to worlds. On such theories, truth is understood as relative to a world. Consider, for example, the sentence: "Grass is green." In ordinary English, this sentence expresses the proposition that grass is green. That proposition is true in some worlds and false in others. We might represent the worlds in which this proposition is true graphically like so:
w u v
w T F T
In this representation, w is our world; u and v are other worlds. As the table shows, in u, grass is not green, but in v it is. We could in principle extend the table indefinitely to include all the possible worlds, and having done so we would be in a position to say for any world whether or not grass is green in that world. Views in which truth is indexed to a single world are one-dimensional views. My proposal is to adopt a version of the two-dimensional semantic framework. In a two- dimensional theory, truth is indexed to pairs of worlds, represented graphically by a two-dimensional array with worlds along both axes. There are many ways of interpreting this array. I offer the following interpretation: expressions are associated with a metaproposition, which is represented by the two-dimensional array. This array encodes information about how the proposition expressed by the expression depends on the world in which the expression is produced; intuitively, it represents something like a Kaplanian character. The worlds of production lie on the vertical axis of the array; the horizontal axis represents the worlds at which the expression is evaluated. Each row of the array thus represents the proposition expressed by the expression when it is produced in the corresponding world. Consider the sentence: "Grass is green" once again. In our world, this sentence (when uttered in ordinary English) expresses the proposition that grass is green. But we can imagine worlds in which the sentence: "Grass is green" expresses a different proposition because "grass" refers to some other substance. Let us stipulate that x and y
Philosophia Scientiæ, 16-2 | 2012 54
are worlds in which "Grass is green" expresses a different proposition than it does here. We can represent this using a two-dimensional array, like so:
w u v
w T F T
x F F T
y F F F
This array tells us that, when produced in x, the sentence: "Grass is green" expresses a proposition which is true in y but false in w and x. And when it is produced in y it expresses a necessary falsehood. On my view, if I say: "Water might be XYZ," I have said something true if there is a world w in which three conditions are met. First, the sentence: "Water is XYZ" has the same basic content6 in w as it does in the actual world. Second, w is consistent with what my audience and I know. Finally, utterances of: "Water is XYZ" express a true proposition when produced in w.
3.1 The formal machinery
On my theory, each expression is associated with a metaproposition, which is a function from worlds in which the expression is produced (or worlds of production and abbreviated WP) to propositions. Propositions are functions from worlds of evaluation
(abbreviated WE)to truth values. WP includes only those worlds in which expressions have the same basic content (in the sense given later) as they do in the actual world. WE is the set of all worlds. WP is thus a subset of WE. We can represent the metaproposition using a two-dimensional array with the worlds in WP along the vertical axis and the worlds in WE along the horizontal. When we adopt this approach, the entire array represents the metaproposition. Each row represents the proposition expressed by the 7 expression when produced in the corresponding world in WP.
All expressions are evaluated at a pair of worlds (wi, w2), where wi represents the world of production and w2 represents the world of evaluation. A sentence s is true at (w1, w2)iff w2 verifies s when s is produced at w1 .We can initially define the modal operators as follows:
• ◊Ms is true at (w1, w2) when associated with the metapropositionf (w) iff there is some world of
evaluation v such that f (w1 )is true at v.
• ◊Es is true at (w1, w2) when associated with the metaproposition f (w) iff there is some world of evaluation u such that f(u)istrueatu.
The necessity operators are defined in the traditional way. That is, □Es is true iff ¬◊E ¬s is true. The same relationship holds between □M and ◊M .Given these truth definitions, we can see that a sentence s is metaphysically possible when produced at w iff there is some point along the relevant horizontal row at which s is true. s is epistemically possible iff there is some point along the diagonal at which s is true. s will be metaphysically necessary when produced at w if s is true at every point along the
Philosophia Scientiæ, 16-2 | 2012 55
relevant horizontal row. Finally, s will be epistemically necessary iff s is true at every point along the diagonal (subject to a few restrictions, described below). Again, we can represent this graphically. Consider "Water might be XYZ." Let us stipulate that w is our world. x is a world that is qualitatively indistinguishable from our world, but it completely lacks H2O. Wherever H2O is found in our world, we instead find XYZ in x. y can be any other world. My claim is that: "Water might be XYZ" is an EPMI, which means that the embedded non-modal sentence: "Water is XYZ" is epistemically possible but metaphysically impossible. Here is what that will look like:
w u v
w F F F
x T T T
y F F F
When the sentence: "Water is XYZ" is produced in our world (that is, in w), it expresses a necessary falsehood—namely, that H2O is XYZ. This accounts for the "metaphysically impossible" portion of the EPMI designation. In x,the sentence produces a different proposition. When an inhabitant of x says: "Water is XYZ," she expresses a necessary truth—that XYZ is XYZ. In particular, the proposition expressed when "Water is XYZ" is uttered in x is true when evaluated at x (as the center point of the array represents). So, by the definition given above, "Water is XYZ" is epistemically possible. That said, the truth definitions given above will not quite capture the behavior of actual epistemic modals. To do that we need to recognize two further constraints. First, we have the basic content constraint: Wp includes only those worlds in which expressions retain the same basic content. "Basic content" is a technical notion; I will introduce it in more detail in §3.3. For now, it suffices to say that the basic content of an expression in a given language determines the intension of the expression at every world of production, where intensions are understood in the traditional way as functions from worlds (of evaluation, in this case) to extensions.8 Holding basic content fixed means we only look at those worlds of production in which the function from world of production to intension is the same as it is here. The second constraint is that the only worlds we need to examine when evaluating epistemic modals are those that are consistent with what is known. We introduce this constraint to capture the epistemic nature of epistemic modals. We restrict Wp to those worlds consistent with what is known. How is this restriction to be understood? Often, this is done by taking what is known to be a set of propositions, each of which is or determines a set of worlds. The intersection of these sets of worlds is the knowledge base. We will adopt this approach.9 The claim that knowledge is propositional in this way is consistent with the claim that propositions are not the object of epistemic modal operators.10 Ultimately, the semantic machinery that I deploy to address epistemic modals does not depend on any particular characterization of knowledge beyond its functional aspect. As long as what is known (whatever it is) determines a set of worlds which can function as a knowledge base, my account should be fine.
Philosophia Scientiæ, 16-2 | 2012 56
With the notions of basic content and the knowledge base in hand, we can revise the truth definition for the epistemic possibility operator like so:
- ◊Es is true at (w1, w2) when associated with the metaproposition f (w)iff there is some world of evaluation u such that 1) f (u) is true at u without change in basic content and 2) u is in the knowledge base. Again, the epistemic necessity operator is defined in the traditional way.
3.1.1 The machinery in action
To see how the proposal developed in the previous subsection functions, I will present two sample cases. For simplicity, the knowledge base will be shared by all members of the conversation in both cases. Case 1: Where’s Carol? Alice and Bob are in Washington, DC wondering where their friend Carol is. Carol is in fact in Zurich, but neither Alice nor Bob know this; in fact, all they know is that she is not in Washington. Alice says to Bob: "Carol might be in Cleveland." On my account, Alice has said something true iff there is a world w such that 1) the English sentence: "Carol is in Cleveland" expresses a proposition which is true when evaluated in w and 2) w is in the knowledge base. The knowledge base in this case consists in those worlds in which Carol is not in Washington.11 There is indeed such a world: namely, the world in which Carol is in Cleveland. So Alice has said something true. Case 2: Who’s Carol? Alice and Bob have noticed that their mutual friends Carol and Eve are never seen together. Alice has begun to suspect that Carol and Eve might in fact be the same person. She approaches Bob and voices her suspicion, saying: "Carol might be Eve." Here is what Alice and Bob know about Carol: Carol has red hair. Carol is short. Carol works at the bank. Here is what Alice and Bob know about Eve: Eve has red hair. Eve is short. Eve works for the federal government. Eve looks very much like Carol. Let us stipulate that Carol and Eve, despite their similar appearance, are different people. Then (given that identity and distinctness are necessary), it is necessarily false that Carol is Eve. Nonetheless it seems like Alice has said something true, so we seem to have an EPMI. On my account, in order for Alice to have said something true, there must be a world w such that 1) the English sentence: "Carol is Eve" expresses a proposition which is true when evaluated in w and 2) w is in the knowledge base. This time, the knowledge base will include those worlds in which Alice and Bob 1) have a friend who is a short person with red hair who works at a bank and answers to "Carol," and 2) have a friend who is a short person with red hair who works for the federal government and answers to "Eve." These people need not be distinct. So the world in which the person who answers to "Carol" is also the person who answers to "Eve" is the world in which "Carol is Eve" expresses a true proposition, and hence Alice has said something true. It is important to note that this world is not a world in which Carol is Eve. Rather, it is a world in which at least one of the names "Carol" and "Eve" denote someone other than Carol and/or Eve and hence the expression: "Carol is Eve" expresses a different proposition, though its basic content is unchanged. Case 3: Could Carol be a Cylon? Alice and Bob are philosophers. They wonder if their mutual friend Carol has any necessary properties. In particular, they wonder if Carol must be made of matter. Alice says: "For all we know, it might be that Carol might have
Philosophia Scientiæ, 16-2 | 2012 57
been an artificial biological life form." Let us stipulate that the outermost modal in this case is epistemic, but the innermost modal is metaphysical. Let us further suppose that Carol must not be an artifical being but Alice and Bob do not know this to be the case. On my theory, Alice has said something true if there is a world of production in the knowledge base in which "Carol might have been an artificial biological life form" expresses a true proposition. Since Carol is not an artificial biological life form, and Alice and Bob know this, we must look for a world w in which "Carol" denotes an object which is not an artificial biological life form in w but in which "Carol is not a artificial biological life form" does not express a necessary truth. Here, we will run into difficulties. We require "Carol" to have the same basic content in w as it does in the actual world. Since "Carol" is a rigid designator in the actual world, it will have to be a rigid designator in w as well (though it may not designate the same object in w as it does in the actual world). This means that we will not find a world in WP that has the required properties and that Alice is mistaken in saying that it might be that Carol might have been an artificial being, despite the fact that Alice doesn’t know whether or not she might have been an artifical being. This may seem counterintuitive, but in fact this result is what we should expect. First, it is important to note that one traditional gloss for epistemic possibility is problematic. Traditionally, the statement: "s is epistemically possible for some agent A" is taken to mean something like: "A doesn’t know that not-s." This rendering entails that s is epistemically necessary iff s is known. However, epistemic necessity and knowledge have different properties and obtain in different circumstances. For instance, if the epistemic necessity operator is defined as a quantifier over points of evaluation (including worlds in a one-dimensional approach and pairs of worlds for the two- dimensional approach) that uses Kripke models, then epistemic necessity will be closed under entailment [Hintikka 1962]. Knowledge, on the other hand, is not.12 Often, the problems involved with identifying knowledge with epistemic necessity are addressed by treating epistemic necessity as an idealization of knowledge—say, as knowledge for ideal reasoners or some such. I have a different strategy. Rather than treat epistemic necessity as an idealization of knowledge, I offer a different (and, I think, superior) intuitive rendering of epistemic necessity. My proposal is to intuitively treat epistemic necessity as follows: s is epistemically necessary for A iff s is known or is entailed by what is known by A. s is known by A if A knows the proposition expressed by s in the actual world. This entails that s is epistemically possible for A iff not-s is not logically entailed by what A knows, or equivalently that s is consistent with what A knows.13 One reason to prefer my approach is that it permits us to treat epistemic necessity as an independent object of study with interesting connections to knowledge without requiring us to adopt a rarefied conception of knowledge itself. Furthermore, my preferred gloss on epistemic possibility is itself a fairly common gloss on epistemic possibility, but the fact that it is not equivalent to the other traditional interpretation given above has not been widely discussed. So there is precedent for adopting my intuitive rendering of epistemic modals. It is important to note that this is just an intuitive gloss on epistemic modality, and any formal account may deviate from the intuitive notion at various points. This is to be expected and perhaps even desired. After all, if we had perfectly clear intuitions on epistemic modality we might not need an explicit analysis, and we likely wouldn’t find any hard cases where it is unclear whether or not a given expression is epistemically possible or necessary.
Philosophia Scientiæ, 16-2 | 2012 58
Moreover, in investigating our intuitions regarding epistemic modality we might find that they are confused and contradictory; in this case no consistent theory will adequately capture all our intuitions, but we should not want such a theory. My formal account of epistemic modality is intended to stick close to the second, superior intuitive gloss given above, but the theory may not capture the intuitive gloss completely. Cases where the theory and the intuitive notion come apart should be noted but in general, one should not assume that any individual case not covered by the theory should refute it. When we understand epistemic necessity and possibility in this way, we can see that it is not consistent with Alice’s knowledge that Carol might have been an artificial being. Alice knows that Carol is a natural being, and this entails that it is metaphysically necessary that Carol is natural (assuming that Kripkean views of metaphysical necessity are correct). Hence it is epistemically necessary for Alice that Carol is necessarily natural. It is instructive to contrast this with the case in which Alice doesn’t know whether or not water is H2Oand says: "For all we know, water might be XYZ." "Water" is still a rigid designator in this scenario, and it is a rigid designator in every world in Wp. However, the crucial difference here is that Alice doesn’t know that water is H2O, and so even though it is metaphysically necessary that water is H2O, this is not logically entailed by herknowledge. We will see the same result if we consider the case in which Alice doesn’t know if Carol is natural or not, and says: "For all we know, Carol might be artificial." It is the nested metaphysical modal that leads to the seemingly counterintuitive result. In this case, "For all we know, it might be that Carol might have been an artificial biological life form," looks like an EPMI, but it is not. Alice and Bob know that Carol is a natural being, and hence "Carol is a natural being" is epistemically necessary for them given the interpretation of epistemic necessity given above. There is a peculiar feature of the sentence: "Carol is a natural being" that deserves further attention. Given that Carol is a natural being, it follows from the basic content of the sentence that it is metaphysically necessary that Carol is a natural being. Since we hold basic content fixed, there is no way for the sentence to produce a contingent proposition in any world of production (though it could produce a necessarily true proposition or a necessarily false proposition). There are other counterintuitive cases that warrant some analysis. Consider the following example: "For all Andrew Wiles knew in 1992, Fermat’s theorem might have been false."14 This might strike us as true, but given the understanding of epistemic necessity and possibility given above (and given certain plausible assumptions about Wiles’ knowledge), we should expect this sentence to be false. Fermat’s theorem is presumably a necessary truth, and while Wiles did not know that Fermat’s theorem was true in 1992, it was likely a consequence of facts that he did know, as Wiles had been working on the proof for years. So we should expect that Fermat’s theorem was in fact epistemically necessary for Wiles in 1992. It might be thought that this interpretation of epistemic necessity and possibility breaks the connection between these technical notions and the English words used to express them, such as "might" and "must." This is not the case. Notice that we intuitively judge the sentence: "Given what Wiles knew in 1992, Fermat’s theorem must have been true" to be true, as predicted by my preferred intuitive gloss of epistemic possibility. A natural reading of this sentence is that it is true if Fermat’s theorem is a
Philosophia Scientiæ, 16-2 | 2012 59
consequence of Wiles’s knowledge in 1992. So our intuitions seem to be inconsistent here. Any systematic approach to epistemic modality will thus run into counterintuitive cases. We get similar results with unknown truths of mathematics. It is likely that no one currently knows whether or not the Riemann hypothesis is true. As such, we might think that the Riemann hypothesis and its negation are both epistemically possible for everyone. But this will only be true on one of the two intuitive interpretations of epistemic possibility. On the interpretation I favor, if the Riemann hypothesis is a consequence of what is known, then it is epistemically necessary even though its truth value is unknown. Similarly, if its negation is a consequence of what is known, then it is epistemically impossible even though its truth value is unknown.
3.2 The metapropositional account in context
My theory is in many ways analogous to Kaplan’s account of indexicals in [Kaplan 1989]. On Kaplan’s account, all utterances occur within a context of utterance and are evaluated with respect to a circumstance of evaluation. This context includes (at least) the speaker, the audience, and the time and place of utterance. Kaplan also maintains that all utterances have a character, which is a function from contexts of utterance to intensions. For many terms, this character returns the same intension regardless of context of utterance. Indexicals are unusual in that they have different intensions in different contexts of utterance; for example, the intension of the word "I" (in its normal use) depends on the identity of the speaker. Given this account, we can take the world in which the utterance was produced to be part of the context of utterance. Names and natural kind terms in my account function like indexicals do in Kaplan’s account,15 except they are not (typically) sensitive to the common contextual variations like changes in the speaker’s identity, the time of utterance, and so on. Rather, they are sensitive to changes in the world of production. Since we cannot change which world we’re in, we can’t normally change the index for the world of production, and hence the interpretation of names and natural kind terms does not vary due to variations in the world of production index. However, when embedded under an epistemic modal, we evaluate the name or natural kind term in the embedded expression as though it was produced in another world. This makes the epistemic "might" and "must" into something like what Kaplan calls monsters (and Evans calls context-shifting operators). Monsters are operators that manipulate one of the indices for the context of utterance rather than the circumstance of evaluation. Most operators are not monstrous; for example, "someday" is a non-monstrous operator. A sentence like: "Someday I will be rich" is true (very roughly) if there is a future time in which I am rich. So in this case, we go looking for a circumstance in which I, Dan Quattrone, am rich, and hence in which the sentence: "I am rich" comes out true when uttered by me. However, note that the indexical "I" in "I am rich" still refers to the original speaker. If I say: "Someday, I will be rich," the sentence will not be true if there is a time in which another person could truly utter the sentence: "I am rich." This is what distinguishes monsters from non-monsters. Monsters affect the index for the context of utterance and in so doing affect the value of indexicals. Kaplan argues that there are no monsters in English and we could not add any to the language. His argument fails. Kaplan’s argument proceeds as follows: if there is any
Philosophia Scientiæ, 16-2 | 2012 60
English expression that functions as a monster, it would be an expression like: "In another context…" But consider the sentence: "In another context, I am tall." Intuitively, we understand this sentence to be true if there is a context in which I would be judged to be tall. But if "In another context…" was truly a monster, then we should expect "In another context, I am tall" to come out true if there is a context containing a tall speaker, who need not be me. That is, most speakers would not judge "In another context, I am tall" to be true because there is a context in which "I am tall" is uttered by Robert Wadlow.16 We might think that, while "In another context…" does not shift the speaker index, it does shift some other feature of the context. I am in fact of roughly average height for an adult male, but I am tall compared to the average height of a child. If I were to say: "In another context, I am tall," we might judge it to be true because "tall" is itself context-sensitive (though it is a gradable adjective rather than an indexical), and because there are contexts in which the relevant height standard is different. However, the shift here is actually part of the circumstance of evaluation. We can see this by considering cases where there is a large gap between context of utterance and circumstance of evaluation. Suppose I record myself saying: "I am tall." We stipulate that the relevant standard for height at the time I initially make the recording is such that I count as tall. Years later, average heights have increased, and with it the standards for tallness. The recording is played in this situation. Intuitively, we would judge my utterance to be false when we hear it. This suggests that "tall" is (at least on some occasions; see below for more discussion) sensitive to features of the circumstance of evaluation rather than features of the context of utterance. So "In another context…" is not a monster. But if "In another context…" is not a monster, then surely nothing else could be. I agree with Kaplan that "In another context…" and expressions like it are, at least initially, the most plausible candidates for monsterhood in English. I also agree that such expressions are not monstrous. However, it does not follow that there are no monsters in English. First, note that Kaplan’s argument is an inductive argument with a very small initial sample, and so needs further support. Second, and more importantly, there is empirical evidence suggesting that English does contain monsters. In [Schlenker 2003] Philippe Schlenker has argued that expressions like: "two days ago" and "in two days" display monstrous behavior, i.e. shift the context index. Consider the following example (a modification of one of Schlenker’s examples): Bob met Alice exactly one year ago. In two days, she would be dead. The indexical phrase "in two days" in the second sentence can be heard as referring to two days after Bob met Alice. However, the context of utterance is one year after Bob met Alice. If Kaplan were right and there were no monsters in English, it should be impossible to hear the phrase "in two days" as referring to anything but two days from the time of utterance. Similar phenomena occur when we translate these expressions into French, which lends credence to the notion that these phenomena are not peculiar to English. Schlenker also shows that the first-person pronoun can function monstrously in other languages. In particular, he shows that the first-person pronoun in Amharic can pick out persons other than the speaker in disquotational contexts, which suggests that the operators that signal disquotation (e.g. "he said") can act as monsters in Amharic. So the Amharic sentence that would be lexically translated as: "Alice said I am hungry" would be better read as: "Alice said she is hungry." This gives us evidence for monsters
Philosophia Scientiæ, 16-2 | 2012 61
in other languages, which makes the hypothesis that English has monsters of its own more plausible. Consider another example:17 Scenario: There is a picture of Superman hanging on the wall. Lex Luthor comes in and places a placard next to the sign reading: "I am Clark Kent." In this scenario, Luthor is the person producing the sentence: "I am Clark Kent." If Kaplan is right and there are no monsters in English, then we should expect that the "I" in "I am Clark Kent" to pick out Luthor. But that is not what happens. Instead, we have a case where Luthor can put words in Superman’s mouth (as it were), and we hear the "I" as referring to Superman and not to the person who actually produced the expression. This case is unusual in that there is no explicit operator which causes the context index to shift; that said, the indexical is still behaving as though it were governed by a monster, which suggests that such behavior can be observed when there are explicit operators as well. Finally, let us return to the case of "tall." We have seen that "tall" is sometimes sensitive to features of the circumstances of evaluation rather than the context of utterance. But that does not show that it is entirely insensitive to features of the context of utterance. Consider, for example, the following examples:18 - Had I taken human growth hormone, I would have been tall. - Had I lived among the Kalahari Bushmen, I would have been tall. Both of these sentences seem, intuitively, to be true, but for different reasons. In the first case, the sentence is true using the ordinary standards for tallness. But in the second case, the standards for tallness seem to shift; rather than use the standards for early 21st-century Americans, we adopt the standards appropriate for the Kalahari bushmen. This seems to be monstrous behavior. Taken together, what these examples show is that while there are English expressions which we would expect to be monsters but are non-monstrous, there are also cases in which English indexicals behave as though they are governed by a monstrous operator. Admittedly, this does not show that epistemic modals are monsters; however, it does show that the hypothesis is not to be dismissed. Moreover, recent work by Paolo Santorio [Santorio 2011] offers direct support for the thesis. Further theoretical support is found in Brian Rabern’s [Rabern s. d.], wherein he argues (among other things) that Kaplan’s own account of demonstratives includes monsters. Given that the hypothesis is consistent with the available evidence and offers considerable explanatory power, we should at least tentatively accept it as (likely to be) true.
3.3 Basic content
One constraint on the theory developed above is that Wp includes only those worlds in which words have the same basic content as they have in the actual world. In this section I will briefly discuss this constraint and present some reasons for thinking it plausible that there is such a thing as basic content in the relevant sense. Basic content determines an expression’s intension at every world of production. We can think of it as a function from worlds of production to intensions, and intensions as functions from worlds of evaluation to extensions. We make use of this concept because we do not want epistemic possibility claims for a metaproposition p to depend on what the sentence expressing p says in some other language or under unusual linguistic
Philosophia Scientiæ, 16-2 | 2012 62
conventions. At the same time, the basic content of a term cannot include the term’s extension. On the metapropositional view, the intension of a term (and, a fortiori its extension) depends on the world in which it is produced. Since epistemic modals behave like monsters and (effectively) change the index for the world of production, it follows that terms embedded in an epistemic modal can have different extensions than they normally have. Since the basic content of a term is always held fixed (even when embedded in an epistemic modal), and the extension can sometimes vary, basic contents cannot include or be identified with extensions. This constitutes a break with some semantic externalists, notably Kripke, who argues that the semantic content of a name or natural kind term is exhausted by its reference. My claim is that names and natural kind terms (and, in fact, almost all terms) have some semantic content (where "semantic content" is broadly construed) beyond their reference. Putnam’s externalism (at least as described in [Putnam 1996]) is prima facie compatible with this notion of basic content, since Putnam allows for semantic contents other than reference. The notion of basic content is fairly intuitive. In Putnam’s original Twin Earth thought experiment, we might notice that if Oscar and his twin switched places, such that Oscar was on Twin Earth and his duplicate was on Earth, neither Oscar nor his twin would have trouble navigating their new worlds. If a Twin Earth native were to say to Oscar: "Please bring me a glass of water," Oscar would be able to satisfy this request, even though he might think he’s providing a glass of H2O. Twin Earth natives interacting with Oscar would judge him a competent user of the language. However, if Oscar were transported to a world in which "water" denoted gasoline, he might not be so fortunate. Suppose that the world Oscar finds himself on is chemically identical to Earth. However, in this world, "water" denotes gasoline and another word denotes H2O (and XYZ is nowhere to be found). Call this world Gas Earth. If a Gas Earth native were to say to Oscar: "Please bring me a glass of water," Oscar would not be able to satisfy the request (at least not until he became assimilated to the peculiar linguistic practices of Gas Earth). Oscar’s linguistic behaviors will be judged by Gas Earth natives to be incorrect, and Oscar may have the same to say about the linguistic practices on Gas Earth. The upshot of this is that there are behavioral similarities shared by the linguistic communities on Earth and on Twin Earth, but which neither of them share with the linguistic community on Gas Earth. Basic content is supposed to be the explanation for these behavioral patterns. My suggestion is that the word "water" has the same basic content on Earth as it does on Twin Earth, but not as it does on Gas Earth. Very roughly, I take the basic content of an expression to be those facts that are such that anyone who didn’t know them would be judged not to understand the expression. For example, if someone did not know that water is a liquid under normal conditions, we might very well think that they don’t know what "water" means, and as such lacks the basic content associated with "water." This rough characterization might seem to give rise to a problem. Consider sentences like: "Some bachelors might be married" or "Some attorneys might not be lawyers." In both cases, we might envision a situation where someone utters a sentence like this and believes that they have said something true. But on my view, "Some attorneys might not be lawyers" can only express a truth if "attorney" and "lawyer" have different basic contents. But if the basic content of an expression is the facts that we’d say someone
Philosophia Scientiæ, 16-2 | 2012 63
needs to know in order to understand the expression, then it seems likely that "attorney" and "lawyer" have the same basic content. Similarly, it seems likely that the basic content of "bachelor" includes the fact that bachelors are unmarried. This issue generalizes, as well; the examples above can be multiplied fairly easily. But this is only a problem if someone can say: "Some attorneys might not be lawyers" (or whatever example is chosen) and have it actually express a truth. To be sure, the speaker might think they have said something true, and their audience might agree— but that doesn’t mean they’re right. The only cases I can imagine where the speaker or the audience might judge the sentence to be true are cases where the speaker or the audience doesn’t understand the words "lawyer" or "attorney." The same goes for "Some bachelors might be married." In general, I would suggest that these are cases of linguistic confusion and do not weigh against my theory. I would also note that we can be mistaken about whether or not something is epistemically possible, and that mistakes in this arena can come from many different sources. There may be things we do not know we know, for instance, which may constrain our epistemic possibilities. And there may be things we think we know but which are in fact false (and hence not known). It does not seem strange to add linguistic confusions as another source of error here.
4 Chalmers’s alternative
There are other approaches to the issue of epistemic possibility that use the two- dimensional framework. The most prominent defender of two-dimensionalism in this area is David Chalmers, and so this section will focus on his account, developed primarily in [Chalmers 2006]. At the outset, it is important to note that while Chalmers’s project does involve epistemic modality, he is also interested in validating what he calls the "Core Thesis." On Chalmers’s view, a sentence S has two intensions, called 1-intensions and 2- intensions, respectively. The nature of these intensions will be explained shortly. Chalmers seeks to show that the following is true: Core Thesis: For any sentence S, S is apriori iff S has a necessary 1-intension. To accomplish this task, he introduces what he calls the epistemic understanding of the two-dimensional semantic framework. This epistemic understanding leads Chalmers to adopt a different interpretation of the two-dimensional framework: The core idea of two-dimensional semantics is that there are two different ways in which the extension of an expression depends on possible states of the world. First, the actual extension of an expression depends on the character of the actual world in which an expression is uttered. Second, the counterfactual extension depends on the character of the counterfactual world in which the expression is evaluated. Corresponding to these two sorts of dependence, expressions correspondingly have two sorts of intensions, associating possible states of the world with extensions in two different ways...[Chalmers 2006] These two intensions correspond to two different ways of thinking of possibilities. In the first case, one thinks of a possibility as representing a way the actual world might turn out to be: or as it is sometimes put, one considers a possibility as actual. In the second case, one acknowledges that the actual world is fixed, and thinks of a
Philosophia Scientiæ, 16-2 | 2012 64
possibility as a way the world might have been but is not: or as it is sometimes put, one considers a possibility as counterfactual. [Chalmers 2006] So we have two intensions. Chalmers calls them 1-intensions and 2-intensions. 1- intensions correspond to possibilities considered as actual, and 2-intensions to possibilities considered as counterfactual.19
For instance, the sentence: "Water is H2O" is true in a world considered as counterfactual when H2O is H2O. In a world considered as actual, though, "Water is H2O" is true (roughly) when the colorless, tasteless, potable liquid in that world is H2O. So the
1-intension of "Water is H2O" assigns the value "true" to all those worlds meeting the latter condition, and the 2-intension assigns the value "true" to all those worlds meeting the former condition (i.e., all of them). Similarly, the 1-intensionof "water" maps "water" onto the colorless, etc. liquid in each world, without regard to its chemical properties, while the 2-intension of "water" behaves like we would expect if "water" were a Kripkean rigid designator. The question arises: why should we think that terms like "water" and sentences like:
"Water is H2O" behave differently when evaluated with respect to possibilities considered as actual than they do when evaluated with respect to possibilities considered as counterfactual? The underlying intuition looks something like this. We know that water is H2O. But we can imagine that things were different. Dalton, for instance, thought water was HO, in part because his tests could not distinguish between
H2O and HO. Perhaps we’re actually in a similar position, and the actual world is not as we believe it to be. In fact, water is XYZ, and our tests are incapable of distinguishing between H2O and XYZ. If things are actually this way, we do not know that water is H2O after all, because water isn’t H2O; it’s XYZ.
That is, given that water is actually H2O, it turns out that there is no way things might have been (i.e., no possibility considered as counterfactual) in which water is XYZ. But if the actual world is different than the way we think it is, then perhaps water is not
H2O. And we don’t always know which world is the actual world—or at least we don’t always know how to distinguish the actual world from similar worlds by description. And even when we can identify a given world w as non-actual, we can still consider how things appear to someone who believes that w is actual. Thus far, we have been treating possibilities as worlds, as is traditional (and as we do on my metapropositional account). But this is a bit misleading where Chalmers is concerned, because in [Chalmers 2006] he opts instead to analyze epistemic possibilities in terms of what he calls scenarios. Roughly, according to Chalmers, scenarios are to epistemic possibilities as worlds are to metaphysical possibilities. That is, scenarios are maximal epistemic possibilities situated in a space of all epistemic possibilities, which he calls epistemic space. Chalmers offers up two ways of understanding scenarios. First, he provides an account of scenarios in terms of centered worlds. Centered worlds are ordered pairs consisting in a possible world and a privileged point (called a center). This point specifies a place, time, and an agent in the world and is used to evaluate indexical expressions. Alternatively, he suggests that we can understand scenarios as equivalence classes of infinitary "epistemically complete" sentences in a constructed language L. A sentence S is epistemically complete if it has the following properties: 1. S is epistemically possible.20 2. There is no sentence T in L such that S & T and S &¬T are both epistemically possible. The language L itself has a limited vocabulary V with the following property:
Philosophia Scientiæ, 16-2 | 2012 65
Scrutability of Truth: There is a relatively limited vocabulary V such that for any truth S, there is a V-truth D such that D implies S.21 We need not concern ourselves with the details of these accounts of scenarios. Chalmers does not definitively adopt either story, and we do not need to do so in order to see how Chalmers’s account differs from my own or why we might find Chalmers’s account problematic. There are two features shared by both accounts that give rise to difficulties. First, Chalmers understands scenarios as points in epistemic space. He characterizes epistemic space in terms of aprioriepistemic possibility. But characterizing epistemic space in this way means that our notion of epistemic space depends on our understanding of epistemic possibility. Indeed, Chalmers is fairly explicit in taking deep epistemic necessity as a primitive (See, for example, [Chalmers 2006, 79]). I take it that part of what it is to offer an analysis of some phenomenon is to offer an explanation for that phenomenon. Ideally this explanation will allow us to understand the phenomenon to be explained in terms of some other phenomena which we already understand. But taking epistemic necessity as a primitive makes it impossible to offer this sort of explanation. Since Chalmers’s theory takes epistemic necessity as a primitive, it seems like no matter what other virtues it has, we will not see any improvement on whatever grasp we had on epistemic modality prior to encountering his account. That is, if we’re confused about the nature of epistemic necessity (and/or epistemic possibility) before encountering Chalmers’s theory, we’ll be confused after encountering the view as well. My metapropositional approach does not take epistemic possibility (or epistemic necessity) as a primitive and so it offers up the possibility of a genuine analysis of epistemic modality. That said, it would be good to have a theory which allows us to determine the truth conditions for an epistemic modal, for instance, even if that theory doesn’t explain why any given epistemic modal has its particular truth conditions. Even if Chalmers’s account fails as an analysis of epistemic modality, it might succeed at some other worthy tasks. It is worth noting that, whatever Chalmers’s goal may be in presenting his account, the fact that it fails as an analysis of epistemic modality makes it less attractive compared to the metapropositional approach I offer. The metapropositional approach, like any theory, has its primitives, but neither epistemic necessity nor epistemic possibility are among them. The second, and more significant, issue with Chalmers’s account has to do with a property he calls "scrutability." Chalmers claims that scenarios are scrutable, and he characterizes scrutability thusly: If we come to know that the world has a certain character, we are in a position to conclude that the expression has a certain extension. And if we were to learn that the world has a different character, we would be in a position to conclude the expression has a different extension. That is: we are in a position to come to know the extension of an expression, depending on which epistemic possibility turns out to be actual. Scrutability is a strong requirement, and it gives rise to problems. Chalmers claims that there are relativelylimited vocabularies that allow us to derive (using apriorireasoning alone) all the facts about a world from a global description of that world, but there is reason to think this claim is false. While it may be that some worlds can be described in such a way as to make them scrutable, it is not clear that all worlds have this property. Consider the following examples (inspired by [Schroeter 2003]):
Philosophia Scientiæ, 16-2 | 2012 66
Case 1: Mixed Earth Mixed Earth is a world much like Earth. However, while Earth has
H2O, Mixed Earth is a world in which we find both H2O and XYZ in roughly equal quantities. Lakes, rivers, and oceans are comprised of a mixture of H2O and XYZ, as are the bodies of Mixed Earth’s residents. Mixed Earth’s residents can drink H2O, XYZ, or the mixture of XYZ and H2Oandrespondin the same way to all three options.
Case 2: Partitioned Earth Partitioned Earth is also a world in which we find both H2O and XYZ in roughly equal quantities. However, any given lake, river, or ocean is either entirely H2O or entirely XYZ. Roughly half of Partitioned Earth’s residents have H2O as part of their makeup; the other half have XYZ. H2O-people can drink XYZ and vice versa. Case 3: Coke Earth Coke Earth is a world like Earth. In particular, Coke Earth contains H2O in all the places that Earth does. However, due to a lucrative marketing arrangement, the people of Coke Earth never imbibe H2Owithout mixing it with other chemicals. In fact, they exclusively drink Coke Classic, Cherry Coke, and other soft drinks produced by the Coca-Cola Company.22 The residents of Coke Earth have in fact been genetically modified to be unable to drink H2O except when it is founding Coke products. In all of these cases, we can ask the same question: what is the referent of the term "water" if these worlds are considered as actual? Chalmers thinks we have fairly clear intuitions about the answer to this question in the case of Twin Earth (and not without reason). But what about Mixed Earth and its cohorts? I, at least, lack clear intuitions about these worlds. First, note that all of these cases appear to be deeply epistemically possible—that is, they all can be considered as actual given what we know apriori (though they are all inconsistent with our a posteriori knowledge of the actual world). The scrutability requirement applies to all scenarios, and since all deep epistemic possibilities are covered by some scenario or other, we should be able to say what "water" refers to in each case. Let’s start with Mixed Earth. When we consider Mixed
Earth as actual, we don’t seem to have any reason to think "water" refers to H2O rather than XYZ (assuming it can’t refer to both). Perhaps "water" on Mixed Earth functions like "jade" does (or did) in the actual world—but perhaps it doesn’t. I, at least, lack strong intuitions one way or the other. And now consider Partitioned Earth. Partitioned Earth has the same kinds of stuff as Mixed Earth, but in different arrangements. Here, too, I lack clear intuitions, excepting the following: it seems less likely to me that "water" functions like "jade" does in the actual world if Partitioned Earth is considered as actual than it does if Mixed Earth is considered as actual. And so it goes for Coke Earth as well; since the liquid found in lakes and rivers is not the drinkable liquid that comes from our taps on Coke Earth, it’s not clear which liquid should be the referent of "water." Here is why cases like these are problematic for Chalmers. Chalmers claims that scenarios are scrutable, which means we can infer (using only apriori means) the reference of various expressions from the description of a possibility. Cases like 1-3, though, suggest that there are at least some worlds where this inference is not possibility. Admittedly, cases 1-3 trade on our intuitions (or more precisely our lack of intuitions) about particular cases, and intuition is not the same as apriori reasoning. But Chalmers trades on our intuitions as well, using examples like Twin Earth to motivate his scrutability claim. Furthermore, the fact that we lack clear intuitions about cases 1-3 gives us reason to doubt that they are scrutable.
Philosophia Scientiæ, 16-2 | 2012 67
Once we have a few examples like cases 1-3 above, it is easy to produce more. What about the world which is like Coke Earth, except that the inhabitants cannot drink H2O at all? Or the world in which its inhabitants are surrounded by H2O but drink XYZ, or vice versa? Again, these cases are not ruled out by our apriori knowledge, and so there is a scenario in which these cases obtain. We ought, on Chalmers’s view, to be able to consider such possibilities as actual. The ease with which we can construct problematic cases like these suggests that Chalmers can’t beat this objection simply by addressing a few individual cases. Chalmers might try to escape this criticism by claiming that the descriptions given above are insufficiently detailed. Scenarios are, after all, epistemically complete, while the descriptions in cases 1-3 certainly not. This is, I think, an unsatisfactory response. First of all, cases 1-3 are described in as much detail as Twin Earth, and while it may very well be true that some worlds require more description than others in order to be scrutable this shows that complete descriptions are not always necessary in order to discern the referent of at least some terms. Second, epistemically complete descriptions are inaccessible for actual humans; even if we are to leave aside the fact that they are not expressed or expressible in any natural language, the fact that they are infinitary sentences puts them outside the reach of our cognitive machinery. If scrutability is to mean anything it has to apply to incomplete descriptions of scenarios. Perhaps, with more information, it would be possible to resolve cases 1-3 above—but that doesn’t mean that all problematic cases can be handled in this way. Ultimately, I think these considerations show that we would have to accept a large promissory note in order to buy the scrutability claim. The metapropositional approach presented in §3 does not have to worry about this objection. The basic content constraint and the knowledge base constraint serve to rule out many of the worlds like Mixed Earth and its cohorts. It may be that some cases like 1-3 remain, but as I have not made any claim comparable to Chalmers’s scrutability claim their existence is largely unproblematic for my preferred view. Scrutability also causes other problems. Chalmers’s arguments for scrutability involve generalizing from the actual world. But consider alien properties. Alien properties are properties that are uninstantiated in the actual world, but are instantiated elsewhere. For the moment, let us stipulate that there are alien properties.23 Then there are worlds that instantiate properties that are not instantiated here. And we have no reason to think that such a world could be described using whatever limited vocabulary allows us to produce an epistemically complete description of the actual world. That said, Chalmers does not say that we can offer an epistemically complete description of every world using some limited vocabulary. His claim, rather, is that every (deep) epistemic possibility (i.e., every scenario) can be so described. But remember that for Chalmers, a sentence is deeply epistemically possible if it’s not ruled out by apriori reasoning. It seems highly likely that we do not have apriori knowledge of precisely which properties are instantiated in the actual world. That is, our apriori knowledge does not allow us to specify which properties there are; given a list of all possible properties, we may not be in a position to say which ones are instantiated in the actual world. Consider, for instance, the positions of some ancient Greek philosophers, who thought that all material objects consisted in various amounts of fire, earth, water, and air; it seems odd to say that these philosophers could have
Philosophia Scientiæ, 16-2 | 2012 68
realized their error as a result of apriorireasoning rather than as a result of empirical science. The upshot of all this is that whether or not there are alien properties, it is plausible that there are deep epistemic possibilities (i.e., scenarios) that instantiate properties not found in the actual world.24 And we have no reason to think that these scenarios can be described using whatever limited vocabulary we find that allows us to produce an epistemically complete description of the actual world. Chalmers’s approach, then, has some significant issues stemming mainly from his characterization of scenarios as 1) points in epistemic space and 2) scrutable. Since the metapropositional approach that I favor does not involve epistemic space or have a scrutability requirement, it comes as no surprise that it does not suffer from the same flaws. Chalmers also offers up a typology of two-dimensional accounts. On his typology, my view would be closest to what he calls a semantic contextual understanding of the two- dimensional framework. Chalmers rejects this understanding (along with all the other understandings) as being incapable of validating the Core Thesis. As I have no particular interest in validating the Core Thesis, I do not find this to be adequate reason to reject my view.
5 Conclusions
The upshot of this paper is this: if you’re going to use worlds (or situations) to account for epistemic modality, two-dimensionalism is the most promising extant approach. Since the possible worlds framework has been successful thus far in philosophy and linguistics, I opt for the two-dimensional alternative. My proposed version of the two- dimensional solution to the problem of EPMIs is not the only possible version; in particular, David Chalmers has his own understanding of the two-dimensional framework (put forward, among other places, in [Chalmers 2006]) which differs from my own on several significant issues. I have also given reason to think my view is more promising than his approach. My main purpose here, though, is simply to present the problem of EPMIs and offer a sketch of one two-dimensional solution along with some reasons to think that two-dimensionalism is a promising line of inquiry, and that purpose, has, I think, been fulfilled.
BIBLIOGRAPHY
CHALMERS, DAVID 2006 The foundations of two-dimensional semantics, in Two-Dimensional Semantics: Foundations and Applications, edited by GARCIA-CARPINTERO, M. & MACIA, J., Oxford: Clarendon Press, 55-139.
HINTIKKA, JAAKKO (ED.) 1962 Knowledge and Belief, Ithaca: Cornell University Press.
Philosophia Scientiæ, 16-2 | 2012 69
JOHNSTON, MARK 1997 Manifest kinds, The Journal of Philosophy, 94, 564-583.
KAPLAN, DAVID 1989 Demonstratives, in Themes from Kaplan, edited by ALMOG, J., PERRY, J., & WETTSTEIN, H., New York: Oxford University Press, 481-564.
KRATZER, ANGELIKA 1977 What ’must’ and ’can’ must and can mean, Linguistics and Philosophy, 1, 337-355.
KRIPKE, SAUL 1980 Naming and Necessity, Cambridge: Harvard University Press.
PORTNER, PAUL 2009 Modality, Oxford: Oxford University Press.
PUTNAM, HILARY 1996 The meaning of "meaning", in The Twin Earth Chronicles, edited by PESSIN, A. & GOLDBERG, S., New York: M.E. Sharpe, 3-51.
RABERN, BRIAN s. d. Monsters in Kaplan’s logic of demonstratives, Philosophical Studies, Forthcoming.
SANTORIO, PAOLO 2011 Modals are monsters: On indexical shift in english, Proceedings of SALT 20, 289-308.
SCHLENKER, PHILIPPE 2003 A plea for monsters, Linguistics and Philosophy, 26, 29-120.
SCHROETER, LAURA 2003 Gruesome diagonals, Philosophers’ Imprint, 3(3), 1-23.
WEATHERSON, BRIAN 2001 Indicative and subjunctive conditionals, Philosophical Quarterly, 51, 200-216.
NOTES
1. A note on notation: ◊E indicates epistemic possibility. □E indicates epistemic necessity. ◊M and □M indicate metaphysical possibility and necessity, respectively. 2. Unless otherwise stated, all discussion of possible worlds involves metaphysically possible worlds. 3. As we will see this assumption is not required in order to generate the problem under consideration, but it does make it easier to produce examples. 4. This formulation is missing a few refinements which will be introduced shortly. 5. This claim must be understood as a de re modal claim. That is, to claim that Figure 1 is necessarily four-sided is to claim that that very object could not have had three sides. Alice could have created a different painting, and that painting could have been called Figure 1, but it would not have been the very same object. 6. "Basic content" is a technical notion which will be defined in §3.3. 7. A similar application of the two-dimensional framework can be found in Brian Weatherson’s [Weatherson 2001]. Weatherson uses the two-dimensional framework to give truth conditions for indicative and subjunctive conditionals. Indicative conditionals have, as he puts it, a "well-known epistemic feel," and the two-dimensional framework is employed in order to capture that feel.
Philosophia Scientiæ, 16-2 | 2012 70
8. The language itself also needs to be held constant. If the morpheme "gap" is used by an English speaker it denotes a gap; in Polish, this morpheme denotes an onlooker. Consider the English modal sentence: "For all I know, the gap between the door and the platform might be six inches across." When we evaluate this modal, "gap" will retain its English meaning. Similarly, we require that the sentence be properly disambiguated. The sentence: "For all I know, that might be a ball" could be about a formal dance or about a round children’s toy (among other interpretations). We must disambiguate in order to determine which sense of "ball" is in play and thus which basic content is relevant. 9. For our purposes, all that matters is that the object of knowledge determines a set of worlds. We need not get embroiled in arguments regarding the object of knowledge as long as it has this property. If the objects of knowledge are propositions, then that satisfies our requirements. For simplicity I will continue to speak as though the objects of knowledge are propositions and propositions are sets of worlds, but this is not strictly speaking a requirement of the theory. 10. Notice that while this restriction involves the epistemic status of some agent or collection of agents, it does not invoke any preexisting understanding of epistemic possibility. To determine what worlds go in to Wp, we attend to the epistemic status of the relevant agent or agents in a single world—that is, what the agent or agents know about the world they occupy and what further facts are consistent with that knowledge. But this is as it should be, since epistemic possibility and epistemic modality are relative to what is known by the relevant agent or agents. 11. The knowledge base will actually be smaller than indicated here, as Alice and Bob have all sorts of incidental knowledge which is not relevant to the evaluation of the modal sentence. For example, if Bob is wearing a red shirt (and is not red-green colorblind), then he will likely know he is wearing a red shirt. So the knowledge base will include all the worlds in which Carol is not in Washington and Bob is wearing a red shirt. But these other bits of knowledge are irrelevant and so have been glossed over. 12. I take no position on whether or not knowledge is closed under known entailment or under some other sort of operation. It is clear, though, that knowledge is not closed under entailment simpliciter because this would entail logical omniscience. 13. I prefer to define epistemic necessity and possibility relative to knowledge bases, not agents, but I am using agents here to bring out the issues that arise when we associate epistemic necessity with knowledge in the traditional way. A statement can be said to be epistemically necessary relative to an agent if it is epistemically necessary relative to the knowledge base of all worlds compatible with everything that the agent knows. 14. Andrew Wiles first announced that he had proved Fermat’s Last Theorem in 1993. While this version of the proof was flawed, his subsequent attempt in 1995 was successful. 15. Note that this fits well with Putnam’s suggestion that natural kind terms have an indexical component. If Putnam is right, that would explain why natural kind terms behave as they do. I am inclined to think Putnam’s claim is correct, but nothing here rests on whether or not that is the case. 16. Robert Wadlow is listed in the Guinness Book of World Records as the world’s tallest person, measured at 8 feet 11.1 inches just before his death. 17. Adapted from examples by Wayne Davis. 18. Adapted from examples by Steve Kuhn. 19. Chalmers takes the analysis of the two-dimensional framework in terms of possibilities considered as actual and as counterfactual to be characteristic of two-dimensional theories in general, but this is not obvious. For instance, the metapropositional approach I have developed is best understood in terms of worlds of production and worlds of evaluation. Chalmers is of course free to use possibilities considered as actual or counterfactual as his intuitive starting point even if he’s wrong about it being a common starting point among two-dimensional theories. 20. Note that here, as before, Chalmers takes epistemic possibility as a primitive.
Philosophia Scientiæ, 16-2 | 2012 71
21. Chalmers calls this Scrutability of Truth II; I’m omitting Scrutability of Truth I and leaving off the number to avoid confusion. 22. I have received no promotional considerations from Coca-Cola or any other soft drink manufacturers. 23. The existence of alien properties is controversial, but as we will see nothing in my final argument depends on their existence. They are being used as a way of introducing some unusual epistemic possibilities, and that’s it. 24. These properties, strictly speaking, wouldn’t be alien properties, since they might not be instantiated at any world.
ABSTRACTS
Not everyone knows that water is H2O. Suppose Alice is one of those people. Alice says: "For all I know, water might not be H2O." Intuitively it seems like Alice has spoken truly. That is, it seems like it is epistemically possible (for Alice) that water is not H2O. However, conventional accounts of modality in linguistics and philosophy of language predict that any metaphysically impossible statement will also be epistemically impossible (for anyone). And there are plausible arguments, from Kripke and others, that purport to show that it is metaphysically impossible for water to be anything other than H2O. So according to the standard accounts of modality, Alice has in fact said something false.
Tout le monde ne sait pas que l’eau est du H2O. Supposons qu’Alice soit l’une de ces personnes.
Alice dit : « Pour autant que je sache, l’eau pourrait ne pas être du H2O. » Intuitivement, il semble qu’Alice ait dit quelque chose de vrai. Autrement dit, il semble qu’il soit épistémiquement possible (pour Alice) que l’eau ne soit pas du H2O. Pourtant, les conceptions traditionnelles de la modalité en linguistique et en philosophie du langage prédisent que tout énoncé métaphysiquement impossible est également épistémiquement impossible (pour qui que ce soit). Or, il y a des arguments plausibles, venant de Kripke et d’autres, qui prétendent montrer qu’il est métaphysiquement impossible pour l’eau d’être quoi que ce soit d’autre que du H2O. Selon ces conceptions standards de la modalité, Alice a donc en fait dit quelque chose de faux. Ce résultat est hautement contre-intuitif. Je propose une nouvelle théorie de la modalité qui est capable de représenter ce que j’appelle des IMEPs : des impossibilités métaphysiques épistémiquement possibles. Des phrases comme : « L’eau pourrait ne pas être du H2O» et « Hesperus pourrait ne pas être Phosphorus » sont des exemples d’IMEPs, et d’autres peuvent être facilement trouves (y compris certains qui ne reposent pas sur des considérations kripkéennes touchant a la possibilité métaphysique). Ma théorie explique l’existence d’IMEPs tout en conservant la souplesse et la puissance explicative des conceptions standards.
AUTHOR
DAN QUATTRONE Georgetown University (USA)
Philosophia Scientiæ, 16-2 | 2012 72
Modal Integration
Scott A. Shalkowski
1 Introduction: The integration problem
There are two quite different focal points for the epistemology of modality. The first, perhaps narrower, focus is on the manner in which quite specific modal claims are warranted, if at all. If it is genuinely possible that I might have taken a plane rather than a train from Leeds to Nancy, how do I know this? Do I know it because I can conceive of taking a plane and not the train, because I have a modal intuition that I could have done so, because no contradiction is derivable from the claim that I took a plane rather than a train, or on the basis of principles of understanding that account for my grasp of the claim that I took a plane rather than a train, etc.? This focus clearly makes modal epistemology part of epistemology, as that philosophical specialty is normally understood.
1 A second focus is on the warrant for a theory of the modal. This is a big picture concern about our knowledge, if any, of the nature of the modal. Whether we say that the modal is really a matter of cognition, of abstract linguistic facts, of "logical" form and consequence, of concrete linguistic conventions, of abstract mathematical models, or of a plurality of concrete worlds, any such claim about the modal has some normative claim on our assent only to the degree that it is sufficiently warranted.
2 There are obvious ways in which the results of one inquiry might relate to the other. An account of the nature of the modal might well have implications for the epistemology of particular first-order modal claims. If modality is fundamentally about the form of a claim and its implications, then the epistemology of specific modal claims is a matter of the epistemology of form and derivation. Indeed, having a ready-made epistemology for a perfectly respectable domain might well provide good grounds for attempting an account of the modal that permits the extension of that ready-made epistemology from a non-modal domain to the modal domain. Those thinking that we have a ready-made epistemology of form and derivation have theoretical motivations for attempting a theory of the modal to which that epistemology applies, thus taking the modal just to be matters regarding form and derivation.
Philosophia Scientiæ, 16-2 | 2012 73
3 The immediately obvious virtue of applying a ready-made epistemology to the modal is that tacitly it gives credence to, as well as an answer to, the "integration problem" that confronts all philosophical claims. In its general form the integration problem is this: all philosophical claims should be integrated into a larger framework of both philosophical and non-philosophical beliefs.1 Integration into a larger framework of beliefs involves many things, such as producing no inconsistency and resulting in a coherent intellectual framework. The coherence of that framework might involve many things, but the one that interests us here is the following epistemological principle: if things are as I say they are, it should be no mystery that I am warranted in saying that things are as I say they are. This principle should strike us as so obvious as to be a platitude. The platitude, though, obscures the distinction of the two epistemological focal points for philosophers of modality.
4 Metaphysicians are notorious for ignoring the fullness of the integration problem. They have their metaphysical views but they are often less explicit about the general nature of the warrant they possess—or even could possess— for their peculiar claims. Arguments used to warrant specific metaphysical claims fail to address the integration problem. For example, one might argue for an ontology of universals on the basis of the semantics for abstract nouns in the context of true sentences. Agreeing that 'Justice is a virtue' is true and that 'justice' appears to play a referential role in that sentence leads some to think that 'justice', like other abstract nouns, has a referent which is itself a genuine article in the ontology of reality. None of the philosophical argumentation used to warrant the claim that there are universals, though, reduces any puzzlement regarding how, given that 'justice' has an abstract referent, we manage to know that justice is a virtue. We have grounds for thinking that 'justice' and 'virtue' have referents on the basis of the argument sketched. Other arguments tell us that justice and virtue are related in familiar ways that we can represent using Venn diagrams or sets. If justice and virtue, though, are what platonist philosophers say they are, it is still a deep mystery how we manage to figure out what started it all, i.e., that justice is a virtue. Since the proponents of universals tend to be satisfied with the conclusion that 'justice' has an abstract referent and before they address the integration problem, they quit too soon.
5 Philosophers of mathematics, on the other hand, have been somewhat more sensitive to the integration problem. Paul Benacerraf famously discussed a dilemma confronting philosophers of mathematics [Benacerrraf 1973]. They can have either a satisfactory account of the nature of mathematical truth but thereby be doomed to have no satisfactory epistemology of mathematics or else they can have a satisfactory epistemology of mathematics but then be fated to have an unsatisfactory account of the nature of mathematical truth. Truth iff no epistemology would, indeed, be a problem for any systematic philosopher.
6 Benacerraf's presentation of this problem relied upon the causal theories of knowledge and justification that were in vogue at the time, but the problem can be generalised. Hartry Field did so by focusing on the fact of mathematical reliability—that mathematicians are reliable regarding mathematical claims— without tying the nature of warrant to causal connections between knower and known. [Field 1989]. The integration problem is more general still, since it fails to make integration a matter of even reliability. For our purposes, we can remain silent on the specifics of adequate integration, save for this: successful integration of the modal should address both the
Philosophia Scientiæ, 16-2 | 2012 74
specifics of our knowledge of individual modal claims as well as the warrant for the theory itself. Warrant for the theory absent even a skeleton of a theory for the integration of specific modal claims with our wider epistemology constitutes grounds for rejecting the theory itself. The remainder of this paper concerns David Lewis's attempt to solve the integration problem with respect to his theory of the modal.
2 Lewis's integration: The narrow issue
David Lewis is not terribly interested in the narrow version of the integration problem. For the most part, he thinks that it arises out of some failure on the part of his critics. They fail to understand that the plurality thesis is a thesis about a plurality of other, self-contained worlds and not merely a theory of how much more actuality contains. Or, they fail to understand that while it is contingent whether there are (actually) any talking donkeys, it is not a contingent matter that there might be some. Or, they fail to have any usable grasp on the concrete/abstract distinction, of which they think Lewis runs afoul [Lewis 1986, 108-115]. His concern in that section, "How Can We Know?", is wholly defensive. He provides no account of modal knowledge, save that we can have knowledge of his theory of the modal, which will be the concern of the following two sections of this paper.
7 In his own defense, however, he does propose an ad hominem argument urging humility [Lewis 1986, 109]. The ad hominem argument is that Lewisian worlds resemble mathematical objects in one crucial respect: ex hypothesi each is spatio-temporally isolated from us. We all (have we not?) made our peace with mathematical objects in the absence of any illuminating treatment of the "mathematical integration problem", so no one is in a position to object to Lewis's modal metaphysics on that basis. Whatever problems afflict modal knowledge due to the spatio-temporal isolation of worlds, those very same problems afflict mathematical knowledge no less. Lest, however, you be tempted to rethink the nature of the mathematical, you should not. Mathematicians know what they are doing and they know whereof they speak. Only the most foolhardy philosopher would stray from the world of intellectual controversy, strife, and discord that is philosophy to the world of rigor, proof, and agreement that is mathematics to declare that there are no mathematical objects or that those objects are not what mathematicians think they are [Lewis 1991, 58]. To do so would be to exhibit "hubris" [Lewis 1986, 109].
8 The analogy with mathematics, however, has positive ad hominem force for Lewis only on the assumption that we do and should defer to mathematicians in their platonistic accounting of their subject matter. Otherwise, there is no good reason to think that mathematical and modal objects share the quality of being spatio-temporally disconnected from us. How peculiar, though, for philosophers to defer to mathematicians regarding the philosophical accounting of mathematics. Whether Peano Arithmetic is provably consistent relative to ZFC set theory is something on which philosophers should happily defer to mathematicians, being the straightforward mathematical issue that it is. Lewis asks philosophers to defer to mathematicians, however, regarding the philosophical accounting of arithmetic. If we defer to practitioners of a given discipline regarding the most fundamental philosophical claims pertaining to their discipline, philosophers really are of use to neither man nor beast. If we have indeed made our peace with mathematicalia, it should not have been on the
Philosophia Scientiæ, 16-2 | 2012 75
basis of deference but on grounds subject to normal philosophical scrutiny, even were mathematicians rather than philosophers to produce them.2 To the degree that the warrant for believing in mathematicalia is based on deference, there is no good philosophical warrant behind the ad hominem component to Lewis's dealing with the integration problem. Unwarranted mathematical platonism is no basis for the claim that there is no special problem regarding our modal knowledge.
3 Lewis's integration: The wider issue
Deference may be more appearance than substance, however. So mathematics will do as a precedent: if we are prepared to expand our existential beliefs for the sake of theoretical unity, and if thereby we come to believe the truth, then we attain knowledge. In this way we can even attain knowledge like that of the mathematicians: we can know that there exist countless objects causally isolated from us and unavailable to our inspection. Causal accounts of knowledge are all very well in their place, but if they are put forward as general theories, then mathematics refutes them. [Lewis 1986, 109] As best we can, I think by seeking a theory that will be systematic and devoid of arbitrariness, we arrive at a conception of what there is altogether: the possible worlds, the possible individuals that are their parts, and the mathematical objects, even if those should turn out to be pure sets not made out of the parts of the worlds. This conception, to the extent that it is true, comprises our modal and mathematical knowledge. [Lewis 1986, 111-112]
9 This is Lewis on the wider issue of integration. Assuming that 'explanation' is sufficiently close to its use in the context of scientific inferences, the overall structure of Lewis's warrant for his modal metaphysics is an inference to the best explanation or an argument from theoretical utility [Divers 2002, 151-158]. There are things we want a metaphysical theory to do; Lewis's does them; his does more of them better than do alternatives; and his does so in a unified fashion. Thus, his theory is preferable to competitors, so say his defenders.
10 The very use of inference to the best explanation is one small step in solving the wider integration problem. The form of argument is the very same as one we use in ordinary and scientific contexts. If one hopes to show that philosophy is continuous with science, this is one way of showing differences to be those of degree rather than of kind. More importantly for our purposes, this permits Lewis to integrate his modal metaphysics with philosophy more widely and if successful it promises to yield sufficient grounds for his modal metaphysics. This is not really a well-developed ready- made epistemology, but it is a mode of argument that both philosophers and non- philosophers recognise and most countenance as valuable.
11 Elsewhere, I have cast some doubt on the appropriateness of inference to the best explanation in the context of metaphysical theories [Shalkowski 2010]. The short version of that critique is this. First, forms of inference are treated as good only if there are grounds for thinking that form of inference is sufficiently reliable. Deductive arguments are to have grounds for their guarantee of the conclusion, given the premises. Non-deductive arguments are to have grounds for thinking the conclusion more likely, given the premises. These grounds for reliability are unavailable for inference to the best explanation in the context of metaphysics. There is no way apart from uses of the inference in question to determine whether the inference leads us to
Philosophia Scientiæ, 16-2 | 2012 76
the truth. All we can have in this situation is that uses of the inference lead where they lead, not whether they lead to correct conclusions about how things are.
12 Adequate grounds cannot take the following form: pragmatic virtues of the theory confer on it truth-indicative virtues such as warrant. If we work with the distinction between using a theory and taking it to be true, the pragmatic virtues warrant using a theory but not taking it to be true. Simplicity is an oftcited theoretical virtue. Simple theories are easier to work with than are more complicated theories. There are, however, no a priori grounds for thinking that reality is simple and without some grounds or other for thinking that the reality in question is simple, there are no grounds for thinking that a simple theory is a better candidate for truth than are its more complex competitors. So, for example, it may, be "simpler" to think of propositions as sets of worlds instead of sui generis entities, but there are none of the usual grounds for thinking that there is a connection between this fact and the natures of things.
13 The word 'simple' is used to describe both a virtue that some theories possess and also some characteristic of some system that some theories purport to describe. There is no obvious connection between these two quite different attributes of simplicity that warrants the inference of, say, metaphysical simplicity from theoretical simplicity. Yet, this is precisely what one must have whenever one infers the truth of some metaphysical theory based, even in part, on the simplicity of the theory itself. If the appeal to simplicity does not involve an inference of this kind, then the inference merely masks the assumption and the tacit statement that reality is simple and we have no inference at all, much less an inference to the likely truth of any theory based on its character, i.e., it’s theoretical virtues. We have, then, merely a conflation rather than an inference.
14 Worse, we are here talking about metaphysics and the usual inductive grounds for thinking reality is simple are unavailable. To the degree that those inductive grounds warrant some claim expressed by 'reality is simple' the reality that is said to be simple is our small portion of modal reality, not the totality of Lewis's modal reality. All possibilities are supposed to be contained within that plurality of worlds. Some are simple; some are not. Indeed, all possible degrees of worldly complexity are realised within the plurality. So, not only is Lewis's reality not simple, it is as complex as any reality could be.3 If this last remark is thought to misunderstand the kind of simplicity the metaphysician has in mind— which has something to do with a relatively few distinct kinds of entities along with many and deep explanatory relations among those kinds—we have merely come back to my initial complaint: there are no grounds for thinking that the character of the appropriate reality answers to these theoretical niceties.
4 Daly and explanationism
Chris Daly defends Lewis on this count [Daly s. d.]. We can set aside the concern that the "best explanation" is merely the best of a bad lot. In simple terms, being the best theory available is perfectly consistent with it possessing a probability of a good bit less than 0.5. The evidence might warrant the belief that our best theory is most likely false. Lewis might be able to claim superiority over all extant rivals without being able to make a claim on our rational belief. Perhaps this explains the seemingly common
Philosophia Scientiæ, 16-2 | 2012 77
phenomenon that metaphysicians judge Lewis to have won sufficiently many of the specific and general arguments that pertain to his plurality thesis while they fail also to advocate that plurality thesis.4
15 Daly argues for a rehabilitation of inference to the best explanation in metaphysics. Call the doctrine that inference to the best explanation can be a form of inference that yields warrant for believing the conclusion of that inference "explanationism". A criticism levelled against explanationism by van Fraassen [van Fraassen 1995] and me [Shalkowski 2010] is that abductive arguments, unlike deductive arguments, require independent access to the facts, i.e., access to the relevant facts independent of the form of inference in question. Van Fraassen is concerned about observable entities countenanced on the basis of explanatory claims for scientific theories. I was concerned with typical metaphysical entities, most notably Lewisian worlds. Van Fraassen's concern arises out of his constructive empiricism; mine arises from a general feature of the justification of inferences. According to each of us the consequence seems to be that inferences to best explanations can never warrant their conclusions on their own, because there can be no grounds for judging those inferences to be reliable. Whether quarks or Lewisian worlds, the items in question are not observable and regarding worlds, Lewis proposes no other means of access, having dismissed the need on the basis of the non-contingency of the plurality. Consequently, there is no prospect of checking the results of our inferences to determine when, if ever, we go from assessments of the theoretical virtues of theories to conclusions about the matters that are the concerns of those theories. Daly seeks to undermine this "independence" criticism.
16 The explanationist may adopt some form of externalist epistemology. As Daly does, let us make our lives easy and frame matters in terms of reliabilism. He takes the following claims to be important for the defence of explanationism: 1. Reliability is sufficient for knowledge,5 2. No independent justification needed, 3. Knowledge of reliability by track record.
17 1) is the externalist position to show that explanationism stands in spite of the independence criticism. 2) follows from 1), because reliability is silent on the existence of multiple reliable methods. Reliability is not a function of checks on that reliability. A method is (sufficiently) reliable or it is not, regardless of whether anyone is convinced that it is or whether there are any independent means of coming to know the facts in question. Furthermore, the lack of independent evidence is precisely what makes reliability relevant to warranted perceptual belief, say reliabilists, and there are no independent checks on our most basic perceptual mechanisms or at least none that are both relevant and at least as good at generating warrant for beliefs. Knowledge iterates, so 3) follows as well, so long as there are reliable methods by which I arrive at the conclusion that inference to the best explanation is reliable for metaphysical conclusions. Moreover, one can know that a particular process is reliable by repeated use of that very procedure. Circularity is avoided because the items known differ with each iteration. In the first instance it concerns, perhaps, non-epistemological facts. Track record inferences are about epistemological facts, in particular that the process used at a previous level is reliable.
Philosophia Scientiæ, 16-2 | 2012 78
18 Externalism is the right test for explanationism, even if explanationism is not especially externalist in character. In fact, explanationism looks quite friendly to the internalist. We self-consciously examine a theory, determine its virtues, rank its virtues, compare its virtues with those of other theories, and then on the basis of this analysis we infer the([most] likely) truth of the most theoretically virtuous candidate.
19 The primary feature of externalism that the explanationist must rely upon is the inaccessibility of the knowledge-making features of some beliefs. At issue are the merits of accessibility internalism not mental internalism. The issue is not whether matters of justification are mental; what matters is whether a knower has the right kind of access to the conditions that make for knowledge to judge that they have been satisfied in all instances, whether those conditions are mental or not. This is the kind of externalism that operates in plausible accounts of basic perceptual knowledge. This knowledge is not inferential, so some conditions other than the standards of good inference constitute warrant in these cases. If the reader disagrees, treat my claims as conceding for the sake of argument that some form of externalism has some appropriate application. It will be enough if I can show that such externalism is not the entire story of epistemic justification, especially if I can show that externalism cannot be the entire story when warrant for using inference to the best explanation is at issue. If it is not, then this particular defence of explanationism fails.
20 Let us distinguish Three Grades of External Involvement, reflecting the degree to which one's account of epistemic warrant is framed in terms of external factors: A) None (Internalism) B) Some (Partial Externalism) C) All (Complete Externalism).
21 Internalism is quite obviously a nonstarter for Daly's argument. For the philosophical enterprise, we should probably reject complete externalism. The activity we are engaged in at the moment shows that we should admit room for internal factors that produce warrant. Engaging in philosophical activity requires it. This activity is largely about the giving and assessing of reasons and the giving and assessing of reasons is the paradigmatic example of when there must be transparency regarding the weight of considerations for or against some claim. This requires that we give up complete externalism. My critique of Daly's defense of explanationism relies only on uncontroversial metaphysical and epistemological assumptions.
22 Metaphysics, for our purposes here, is realist, truth-telling metaphysics of the "fact of the matter" variety. Standardly, realists separate evidence from fact. This separation is not that controversial among metaphysicians, since it is merely the admission of the possibility that weighty evidence warrants an ultimately false claim. Conditions of adequate warrant for knowledge are not constitutive of conditions of truth. That is the metaphysical assumption I require, since it is the assumption of metaphysicians who take inference to the best explanation to provide grounds for belief in the best explanation. Applying this to our discussion of inference to the best explanation, theoretical virtues do not entail the correctness of the most explanatory theory. In this context, 'explanatory' is not permitted to be code for 'is (likely to be) true'.
23 Epistemologically, I assume only that knowledge does not entail infallibility. Knowledge entails correctness but not cognitive perfection. This is implicitly conceded in our externalist example, in which warrant is given by merely reliable means. It is a cognitive
Philosophia Scientiæ, 16-2 | 2012 79
virtue to recognise one's own fallibility in acquiring knowledge and reliabilism requires only the regular—not uniform—tendency to acquire correct beliefs by way of the warrant producing mechanism(s) involved in knowledge.
24 Assuming, then, a realist, fallibilist reliabilism, what is the correct answer to a query about whether one knows something? I ask not what answer is correct, but what is the correct answer to give to such a question. Consider my belief that the cat is on the mat. Assume that the cat is, indeed, on the mat. Assume also that I acquire this belief by way of reliable perceptual mechanisms in contexts appropriate for those mechanisms and that I am thoroughly convinced of my externalism. Consider three different questions: I) What is on the mat? II) Is the cat on the mat? III) Do you know that the cat is on the mat? When asked what is on the mat, I reply "the cat". The question assumes the existence and appropriate placement of the mat so that something may be on it and it queries only what resides on the mat. In good externalist fashion, I answer with no thought to sufficient evidence in favour of my answer that is accessible to me. I hear the question, I look toward the mat and I call things as I see them. Similarly, when I am asked whether it is the cat that happens to be on the mat.
25 The third question is different. Each component of the externalist position we have before us gives the sensible externalist a reason not to answer III) in the same way as I) and II). The realist component simply means that things can seem so without being so. Affirmative answers to I) and II) are done, at most, on the basis of things seeming a given way, with no requirement that one perform any inference from the way things seem to the way things are. One may not even be conscious of how things seem, but conscious only of the cat being on the mat. Nevertheless, the assumed—and assumed to be known—"gap" between seeming and reality is sufficient to require a more careful answer to III).
26 The fallibilist component warrants a more careful answer similarly. With no implication regarding the relations between seeming and being, the fallibilist is aware of making mistakes, even when things seemed so on the basis of reasonable care and attention.
27 Most important is the external character of reliability—the opacity of warrant for the warranted believer. The distinguishing feature of externalist epistemologies is that I may be warranted unbeknownst to me. Put another way, when things seem to me to be a certain way as the result of the functioning of reliable belief-forming mechanisms in suitable contexts, I may be both unaware that those warranting conditions obtain and I may be unable to determine whether they obtain even when I try to examine my warrant. Since Complete Externalists know that their warrant is never transparent, they cannot now insist that the answer to III), which asks after warrant, can be answered straightforwardly. Partial Externalists can do no more, since the proposal before us is that some external facts about inference to the best explanation are to do the work of defending explanationism.
28 Insisting that answering III) affirmatively is just another case of re-applying the externalist's standard of warrant is to say that the warrant is, after all, transparent to me. To what would the opacity of warrant amount, if it does not make possible that I am warranted unbeknownst to me? If I may be warranted unbeknownst to me, and if we assume that my belief is correct, then this can mean only that I can have the
Philosophia Scientiæ, 16-2 | 2012 80
warrant sufficient for knowledge without knowing that I do. This is merely a version of the rejection of the KK principle, the principle that knowledge entails knowledge of that knowledge, i.e., Kp⇒KKp, for arbitrary claim, p. This is just to say that I am not entitled to answer "yes" to the third question in the same way I am entitled to answer the others, i.e., in a way that takes no notice of whether the warranting conditions for that belief obtain. I) and II) ask about the occupier of the mat and the cat. III) asks about warranting conditions for a claim about the cat and the mat. It is not appropriate for me to ignore the relevant conditions of warrant when the question is about those very conditions. How can I answer the question unless the conditions of warrant are sufficiently transparent to me?
29 This much follows straightforwardly for the externalist. It constitutes a problem for the externalist because of the context of questions like III). Recall the general history of the controversy that led us here. Some philosophers endorse explanationism. Our example was Lewis in defense of his plurality thesis. Other philosophers object that explanationism is false because a condition for the warranted use of a good non- deductive inference cannot be met. The reliabilist defense of explanationism is set in the context of philosophers disputing whether there is sufficient warrant for the use of one form of inference. That context is like the context of III) and unlike the contexts of I) and II). That context is one of premises, inferences, objections, and replies. Our context is one that requires the transparency of warrant, if what we philosophers manage to do some of the time when we engage in our peculiar intellectual activity is to assess the merits of grounds for conclusions. When we are disputing the merits of inference to the best explanation for metaphysical claims, we are not in K contexts; we are in KK contexts. Consequently, for the externalist defender of explanationism, the sad fact may be that they are both warranted and correct in embracing explanationism, but that warrant and correctness are no use to them. Correctness is accessible, if at all, by way of warrant and it is warrant that is opaque to those who possess it in the case at hand, given Daly's defense of explanationism. Since the defenders of explanationism engage in the project of convincing others of the merits of explanationism, they place themselves in a context that requires transparent warrant, not opaque.
30 Thus, Complete Externalists have no hope of engaging in the philosophical enterprise, as it is normally understood. They may be right that standard uses of inference to the best explanation reliably yield correct results, even in metaphysics. They may be right that such reliability is sufficient for knowledge and they may even be right that independent access is neither part of what constitutes that reliability nor a necessary condition on that reliability. All of that, however, is useless to them. Their task in normal philosophical contexts is to put us not into a K position, but into a KK position and for that they require transparency of warrant, to which they are not entitled.
31 Partial Externalists can engage in projects of defending positions as those projects are normally understood, but they cannot do so by way of a distinctively externalist defense of explanationism. That defense demands that the warrant for explanationism be inaccessible (even if warrant for other things may be accessible) while at the same time the philosophical context demands sufficient transparency of warrant, making the philosophical enterprise of exhibiting and assessing warrant possible.
32 As to specifics, we must reject Daly's third component: knowledge of reliability by track record. His gloss on that condition is: "you can know by process R that you know by process R that p" [Daly s. d.]. The first reason for rejecting this we have just seen from
Philosophia Scientiæ, 16-2 | 2012 81
the general demands of the project of providing a philosophical defense. There is a second. Our knowledge that we are reliable by way of track record is supposed to permit us to bootstrap our way to knowledge of reliability as follows. From premises to do with the successful use of a given reliable procedure, R, I use R to determine that I have come to know things by the use of R and that R is reliable. If on sufficiently many and varied occasions I use R to have beliefs when the world is the way I believe it to be and if R fails to lead me astray on sufficiently many and varied occasions, then R is reliable.
33 Bootstrapping works, however, only if R is the only procedure relevant to my possessing warrant in the specific instances cited and also in my possessing warrant for believing that R is itself reliable. This uniformity is lacking in this kind of defense of explanationism. It may be that some reliable belief-forming mechanism is at work in all cases, but they will be distinct mechanisms. The premises of any case for the reliability of inference to the best explanation would be of the form:
E) In Case Ci I inferred that the best theory Tk was true and Tk was true. If I have sufficiently many cases to cite, the argument goes, we have adequate grounds for maintaining that inference to the best explanation is reliable.
34 First, this is not, strictly speaking, a case of bootstrapping inference to the best explanation because while the premises concern instances of that form of inference and the truth of the theory inferred, the argument for the reliability of that form of inference is an enumerative induction. Even if both inference to the best explanation and enumerative induction as carried out by the explanationist are reliable, we do not have justification of a single reliable procedure, R, in terms of itself. At best, we have the justification of one reliable procedure in terms of another. That is not nothing, but it is not yet something that satisfies the third component of Daly's defense, which is knowing that one mechanism is reliable by way of that very mechanism.
35 Second, the imagined enumerative induction exhibits the characteristic of philosophical disputes uncovered earlier: the transparency of warrant. Only if the warrant for believing that inference to the best explanation can be discerned by the examination of the relevant premises taken together would we have any basis for recognising the explanationist to be correct. The explanationist case in externalist terms is, therefore, self-defeating. That speaks to the overall structure of the externalist defense.
36 Third, we should not overlook a problem with the premises. Any cogent argument must have not only sufficiently reliable structural features, its premises must individually possess sufficient warrant. The warrant for each premise concerning successful instances of inferences to the best explanation must depend on memory and/or testimony, not inference to the best explanation, but that is a small matter. More importantly, what is the basis for the second conjunct of each of the key premises in the enumerative induction? The first conjunct we may not cavil about since both explanationists and their critics acknowledge that philosophers have used inference to the best explanation. All instances in which there are grounds for embracing the second conjunct of any premise will be instances in which there is independent access
to the relevant facts of the case, i.e., independent of the inference to the best theory Tk. Each assertion of the relevant instance of E) is like our III) above. That each conjunct of each instance is true is insufficient to make each instance properly assertible as a premise in a defense of explanationism. We can know by memory or other grounds that
Philosophia Scientiæ, 16-2 | 2012 82
we inferred to Tk. We can know that our inference did not lead us astray, however, only
if we have some memory or other grounds that Tk was true. If this fails to go beyond the
memory or other grounds for thinking that we took Tk to be true or that we inferred Tk, the defense of explanationism does not go beyond the initial assertion of explanationism. It cannot constitute its defense. Each premise in the enumerative induction would, under those circumstances, amount to no more than the claim that we inferred the best theory from the conditions of its being the best theory, not that the inference was correct. Without a basis for the correctness of sufficiently many of those inferences in instances of E), there can be no defense of explanationism in reliabilist terms. In effect, the premises in the enumerative induction beg the question that divides the explanationists and their critics. The critic says that without something besides inference to the best explanation operating in the relevant domain, there is insufficient basis for thinking that any of the instances of E) is true precisely because there is insufficient basis for thinking the scond conjunct of each is true for the cases that interest the critic. Merely asserting instances of E) is just asserting that in all of those cases, the critics are wrong.
5 Conclusion
37 The problem of modal integration remains unsolved by the defender of Lewis's plurality of worlds as a general metaphysics of modality. The narrow form of the problem cannot be set aside by way of a deferential ad hominem. The wider form of the problem cannot be solved by way of inference to the best explanation. Chris Daly's defense of explanationism in terms of externalism is as good as it is likely to get for those who wish to conduct metaphysical inquiry by way of inference to the best explanation. The critics of the use of this abductive inference in this kind of context, however, should stand their ground. Epistemic warrant might well be the kind of thing that is opaque to us in many important contexts. Many of the deliverances of sense perception and memory might well be warranted without the details of that warrant being accessible to the one warranted. Nevertheless, it cannot be externalism all the way up. Philosophers, of all people, must recognise that philosophical contexts demand a great degree of transparency of warrant, if philosophy is to be a going enterprise at all. This defense of explanationism fails because in order to undermine the independence objection it must be thoroughly externalist in character about the case at hand, but in order to warrant one in embracing explanationism, it must be at least somewhat internalist in character about that very case. However metaphysicians are to ground their theories, inference to the best explanation is not a reputable way to do so.
BIBLIOGRAPHY
BENACERRRAF, PAUL 1973 Mathematical truth, Journal of Philosophy, 19, 661-679.
Philosophia Scientiæ, 16-2 | 2012 83
DALY, CHRIS s. d. Explaining, inferring, believing, ms.
DALY, CHRIS & LIGGINS, DAVID 2011 Deferentialism, Philosophical Studies, 156, 321-337.
DIVERS, JOHN 2002 Possible Worlds, London: Routledge.
FIELD, HARTRY 1989 Realism, Mathematics and Modality, Oxford: Blackwell.
LEWIS, DAVID 1986 On the Plurality of Worlds, Oxford: Blackwell. 1991 Parts of Classes, Oxford: Blackwell.
PEACOCKE, CHRISTOPHER 1999 Being Known, Oxford: Clarendon Press.
SHALKOWSKI, SCOTT A. 2010 IBE, GMR, and metaphysical projects, in Modality: Metaphysics, Logic, and Epistemology, edited by HALE, B. & HOFFMAN, A., Oxford: Oxford University Press, 169-187.
VAN FRAASSEN, BASTIAAN C. 1995 'World' is not a count noun, Nous, 29, 139-157.
NOTES
1. This is essentially the same as what Christopher Peacocke calls 'the integration challenge'. I broaden it slightly to include non-philosophical claims. Christopher Peacocke, [Peacocke 1999, chap. 1]. 2. For an extended treatment of deferentialism and in particular Lewis's deference to mathematics, see [Daly & Liggins 2011]. 3. Strictly speaking, this use of 'could' is an instance of "advanced" or "extraordinary" modalising. It is innocent in this context, since I pose no problem for Lewis that makes this use unavailable to him, given his theory of ordinary modalising. 4. It is hard to acquire useful data on the point, but if this does explain the apparently puzzling phenomenon of defending Lewis on sufficiently many counts but failing to follow him in his metaphysics, it marks out an exception to most other philosophical positions adopted by philosophers. Satisfying conditions similar to those said to be satisfied by Lewis's theory is nearly always taken to warrant adopting the theory, not the cautious hedging of commitments in apparently probabilistic terms. 5. Truth of the belief is assumed. Sufficiency here is merely sufficiency to account for the difference between true belief and knowledge.
Philosophia Scientiæ, 16-2 | 2012 84
ABSTRACTS
Chris Daly defends "explanationism", the view that inference to the best explanation is an acceptable means of providing warrant for a theory. He does so by attempting the bootstrapping operation of warranting explanationism by way of itself. I argue that in the context of metaphysics this defense fails. It fails to be a genuine bootstrapping operation and one of the key premises cannot be warranted by externalist means alone.
Chris Daly défend « l'explicationisme », la position selon laquelle l'inférence a la meilleure explication constitue une façon acceptable de justifier une théorie. Il la défend en tentant de justifier la position explicationiste par ses propres ressources, c'est-a-dire par elle-même. Je soutiens que dans le contexte de la métaphysique, cette défense échoue. L'explicationiste échoue à se justifier par ses propres ressources et l'une de ses premisses centrales ne peut pas être justifiée uniquement de façon externaliste.
AUTHOR
SCOTT A. SHALKOWSKI University of Leeds (UK)
Philosophia Scientiæ, 16-2 | 2012 85
Peacocke’s Epiphany: A Possible Problem for Semantic Approaches to Metaphysical Necessity
Jon Barton
1 Introduction
Peacocke calls the general problem of reconciling our metaphysics with our epistemology in a given area the Integration Challenge. The question is: how do we reconcile our account of what makes the statements of the area true, with our account of how we come to know those statements (when we do)? For the case of metaphysical necessity the challenge promises to be particularly tough. On the one hand there are realists, such as Lewis [Lewis 1986], who put forward what we can call a mind- independent view. For them, possible worlds are concrete worlds just like this one. This gives a most robust metaphysics. However, these worlds are causally disjoint from ours, which prevents any physical interaction. The robust metaphysics brings with it a substantial obstacle to explaining the epistemology. On the other hand, broadly speaking mind-dependent views attempt to explain necessities in terms of facts about ourselves, such as what we are capable of conceiving. Examples of this type of view can be found in [Blackburn 1987] and [Craig 1985]. The approach holds out the promise that the epistemology will be more amenable, since the relevant details are more likely within our grasp. It does, however, run the risk of losing objectivity in the subject matter.
1 Peacocke’s proposal is his principle-based conception. This aims to steer a middle course between the mind-dependent and mind-independent views, reconciling the metaphysics and the epistemology via a theory of understanding for modal notions. He addresses the metaphysics first, by providing an account of the truth-conditions of statements involving metaphysical modalities. These are the Principles of Possibility, which form a substantive set of principles and which determine genuine possibilities. The theory of understanding is made up of possession conditions for the modal
Philosophia Scientiæ, 16-2 | 2012 86
concepts involved; these possession conditions are provided by implicit knowledge of the same principles. Necessity is to be characterized in terms of the substantive account of possibility: this is the Characterization of Necessity, or (following Peacocke) ‘Chzn’ for short. Then, when one reaches a modal judgement based on this understanding, the ‘judgement of the modal truth is explained by the thinker s implicit grasp of principles which make the modal truth hold’ [Peacocke 1999, 162, emphasis in the original]. And thus we should see that such a judgement counts as knowledge.
2 Peacocke speaks of a ‘formidable dilemma of a structural character which the principle-based conception faces [Peacocke 1999, 151]. In short: is the Characterization of Necessity itself necessary? On this question, Peacocke sees himself at risk of being stuck ‘between a rock and a hard place’ [Peacocke 1999, 152]. The epiphany of the title of this paper informs his response to this situation.
3 To show what is involved in Peacocke’s proposed solution I introduce a fictional character, Cautious Peacocke.1 Cautious Peacocke is not lacking in any fact, understanding or knowledge involved in Peacocke s proposal, save for the necessity of the Characterization of Necessity itself, about which she remains agnostic. I claim that the coherence of this character shows that the proposal as it stands is incomplete. Moreover, given the rock and the hard place, it is only by a leap of faith that the proposal can be made good. I conclude with the conjecture that a similar structural issue will affect any such semantic approach to answering the Integration Challenge for metaphysical necessity.2
2 Peacocke’s proposal
The Principles of Possibility are central to Peacocke s proposal. They determine whether a specification of a state of affairs is a genuine possibility, and they also form the implicit knowledge which underpins one s correct understanding of modal notions. The specifications involved are (in Lewis’s terms) ersatz worlds; ‘they are nothing more than sets of [Fregean] Thoughts and/or propositions’ [Peacocke 1999, 141].
4 The approach proceeds in a standard Fregean way, with a semantic assignment giving each atomic concept a semantic value of the correct category; so, for instance, singular concepts receive objects, and monadic predicative concepts receive a function which maps objects to truth-values. Following Peacocke, Iwrite ‘val(C,s)’ for the semantic value of a concept C under an assignment s. I reserve ‘a’ in these contexts to refer to the actual assignment. As well as the atomic cases, there are also complex cases, where the rule for determining the semantic value is a function of the semantic values of its constituents. Writing ‘SV’ for semantic value, these rules are written thus:
R(SV1,...,SVn). Using that notation we can summarise an assignment as follows. Semantic Assignment An assignment s gives (i) an atomic concept C a semantic value: SV = val(C,s)
5 and (ii) a complex concept C a semantic value based on the rule governing C:
val(C, s)= R(val(C1,s),...,val(Cn ,s)). 6 Given the assignments to the atomic concepts, and the rules for complex concepts, the semantic value of a complete Thought can be derived. For an assignment, then, there
Philosophia Scientiæ, 16-2 | 2012 87
will be a corresponding specification which is the set of Thoughts each of which is true under that assignment [Peacocke 1999, 127]. The aim is to identify the genuinely possible specifications by determining whether they are admissible according to the Principles of Possibility; the proposal being that: A specification is a genuine possibility iff there is some admissible assignment which counts all its members as true. [Peacocke 1999, 126] It is the task of the Principles of Possibility to provide the necessary and sufficient conditions for determining the extension of the concept ADMISSIBLE.They are to explain why particular assignments are admissible or not.3
7 The necessary and sufficient conditions form an implicit definition: ‘For the purposes of the theory itself, admissibility can be taken as defined by its role in the theory’ [Peacocke 1999, 138]. Once the concept ADMISSIBLE is adequately defined, we can move to a characterization which gives the truth-conditions for a Thought or proposition to be possible: Characterization of Possibility A Thought or proposition is possible iff it is true under some admissible assignment. [Peacocke 1999, 150] The truth-conditions for a Thought or proposition being necessary are also available: Characterization of Necessity (Chzn) A Thought or proposition is necessary iff it is true in all admissible assignments. [Peacocke 1999, 150]
2.1 The Principles of Possibility
2.1.1 Modal Extension Principle (MEP)
The main Principle of Possibility is the Modal Extension Principle (MEP). This states that ‘the semantic value of [a concept] C according to [an assignment] s is the result of applying the same rule as is applied in the determination of the actual semantic value of C’ [Peacocke 1999, 134]. Using the notation introduced above, this can be written as follows. Modal Extension Principle Where
val(C,a) = R(val(C1,a),...,val(Cn ,a)) then, if an assignment s is admissible,
val(C,s) = R(val(C1,s), ...,val(Cn ,s)) and for dejure rigid concepts, if s is admissible, then val(C,s)= val(C,a). The last clause is to cope with rigid concepts. For instance, ventures Peacocke, one might expect that proper names, if they designate, should designate the same object under all assignments. He writes: [m]y claim is that there is a class of concepts and expressions grasp or understanding of which involves some appreciation that in their case, an assignment is admissible only if it assigns to each one of them its actual semantic value. [Peacocke 1999, 137]
2.1.2 A Constitutive Principle—of Fundamental Kinds
There is another type of Principle of Possibility which Peacocke argues that we must recognise. This is the class of constitutive principles. Where MEP concerns concepts and the level of sense to determine what is genuinely possible, constitutive principles
Philosophia Scientiæ, 16-2 | 2012 88
perform the same role, drawing instead on objects, properties and relations. The proposal needs to take account of the fact that argument might persuade us, for instance, that the racehorse Red Rum has a fundamental kind of ‘horse’. That is: it is an essential property of Red Rum that he is a horse. In that case, no assignment should count as admissible unless it is such that the object which it assigns to ‘Red Rum’ has the property of being a horse.
8 Broadly speaking, argument about the metaphysics of certain objects may lead us to conclude that they have essential properties. Without those properties, the thought runs, the object simply would not be the object that it is. This sort of consideration is captured in the example that Peacocke provides of a constitutive principle: the Constitutive Principle of Fundamental Kinds. If P is a property which is an object x’s fundamental kind, then an assignment is inadmissible if it counts the proposition ‘x is P’as false. [Peacocke 1999, 145]
2.1.3 Principle of Restrained Combination
The two principles introduced so far contribute to the necessary conditions for an assignment to be admissible. In order to complete the notion, we need a sufficiency clause. This is provided thus: An assignment is admissible if it respects the set of conditions on admissibility given hereto. [Peacocke 1999, 149]
9 The Principles of Possibility taken together are to provide the necessary and sufficient conditions to fix ADMISSIBLE. As part of the principle-based conception they provide the explanation of why modal truths hold, and they also form the implicit knowledge which a competent user of modal terms possesses.
2.2 The rock and the hard place
Peacocke finds his proposal is ‘stuck between a rock and a hard place’ [Peacocke 1999, 152]. To articulate the nature of the bind in which he finds himself, we can start by asking the following question. The Characterization of Necessity gives the truth- conditions governing the usage of the necessity operator, but is the characterization itself necessary? A negative answer implies that the proposal has fallen short of its stated aim, since, as Peacocke asserts, the point is to characterize necessity itself, not just some property or properties with which it happens to coincide [Peacocke 1999, 151]. Furthermore, the necessity of the characterization is needed to account for the truth-conditions of iterated modalities. On the other hand, a positive response prompts the question as to whether this further use of ‘necessarily’—Necessarily: A Thought or proposition is necessary iff it is true according to all admissible assignments—is explained by the proposal.
10 Peacocke considers simply adding an assertion to the principle-based conception, to the effect that the Characterization of Necessity necessarily holds [Peacocke 1999, 151]. This will not do, he implies, since if this usage of ‘necessarily’ is not explained by the Principles of Possibility, then the proposal has fallen short of its stated aim [Peacocke 1999, 152]. A bald assertion will not help to explain why the necessity obtains; so the account will fail to provide a satisfactory metaphysics. A theory of understanding based on the implicit knowledge of a set of Principles of Possibility together with such an assertion will fail exactly at that point fully to elucidate the target concept. This failure
Philosophia Scientiæ, 16-2 | 2012 89
will in turn impair the epistemology: the question of how we know that the Characterization of Necessity is necessary will receive no adequate answer. For these reasons Peacocke is committed to (i) the necessity of the Characterization of Necessity, (ii) that this necessity follows from the Principles of Possibility and (iii) that the necessity follows in a fashion which explains why it obtains.
11 The solution which he sees, and which he recounts it took some time for him to realise, is that the Modal Extension Principle applies recursively to itself. He writes: An important point to note about the Modal Extension Principle— one it took me some years to notice—is that it operates recursively. It is self-applicable; it applies to the concept which it helps to define. [Peacocke 1999, 151]
12 How is the recursive self-application intended to help? This is the argument Peacocke gives [Peacocke 1999, 152]. a) The Characterization of Necessity gives the rule for determining the actual extension of ‘necessarily’. b) This rule uses the notion of admissibility, which is constrained by (inter alia)MEP. c) The rule for determining the actual extension of ‘necessarily’ is taken, and MEP is applied to it. d) MEP ensures that on any admissible assignment s, the semantic value of NECESSARILY will include exactly those Thoughts which are true under any assignments which are admissible according to s. e) Therefore on any admissible assignment, the Characterization of Necessity is true. f) Hence the Characterization of Necessity is itself necessary. Thus, the argument concludes that on the principle-based conception, the Characterization of Necessity turns out to be necessary. As the argument states, the Characterization of Necessity uses the notion of admissibility. If the Characterization itself were included as one of the constraints on that concept, then there would be a circularity. But while Chzn is part of the principle-based conception, it is not intended to be one of the Principles of Possibility: precisely not.
13 What I show below is that the recursive self-application of MEP does help, in so far as it supports the equivalents of the modal axioms T and 4 (associated with reflexivity and transitivity respectively) for the Characterization of Necessity itself. However, if Cautious Peacocke is coherent, then that shows us that the recursive self-application is not enough in itself to support the equivalent of the modal axiom 5 (associated with symmetry). That would entail that there is room for coherent dissent from Peacocke’s proposal. For the reasons outlined above, such dissent cannot be dealt with adequately by adding a bald assertion to the principle-based conception.
3 Cautious Peacocke
The question I wish to raise is whether Peacocke’s epiphany issued in a genuine discovery. Did he discover a feature of the theory which had up until then escaped his notice? Or, as opposed to discovering a pre-existing feature of the theory, did he at that moment in some fashion augment it? If the epiphany resulted in a genuine discovery, then Peacocke has indeed avoided the rock and the hard place. On the other hand if it was more a matter of invention, then it has the same effect as the bald assertion discussed above; leading to an unsatisfactory metaphysics, an inadequate theory of understanding and consequently an impaired epistemology. This would put the proposal back between the rock and the hard place.
Philosophia Scientiæ, 16-2 | 2012 90
14 This is an example to illustrate what I mean by a genuine discovery for these purposes, from within the field of mathematics. Suppose Albert has been operating with the differential calculus for a number of years and is proficient with the exponential function, including such facts as:
Suppose also that he understands from his geometry lessons that n is the ratio of the circumference of a circle to its diameter. Last, suppose in the course of his studies he has been introduced to complex numbers, so he is used to manipulating them, and is fully aware that:
It is certainly plausible that Albert remains unaware throughout all of this that in fact these three prima facie distinct mathematical notions from different areas are related by a substitution instance of Euler’s formula (ei0 = cos6 + isin6):
When this is first pointed out to Albert he may well be surprised; for him it is a genuine discovery of a previously unnoticed feature of the mathematical notions with which he is familiar.
15 How might we test for whether we have a genuine discovery or not? I propose that in the case of a genuine discovery, it will not be possible both to understand the rest of the theory and coherently to deny the feature. For Albert to contest the equation will be to betray some misunderstanding of the notions that—we can assume—he has been using perfectly well to date. Provided he is sincere, willing, and bright enough, there is no doubt that we will be able to prove to him that the equation does indeed hold. Conversely, if there is a coherent position available which contests some disputed feature, whilst taking account of the rest of the theory, then we are not dealing with a genuine discovery, but rather the choice of a theorist to go one way rather than another.
16 I claim that the consequence of Peacocke’s epiphany, rather than being a discovery of a previously unnoticed feature of the theory, is more a decision to treat the recursion of MEP as entailing that the Characterization of Necessity be necessary. To justify this claim I introduce Cautious Peacocke. She is a fictional colleague of Peacocke, and is by hypothesis quite as knowledgeable and insightful as Peacocke himself. The one exception is that she does not agree that it follows from MEP’s self-applicable recursion that the Characterization of Necessity is indeed necessary.
17 If the outcome of the epiphany is a genuine discovery of a previously unnoticed feature of the theory, then it will be possible to disclose some incoherence in Cautious Peacocke, since she understands and agrees with Peacocke on the theory up to the moment of revelation. On the other hand, if Cautious Peacocke is coherent, then this shows that the outcome of Peacocke’s epiphany was not a discovery of a previously unnoticed feature of the theory, but instead represents a choice or decision that he made. The leading question, then, is whether or not Cautious Peacocke is coherent.
Philosophia Scientiæ, 16-2 | 2012 91
3.1 A parallel with possible worlds semantics
Can Cautious Peacocke understand Peacocke’s proposal and still contest it? To show that she is coherent I show that by the lights of the theory itself, the Characterization of Necessity can be possibly true and even possibly necessarily true without actually being true. To do this I draw a parallel with Kripke’s possible world semantics, and look at the analogues of the three main relations of accessibility between worlds; reflexivity, transitivity and symmetry.4 This is how the parallel is to work: instead of worlds I consider semantic assignments and instead of accessibility I consider admissibility. What is in focus throughout is the semantic value assigned to the Characterization of Necessity.
18 It is worth emphasising that the analysis offered here is not aimed at answering which modal logic, in general, the principle-based conception supports. That question is taken up by Peacocke in [Peacocke 1999, Appendix A, 191ff]. The answer is that, in general, the principle-based conception supports the modal logic T. He also considers a restricted range of Thoughts, being the range for which the determination of an admissible assignment rests solely with MEP, the Characterization of Necessity, the concepts involved and the Principle of Recombination. For Thoughts in that range, the constitutive principles play no role in the determination of what is genuinely possible [Peacocke 1999, 195]. For this restricted range Peacocke argues that the S4 principle will obtain. The reasoning to establish this runs parallel to that offered above for the necessity of the Characterization of Necessity, and I present it diagrammatically below.
19 As well as the restricted S4, Peacocke suggests that ‘[w]e could also make all the corresponding points for S5’ [Peacocke 1999, 197]. This further suggestion comes in for more scrutiny in what follows.
20 I shall concentrate on one Thought from the restricted range: the Characterization of Necessity itself. What I am examining is whether the structure induced by the Principles of Possibility through the notion of admissibility supports reflexivity, transitivity and symmetry, for the Characterization of Necessity in particular. What I show is that whilst reflexivity and transitivity are unproblematic, there are difficulties associated with symmetry. To facilitate the discussion I introduce the following short- hand for ‘assignment t is admissible from assignment s’: if an assignment t is admissible from s,then I call it s-admissible. That means that t is admissible according to the semantic value assigned to ADMISSIBLE by s. As before ‘Characterization of Necessity’ is abbreviated to ‘Chzn’ .
3.1.1 Reflexivity
First, take the analogue of the modal principle T (□P — P):
21 This holds when assignments are admissible from themselves. Consider figure 1. The rounded rectangles represent assignments, and the arrows show the relation of admissibility between assignments. When a Thought is shown to be true under an assignment, it is written in the appropriate rounded rectangle. We begin with □Chzn being true under s; this entails that Chzn is true under all assignments that are s- admissible.
Philosophia Scientiæ, 16-2 | 2012 92
FIGURE 1: Reflexivity (i)
22 Where reflexivity holds, one of those s-admissible assignments is s itself, as in figure 2. Therefore, if the relation between assignments is reflexive, then whenever □Chzn is true, Chzn is true, which means that T* holds.
23 Inspection of MEP reveals it supports reflexivity. The idea is that admissible assignments are constrained to be determined by the same rules as those employed in the actual assignment. The actual assignment is the actual assignment, and therefore the Principles of Possibility do induce reflexivity.
FIGURE 2: Reflexivity (ii)
3.1.2 Transitivity
Next consider the analogue of 4 (□P — □ □ P):
This is a consequence of transitivity. Transitivity means that where u is t-admissible and t is s-admissible, then u is s-admissible. If transitivity applies, then 4* will hold. To prove this, take any assignment s,where □Chzn. Then on all s-admissible assignments, Chzn is true. Now consider one of those s-admissible assignments, say t. Figure 3 shows the case where Chzn is true under t. Since Chzn is true under t, Chzn is true on any assignment which is t-admissible.
FIGURE 3: Transitivity (i)
24 That means that □Chzn is true under t,where t is any s-admissible assignment (figure 4).
Philosophia Scientiæ, 16-2 | 2012 93
FIGURE 4: Transitivity (ii)
25 Since □Chzn is true under any s-admissible assignment, □□Chzn is true under s (figure 5).
FIGURE 5: Transitivity (iii)
26 Therefore if the relation between admissible assignments is transitive, we have 4*.That is, when □Chzn is true under s,we will also have □□Chzn.
27 Does MEP support transitivity? The answer lies in its recursive self-application. Any s- admissible assignment has the same rule as s for determining the semantic value of ADMISSIBLE. Otherwise it would fail to be s-admissible. If Chzn is true under s,then it will be true under all s-admissible assignments. Hence Chzn will be true under all the assignments admissible according to those, and so on. Thus MEP does grant transitivity; 4* holds good.
3.1.3 Symmetry
Lastly, take the analogue of the modal principle 5◊(◊□P→□P), which is the dual of 5 (□P→□◊P).
28 This is a product of symmetry. Symmetry says that when t is s-admissible then s is t- admissible. If the relation between admissible assigments is symmetric, then 5◊* will hold. To prove this, begin with the antecedent, ◊□Chzn. It is possible that Chzn is necessary, so by the Characterization of Possibility we know that there is at least one s- admissible assignment under which □Chzn is true. Call it t (figure 6).
Philosophia Scientiæ, 16-2 | 2012 94
FIGURE 6: Symmetry (i)
29 Chzn is necessary under t, so by the Characterization of Necessity, Chzn is true under all t-admissible assignments. Assuming that symmetry holds, then since t is s- admissible, s is t-admissible. Since s is t-admissible and Chzn is true on all t-admissible assignments, Chzn is true under s as shown in figure 7.
FIGURE 7: Symmetry (ii)
30 If Chzn is true under s, then Chzn is true on any s-admissible assignment. By the Characterization of Necessity, that makes Chzn necessary under s (figure 8).
FIGURE 8: Symmetry (iii)
31 Hence, on the assumption that admissibility holds symmetrically between assignments, we have shown that wherever we have ◊□Chzn we also have □Chzn, which is for 5◊* to hold. The outstanding question is whether MEP licenses the symmetry of admissibility between semantic assignments, for the restricted range of Thoughts which includes Chzn.
3.2 The Cautious contention
Cautious Peacocke maintains that MEP does not license symmetry in the relation of admissibility between semantic assignments, for the restricted range of Thoughts
Philosophia Scientiæ, 16-2 | 2012 95
under consideration, which includes Chzn itself. She admits that if Chzn is true, then it is so necessarily. However, it is consistent with the structure induced by MEP that Chzn be false. Figure 9 presents Cautious Peacocke’s reason for doubt.
32 Under s it is possible that Chzn is true, and so possible that it is necessarily true. But it need not be true, and so as it happens, need not necessarily be true. Were it to follow from MEP that the relation between admissible assignments turned out symmetric then this position would not be coherent. But where both reflexivity and transitivity do follow—and hence T* and 4*—symmetry does not. And that means that 5◊* fails.
33 This is how things stand, intuitively. The principles which constrain the concept ADMISSIBLE—chiefly MEP—cannot use that very concept. If they did, then the definition would be circular. Since the constraints cannot make use of the concept, the most they can do is to guarantee assignments to ADMISSIBLE downstream, so to speak. Hence we do get transitivity. But because no use can be made of ADMISSIBLE, no guarantee can be made of what has happened upstream, as it were. Hence we have no guarantee of symmetry.
FIGURE 9: Cautious Contention
3.3 Cashing out the contention
Peacocke provides a condition sufficient for symmetry (5) to hold on the principle- based conception. I now introduce that condition, and cash out the intuitive picture from the previous section more formally in order to locate the potential circularity more precisely. To begin with, recall that the actual assignment ‘assigns to each concept its actual semantic value, and to each property its actual extension’ [Peacocke 1999, 194]. Next we introduce the notion of a second-level assignment, which is ‘an assignment which assigns semantic values to the concepts ADMISSIBLE and NECESSARY themselves’ [Peacocke 1999, 194]. A second-level assignment ‘itself is admissible only if it respects the rules determining the actual semantic values of ADMISSIBLE and NECESSARY. According to the principle-based conception, these rules are given in the MEP and Chzn themselves’ [Peacocke 1999, 194]. The suggested condition which is sufficient for 5 to
hold is: ‘if an assignment s1 ... is admissible, then any admissible second-level
assignment s2 is such that s1 is in the extension of ADMISSIBLE according to S2’ [Peacocke 1999, 197].
34 I use ‘ADMS ()’ to denote the semantic value assigned to ADMISSIBLE by assignment s,and
‘a’ refers to the actual assignment, as before. Thus ‘ADMa (s)’is true just when the
Philosophia Scientiæ, 16-2 | 2012 96
semantic value assigned to ADMISSIBLE by the actual assignment includes the assignment s in its extension; which is to say, just when s is admissible. Then, with ‘s’ and ‘t’ ranging over first- and second-level assignments respectively, the condition suggested by Peacocke is equivalent to:
35 ADMa(s) → (∀t)(ADMs(t) → ADMt(s)) With U also ranging over second-level assignments, we can add to Peacocke’s suggestion the condition for transitivity (4):
36 ADMa(s) → (∀t)( ∀u)(ADMs(t) & ADMt(u) → ADMs(u)) and finally reflexivity (T):
37 ADMa(s) → ( ∀t)(ADMs(t) → ADMt(t)).
38 The distinction between the first-and second-level assignments in this fashion is consonant with a basic tenet of the principle-based conception: that for any given concept C there will besomerule R whose application determines the actual semantic value of C’ [Peacocke 1999, 132]. MEP is then brought to bear upon the rule in order to help constrain which assignments are admissible and so determine what is and what is not a genuine possibility. The working assumption is that there is a rule which determines the actual semantic value of ADMISSIBLE. This, however, is a unique case, since the actual semantic value assigned to ADMISSIBLE is to be implicitly defined by the role the concept plays in the theory. For this concept we cannot rely upon a pre- theoretical rule for determining the actual semantic value, since there is no such rule.
39 The actual semantic value given to ADMISSIBLE will depend, in part, on what happens at the second-level assignments. And what happens at the second-level assignments is, by design, dependent on what happens at the actual assignment. For this special, yet crucial, case of ADMISSIBLE, we cannot hold the actual assignment apart from the second- level assignments. There is support for this observation: according to Peacocke’s definition given above, the actual assignment should count as a second-level assignment, since it too assigns semantic values to the concepts ADMISSIBLE and NECESSITY. Assuming that is correct, what is the impact? If the actual assignment should properly be counted as a second-level assignment, then it is legitimate to substitute ‘a’ for ‘t’ in Peacocke’s condition for symmetry:
40 ADMa(s) → (ADMs(a) → ADMa(s)) which highlights the circularity involved. Such circularity does not result from substitutions of ‘a’ in the other conditions. For reflexivity, this is trivially so:
41 ADMa(s) → (ADMs(a) → ADMa(a)). For transitivity, there are two relevant substitution-instances, and neither
42 ADMa(s) → ( ∀u)(ADMs(a) & ADMa(u) → ADMs(u)) nor
43 ADMa(s) → ( ∀t)(ADMs(t) & ADMt(a) → ADMs(a)) exhibits the circularity.
4 Conclusion
The recursive self-application of MEP, together with the implicit definition of the target notion, and under the condition of symmetry, mean that the rule which
Philosophia Scientiæ, 16-2 | 2012 97
determines the actual semantic value of ADMISSIBLE depends upon itself. If that is right, then the concept ADMISSIBLE is impredicatively defined. Supposing that the condition required for symmetry involves an inherent circularity, how harmful is it for the principle-based conception? It would not imply that the condition identified by Peacocke as sufficient for symmetry could not—nor indeed, does not—obtain. But from there onwards the consequences of the condition obtaining are much the same as those following from the inclusion of the bald assertion. Assume the condition does obtain. Then the theory of understanding which embodies the Principles of Possibility within the possession conditions of the modal concepts will fail fully to elucidate the key notion. Furthermore, on the principle-based conception the theory of understanding underpins the epistemology, and therefore a failure fully to elucidate the key notion will impair that epistemology.
44 The concern about symmetry is crucial, since it allows Cautious Peacocke coherently to contest the proposal. According to the test introduced above the coherence of Cautious Peacocke shows that the result of Peacocke’s epiphany is not a discovery of a previously unnoticed feature of the theory. Certainly the epiphany induced the conviction that the actual assignment is one where Chzn is necessarily true, such as assignment t in figure 9. However, the proposal as it stands does not itself fully support this conviction. In particular, as Cautious Peacocke can coherently hold, the actual assignment may be s instead.
45 To escape from the rock and the hard place, the proposal requires symmetry of admissibility between assignments, at least for the restricted range of Thoughts which includes Chzn. The theory as it stands need not be interpreted as inducing this symmetry: that is the lesson of the coherence of Cautious Peacocke. The inclusion of the bald assertion would result in an unsatisfactory metaphysics, an inadequate theory of understanding, and thus an impaired epistemology. Likewise if the condition for symmetry simply happens to obtain. It seems the only solution, then, is the leap of faith which Peacocke is happy to make, and Cautious Peacocke is not.
4.1 Conjecture
46 I finish with a conjecture that the structural issue brought out above will apply to any similar semantic way with necessity. Suppose we have the notion of semantic assignments and some form of accessibility relation between them, where Peacocke has admissibility. We can grant reflexivity and transitivity for the accessibility relation. The conjecture is that in these circumstances, one will be unable to establish symmetry of the accessibility relation without making use of the accessibility relation itself in the specification of that relation. Making use of the relation in its definition will introduce a circularity. In the case where we have no symmetry, and the case where we have a circularity, there will be the possibility of introducing a coherent objection on the lines of Cautious Peacocke above. If this conjecture is correct, then the chances of success of such semantic approaches to metaphysical necessity are slim.5
Philosophia Scientiæ, 16-2 | 2012 98
BIBLIOGRAPHIE
BLACKBURN, SIMON 1987 Morals and modals, in Fact, Science and Morality: Essays in Honour of A. J. Ayer’s Language, Truth and Logic, edited by MACDONALD, GRAHAM &WRIGHT, CRISPIN, Oxford: Blackwell, 119-141.
CRAIG, EDWARD 1985 Arithmetic and fact, in Exercises in Analysis, edited by HACKING, I., Cambridge: Cambridge university Press, 89-112.
HALE, BOB 1989 Necessity, caution and scepticism, in Proceedings of the Aristotelian Society, Supplementary Volume LXIII, 175-202.
HEATHCOTE, ADRIAN 2001 Yes, but what is the mother of necessity?, Philosophical Books, 42, 92-100.
LEWIS, DAVID 1986 On the Plurality of Worlds, Oxford: Blackwell.
PEACOCKE, CHRISTOPHER 1997 Metaphysical necessity: understanding, truth and epistemology, Mind, 106, 521-574. 1999 Being Known, Oxford: Oxford University Press.
SULLIVAN, PETER 1998 The "Modal Extension Principle": A question about Peacocke’s approach to modality, Mind, 107, 653-660.
WRIGHT, CRISPIN 1980 Wittgenstein on the Foundations of Mathematics, London: Duckworth. 1989 Necessity, caution and scepticism, in Proceedings of the Aristotelian Society, Supplementary Volume LXIII, 203-238.
NOTES
1. I suggest that, if coherent, Cautious Peacocke would make room for an Eccentric (the Cautious Man’s heir) about necessity; see [Wright 1980], [Wright 1989] and [Hale 1989]. I do not pursue that suggestion further here. 2. I focus exclusively on the structural issue which Peacocke himself identifies as ’a rock and a hard place’. A broader-brushed scepticism about the principle-based conception can be found in [Heathcote 2001]. An earlier exposition of Peacocke’s approach [Peacocke 1997] prompted [Sullivan 1998], which I have also found instructive. 3. Peacocke makes a simplifying assumption that the assignments are total [Peacocke 1999, 128]. This is for ease of exposition, and he discusses how it might be relaxed in Appendix B [Peacocke 1999, 198 ff]. 4. One might think that employing a broadly Kripkean approach is at odds with the principle- based conception. I do not think Peacocke would share such doubts, since he writes ’[i]t would be quite wrong to see the principle-based conception as in any way incompatible with the Kripke- style semantics’ [Peacocke 1999, 197]. For Peacocke, the issue between the principle-based
Philosophia Scientiæ, 16-2 | 2012 99
conception and Kripke-style semantics is one of explanatory priority, rather than incompatibility. 5. For helpful comments on previous drafts, I should like to thank the two anonymous referees, Oliver Black’s reading group, Bob Hale, Keith Hossack, Colin Johnston, and David Levy.
RÉSUMÉS en Dans son livre intitulé Being Known, C. Peacocke se propose de repondre à la question de savoir comment nous en venons a connaitre des nécessités métaphysiques. Il développe une conception sémantique reposant sur des principes comprenant, d’une part, ses Principes de Possibilité — qui fournissent les conditions nécessaires et suffisantes pour un nouveau concept, « l’admissibilité » — et d’autre part des caractérisations de la possibilité et de la nécessité a l’aide de ce nouveau concept. Je me concentre sur une caractéristique structurelle, a savoir l’application récursive a l’œuvre dans la spécification de «l’admissibilité ». Apres avoir esquisse la proposition de Peacocke, j’introduis un personnage fictif, Peacocke-prudent. Je soutiens que la cohérence de ce personnage montre que la proposition de Peacocke ne peut pas être satisfaite. Je conclus en conjecturant qu’un échec similaire se présentera pour toutes les tentatives de fonder l’épistemologie de la nécessité métaphysique sur de telles bases semantiques.
In his Being Known Peacocke sets himself the task of answering how we come to know about metaphysical necessities. He proposes a semantic principle-based conception consisting of, first, his Principles of Possibility which provide necessary and sufficient conditions for a new concept ’admissibility, and second, characterizations of possibility and of necessity in terms of that new concept. I focus on one structural feature; viz. the recursive application involved in the specification of ’admissibility. After sketching Peacocke’s proposal, I introduce a fictional protagonist, Cautious Peacocke, whose coherence I claim shows that Peacocke s proposal cannot be made good. I conclude with the conjecture that similar failure will attend any such semantic- based attempts to ground the epistemology of metaphysical necessity.
AUTEUR
JON BARTON Department of Philosophy, King’s College London (United Kingdom)
Philosophia Scientiæ, 16-2 | 2012 100
What is Absolute Necessity?
Bob Hale
Preamble
If one believes that the notions of necessity and possibility receive their most fundamental explanation in terms of worlds—so that what is necessary is what is true in all possible worlds, and what is possible is what is true in at least one—then one might seek to explain the notion of absolute necessity by saying that what is absolutely necessary is what is true in absolutely all worlds without restriction. The idea would be, perhaps, to contrast absolute necessity with what holds true only throughout some restricted range of worlds—say, the worlds at which our laws of physics hold, it being supposed that there are worlds which are in some sense possible, but at which our physical laws fail. Although I think there is something right about this explanation, and although I do, of course, recognise the enormous utility of a semantic account of modalities in terms of worlds, or something like them, I do not think that modal notions or modal facts can be adequately explained in terms of, much less reduced to, facts about worlds.1 This is not because I think they can be more adequately explained— in non-modal terms—in some other way. Of course, there have been other attempts to explain modality. In pre-Kripkean times, in the heyday of logical empiricism and the linguistic theory of the apriori, necessity was seen as having its source in facts about meaning—convention was the mother of necessity. Even the most celebrated critic of meanings and analyticity could be found asserting that necessity resides in the way we talk about things, not in the things we talk about’.2 I reject this kind of explanation altogether, even for the so-called3 conceptual or analytic necessities which it seems best suited to explain.
1 Although I think that modal notions and facts involving them are irreducible— i.e., they cannot be explained away, in other, non-modal, terms—I don’t think that means we can’t say anything useful about what necessity and possibility are, or about their source or basis. On the contrary, I think there is a lot to be said—much more than I can cover in a short paper. Broadly speaking, I think a non-reductive explanation of the nature of necessity can illuminate by bringing out the way in which the class of necessities as a
Philosophia Scientiæ, 16-2 | 2012 101
whole is structured, with necessities of a certain kind playing a basic or fundamental role, in terms of which other necessities may be seen as derivative because consequences of more basic ones. I hope this broad idea will become clearer when I get to details later in the paper. The notion of absolute necessity provides a useful starting point.
1 Three conceptions of absolute necessity4
Relative necessity is necessity relative to some body5 of propositions. p is necessary relative to Ф if p must be true, given that all the members of Ф are true. There are as many kinds of relative necessity as there are different bodies of propositions, nearly all of them completely uninteresting. Every proposition p is necessary relative to {p}, as well as to many other bodies of propositions. More interesting kinds of relative necessity can be got by taking the members of Ф to share some interesting property, such as all being laws of physics.6 Whether physical and, perhaps more generally, natural necessity can be adequately explained as forms of relative necessity is a further, and rather controversial, question. I can set it aside here.
7 2 That p is necessary relative to Ф is usually expressed as a strict conditional □(Ф ᑐ p), with □ interpreted as logical necessity. This formulation is not un-problematic (see [Humberstone 1981]), but it is close enough for my purposes.
3 That relative necessity presupposes some non-relative, or absolute, form of necessity— expressed by □ in the usual formulation—seems obvious and indisputable. On the face of it, if □ in □(Ф ᑐ p) were itself relative, there would have to be some Ψ and some □’ such that □(Ф ᑐ p) abbreviates D(Ф ᑐ p)). 4 Claiming that □’ is relative threatens an apparently vicious infinite regress.8
5 What is it for a kind of necessity to be absolute? One might say that it is simply for it to be non-relative. I doubt that this is a sufficient explanation, since our explanation of relativity presupposes a non-relative notion. I can think of three moderately plausible characterizations:
Limit of relative necessity
There is an obvious and simple way to generalise on the idea of relative necessity. A proposition p may be necessary to one body of propositions, Ф,butnot necessary relative to some other body, But there is a kind of limiting case— where no matter what set of propositions Ф we choose, p is necessary relative to Ф. In ordinary, non-limit, cases of □(Ф ᑐ p),it will often be the case that p’s truth-value depends on the truth- value of the conjunctive proposition Ф—i.e., that if Ф were not true, p might not be true either. But in the limit case, since p is necessary relative to every Ф, its truth-value cannot depend on that of any particular Ф. Inview of this, we canregard the limit case as defining a kind of absolute necessity—limit-absolute necessity:
□ limp =df ∀Ф □(Ф ᑐ p).
Absence of competing possibility
The basic idea here is, roughly, that p is absolutely necessary if there is no sense in which the opposite, ¬p, is possible:
Philosophia Scientiæ, 16-2 | 2012 102
27 27 9 □ maxp = df ¬∃ D0 D0 ¬p. 6 This won’t quite do as it stands, since the opposite of just about any plausibly absolute necessity may be epistemically possible—i.e., true for all we know. But it seems clear that the fact that—as things stand—it is possible for all we know that there is a very large even number which is not the sum of two primes ought not to count as showing that Goldbach’s Conjecture, if true, is not absolutely necessary. To make this idea precise, 27 we would need to impose a suitable restriction on the range of D0 to relevantly competing kinds of possibility (see [Hale 1996]). Perhaps it would be enough to restrict attention to alethic modalities.10 Saying that a kind of necessity is absolute in this sense amounts to claiming that it implies, and so is at least as strong as, any other comparable kind of necessity— hence my label maximal’.
Absolutely general counterfactuality: acfacp =df ∀q(q □→ p)
In simple terms, the idea is that what is absolutely necessary is what would be the case, no matter what else was the case. The idea has two parts. First, that we can explain the unary necessity operator, □,bymeans of abinarycounterfactual conditional operator, □→, by generalisation on the antecedent: p is necessary iff p would be true no matter what (else) were true.11 And second, that we can explain absolute necessity in terms of the absolute (i.e., completely unrestricted) generality of the propositional quantifier12—it is absolutely necessary that p iff for absolutely every q, q □→ p.
2 Logical necessity and absoluteness
By logical necessity, I mean the kind of necessity with which the conclusion of a valid inference follows from its premise. If one takes the necessity of logical consequence as basic, one can easily explain what it is for propositions to be logically necessary—a conditional p ᑐ q is logically necessary (i.e., □(p ᑐ q))iff q is a logically necessary consequence of p. And quite generally, □p iff p is a logically necessary consequence of the empty set of premises.
7 Iwrite □ Ф.p to abbreviate □(Ф ᑐ p). Some obvious facts about relative and limit- necessity are:
8 (Inclusion) If Ф Ψ then p entails ⊆ □ Ф 9 (Null) □Øp ⟷□limp. Since what is logically necessary is just what follows from the null set of premises (i.e.,
□p ⟷ □Øp), it immediately follows that, if we interpret □ in the definiens for □lim as
logical necessity, then limit-absoluteness collapses to logical necessity, i.e., □limp ⟷ □p. 10 It is also obvious that at most one kind of necessity can be maximally-absolute. For if □ 27 27 and ■ are both maximal, □p iff ¬∃ D0 D0 ¬p iff ■p,so that □ and ■ must coincide.
11 Under some plausible, but not uncontroversial, assumptions, one can prove that logical necessity is maximal, so that every absolute necessity must be logical. The most 27 important assumptions are that any kind of alethic possibility, D0 ,is closed under logical consequence and conforms to a form of the law of non-contradiction. That is:
27 27 27 ( D0 -closure) If D0 A and □(A ᑐ B) then D0 B 27 27 (LNC D0 ) ¬ D0 (A ᐱ¬A).
Philosophia Scientiæ, 16-2 | 2012 103
Given these assumptions, one can prove: 27 27 (McFetridge’s Lemma) If □(p ᑐ q) then ¬∃ D0 D0 (p ᐱ¬q). Proof.Suppose □(p ᑐ q).Then □((p ᐱ¬q)D q).Since □(¬q ᑐ¬q), □((p ᐱ¬q) ᑐ ¬q).Hence 27 27 27 27 □((p ᐱ¬q) ᑐ (q ᐱ¬q)). Suppose that for some D0 , D0 (p ᐱ¬q). By D0 -closure, it follows that D0 27 27 27 (q ᐱ¬q),contrary to LNC D0 .So by reductio ad absurdum, ¬∃ D0 D0 →(p ᐱ ¬q). □ Using this, we can then prove:
(Logical necessity is maximally-absolute) If □p then □maxp
27 Proof. Suppose □p.Then □((p ᑐ p)ᑐ p). By McFetridge’s Lemma, ¬ D0 ((p ᑐ p)ᐱ ¬p) for any 27 27 27 27 27 D0 .But if ∃ D0 D0 ¬p then since □(¬p ᑐ ((P ᑐ p) ᐱ ¬p)), D0 ((p ᑐ p) ᐱ ¬p) by D0 -closure. By 27 27 reductio ad absurdum, ¬.∃ D0 D0 ¬.p. □
12 The modal principles required for these proofs are the usual Rules of Necessitation and □-distribution across ᑐ,and standard □-introduction and □-elimination. These all hold in any reasonable modal logic. The non-modal principles needed all hold in minimal logic.
13 As far as I can see, the proofs require the principle that if ⊢ A then ⊢ B ᑐ (A ᐱ B). Relevant logicians reject this, because it allows one to prove ‘irrelevant’ theorems such as ⊢ q ᑐ (p ᑐ p). I am not much disturbed by the fact that my proofs can’t be carried out in a relevant logic, since I’m inclined to regard the rejected principle as independently compelling (and so a reason not to insist upon relevance).
14 As I said, both main assumptions are controversial.13 To that extent, at least, the claim that logical necessity is maximally-absolute must be viewed as problematic. But for the claim that logical necessity is absolute in our remaining sense—the generalised counterfactual sense—there is a quite straightforward semantic argument.14
(General counterfactual absoluteness) If □p then ∀q(q □→ p)
Proof. Suppose □p. Then □limp, so that ∀Ф□(Ф ᑐ p).Consider any particular q. Then □(q 15 ᑐ p), i.e., q ᑐ p is true at every possibility. Hence p is true at all q-possibilities, and a fortiori true at all closest such possibilities. So q □→ p. But q was arbitrary, so ∀q(q □→ p). One might think one could prove the converse implication, i.e., that any counterfactually-absolute necessity is logical. For can’t we argue as follows? Suppose ∀q(q □→ p) and consider any r.Then r □→ p. Hence p is true at all closest r-possibilities. But r was arbitrary, and every possibility w is one of the closest r- possibilities, for some choice of r— so p is true at all possibilities. Hence q ᑐ p is true at all possibilities, for any q. So □(q ᑐ p).But q was arbitrary, so ∀q □(q ᑐ p) (i.e.,
□limp, so that □p).
15 The problem lies with the step from ’q ᑐ p is true at all possibilities, for any q’ to □(q ᑐ p),where □ expresses logical necessity. This step assumes that logical necessity can be identified with truth at all possibilities—but this effectively assumes what is to be proved. Truth at all possibilities is necessary for logical necessity (if logical necessity is to be a species of absolute necessity), but the assumption that it is sufficient is tantamount to the assumption that there are no other, non-logical, absolute necessities in the generalised counterfactual sense—i.e., that all such absolute necessities are logical.
Philosophia Scientiæ, 16-2 | 2012 104
16 The failure of the converse implication is important. It leaves open the possibility that there are absolute necessities—in the generalised counterfactual sense—other than logical necessities. If the arguments I gave earlier are correct, limit-absolute and maximal-absolute necessities are always logical—i.e., there can be no non-logical absolute necessities in either of these senses of absolute’. Since I think it is very plausible that there are non-logical absolute necessities— for example, arithmetical ones16—I think this is a quite strong reason to prefer the generalised counterfactual explanation of absoluteness.
17 To sum up, of the three conceptions of absolute necessity considered here, the first two —limit- and maximal-absoluteness—collapse, at least on plausible assumptions, into logical necessity; but the third—general counterfactual absoluteness does not. If one believes, as I do, that some non-logical necessities are absolute, this gives one a strong reason to prefer my third conception, and I shall assume it in the sequel.
3 The logic of absolute necessity
It is a further advantage of the generalised counterfactual explanation that it supports a straightforward argument to show that absolute necessity conforms to the S4 and S5 principles, i.e., that □pᑐ□□p and that ◊□pᑐ□p. 18 The argument is semantic. We assume the standard Stalnaker-Lewis semantics17 for □→. It is easily verified (Appendix 1) that if we define □p as Vq(q o→ p), this semantics induces the standard truth-condition for □p to be true at any given possibility: □p is true at w iff for every w’ accessible from w, p is true at w’.
19 This requires no special assumption about the accessibility relation. But given that our intention is to capture an absolute notion of necessity, it is reasonable to require that the accessibility relation be universal—i.e., each possibility is accessible from itself and every other. When we define □p as a universally quantified counterfactual, ∀q(q □→ p),the quantifier ∀q is to be understood as absolutely unrestricted—as ranging over all propositions whatever. This gives it akind of modal strength additional to that carried by a singular counterfactual. Since no proposition, whether actually true or not, is excluded from the range of its quantifier, the claim is effectively equivalent to the claim that no matter how things might have been, it would still have been true that p— expressed in terms of possibilities, that it is true that p at every possibility without restriction. As we have seen, the induced condition for □p to be true at a possibility w is the usual one—that p be true at every possibility w’ accessible from that possibility. If there were possibilities inaccessible from w at which p is false, then, since those possibilities are possibilities (although not possibilities relative to w), p would not be true at all possibilities without restriction—it would be true only at all possibilities possible relative to w. In that sense, its necessity would be merely relative (truth throughout a restricted class of possibilities).
20 If that is right, we can assume that in any model, all possibilities are accessible from any given possibility—so that we can just suppress reference to accessibility. It is then no surprise that we can prove the characteristic S4 and S5 principles (Appendix 1).18
Philosophia Scientiæ, 16-2 | 2012 105
4 Logical and metaphysical modalities
Our discussion thus far has been quite general and abstract. With the exception of logical necessity, I have avoided reference to specific kinds of alethic modality. My aim has been to explain a notion of absolute necessity which leaves it open which specific kinds of alethic necessity are absolute. If it is agreed that logical necessities must be true at all possibilities, then the semantic argument discussed in the preceding section establishes that logical necessities are absolute. 19 But beyond that, nothing is settled— our definition of absoluteness leaves it open whether there are non-logical absolute necessities.
21 It is widely accepted that there are metaphysical necessities which are not logical necessities. If we also accept 20 that there are no logical necessities whose negations are metaphysically possible—i.e., that logical necessities are always metaphysically necessary—then logical necessities are a proper subclass of metaphysical necessities.
22 It follows that in a standard sense of stronger’, logical necessity is stronger than metaphysical—if we write □ for logical and ■ for metaphysical necessity, whenever □A, ■A, but not conversely. If the corresponding kinds of possibility are related to □ and ■ in the usual way—so that ◊A iff ¬□¬A and 4A iff ¬■¬A—then whenever ♦A, ◊A, but not conversely. That is, ◊ is weaker than ♦
23 How should we picture this relationship in semantic terms? If we assume that logical possibility is not just weaker than metaphysical, but weaker than any other kind of possibility, one picture of the space of possibilities we might adopt has the whole space filled by logical possibilities, and a proper subspace filled by metaphysical possibilities:
24 But this picture is not mandatory. It involves seeing metaphysical necessities as holding, not at all possibilities whatever, but only throughout a restricted class of them. The picture is indeed inevitable, if we think of the points in the space of possibilities as logical possibilities—for then our assumption that it may be metaphysically but not logically necessary that p, or logically but not metaphysically
25 possible that p, demands that there be possibilities which are not metaphysical possibilities. However, we could instead think of the difference between logical and metaphysical modalities in a quite different way. For we are not forced to understand the difference in terms of different (more or less inclusive) kinds of possible situations in which logical and metaphysical necessities and possibilities are true. Instead, we could think of necessities of both kinds as being true throughout the whole space of possibilities, and view the difference between them as like the difference between broader and narrower kinds of logical necessity, rather than like that between, say, logical necessity and some kind of merely relative necessity such as biological or technical necessity.
Philosophia Scientiæ, 16-2 | 2012 106
26 Let me explain this more fully. What is biologically necessary is, roughly, what must be so, given the actual laws of biology, or the nature of living organisms. What is biologically impossible may well be logically possible. So the right picture, in terms of possibilities, identifies the biologically necessary as what holds true throughout only a restricted range of possibilities. But with logical necessity a different picture seems appropriate. We can distinguish between narrower and broader kinds of logical necessity. There are, for example, the logical necessities of propositional logic, those of first-order logic, and so on. One might think of logical necessities as those necessary propositions which can be expressed making essential use of just logical vocabulary. Alternatively, one might adopt a broader, more generous conception which encompasses what might otherwise be classed as analytic or conceptual necessities, and so recognises as logically necessary truths whose expression essentially involves non- logical vocabulary. There is no need to resolve that issue here. Even if one restricts logical necessities to truths whose expression essentially involves only logical vocabulary, there are broader and narrower classes of logical necessities. But it does not seem correct to think of the necessities of propositional logic as holding true throughout a more extensive class of possibilities than those of first-order logic which depend on their quantificational structure. Rather, we should surely think of necessities of both kinds as holding throughout the whole space of possibilities. There is, for example, no possibility at which it is true that my socks are red but not true that something is red, for all that the inference ‘My socks are red. So something is red’ is not valid in propositional logic. The difference between the necessities of propositional logic and those of first-order logic is not a difference in the ranges of possibilities throughout which they hold. At the linguistic level, it is simply a difference in the kind of vocabulary required for their adequate expression. At what one might think of as a more fundamental—ontological or metaphysical—level, it is a difference in the range of entities essentially involved in explaining why these different kinds of necessities hold.
27 Once we reject the more and less inclusive classes of possibilities picture for different kinds of logical necessity, we can just as easily reject it as the right picture for the relation between metaphysical and logical necessities. Logical necessities are properly included among metaphysical necessities, just as the necessities of propositional logic are properly included within those of first-order logic. But logical and metaphysical necessities alike may be true throughout the whole space of possibilities. In particular, there may be no possibilities at which some metaphysical but non-logical necessities fail to be true.21 The difference between logical and metaphysical necessities lies, not in the ranges of possibilities throughout which they hold, but—at the linguistic level—in the kind of vocabulary essential to their expression, and more fundamentally, in the kinds of entities essentially involved in explaining them.
5 The essentialist theory of modality
The alternative picture of the relations between logical and metaphysical necessities I’ve just sketched fits very badly with the view that necessity and possibility are fundamentally matters of what holds true at all or some possible worlds.22
28 But it fits very well with, and can be explained by, what I shall call the essentialist theory of modality. A full exposition and defence of this theory lies well beyond the scope of this paper. Here I shall be able to give only a brief outline of the main ideas.23
Philosophia Scientiæ, 16-2 | 2012 107
29 The theory can be seen as answering the question: What is the source, or basis, of necessity and possibility? Some philosophers—most famously David Lewis—have answered: There are many possible worlds besides the actual world. Necessity is simply truth in all of them, and possibility truth in at least one. Other philosophers, mainly before Lewis, have said: Necessity is just truth in virtue of meaning. It is not in the world apart from us, but is simply the product of our conventions for using words. The essentialist theory rejects both these answers, and says: Necessity has its source in the natures of things.
30 To understand this theory, the first things one needs to know are what things are, and what the nature of a thing is.
31 By things, Imeanthings of all kinds or types—so not just objects (including abstract objects such as numbers and sets, as well as concrete objects such as particles and people), but also properties, relations and functions of all types and levels—properties of concrete objects, such as being white, or having negative charge; properties of abstract objects, such as being a natural number, or being prime; properties of properties of objects, such as being rare (i.e., being a property possessed by few objects); and similarly for relations and functions. Anything we can talk about is a thing.24
32 By the nature, or essence, of a thing, I mean what it is to be that thing. This is what is given by a definition of the thing. For example, the definition of circle is: set of points in a plane equidistant from some given point. The definition of mammal is: air-breathing animal with a backbone and, if female, mammary glands.25 This is definition in an Aristotelian sense—what is defined is not, or not primarily, a word for the thing, but the thing itself. A correct definition may serve to state what the word means—as with the previous examples—but it need not: for example, gold is the element with 79 protons per atom, but this is not what the world ‘gold’ means.
33 The simplest way to explain the theory is by examples. So consider first the propositions:
34 1 < 2
35 1 + 1 = 2. I claim that these are necessarily true, and indeed absolutely necessary. Why is that? The essentialist answer is that the first is necessary because true in virtue of the nature of the natural numbers 1 and 2, and of the relation of being less than—to be the number 2 just is to be the natural number which immediately follows 1, and for a natural number x to be less than a natural number y is just for y to follow after x in the sequence of natural numbers. Similarly, the second is necessary because true in virtue of the nature of the numbers 1 and 2 and of the operation (function) of addition: addition (of natural numbers) is that function of two natural numbers x and y whose value is the natural number z iff z is the yth successor of x. Here is another example. Consider the proposition: If a conjunction of propositions A and B is true, A is true. I claim this too is absolutely necessary. Why? The essentialist answer is very simple: it is necessary because it is true just in virtue of the nature of conjunction. Conjunction just is that function of two propositions which has a true proposition as its value for those propositions as arguments if and only if both arguments are true.
36 Some necessities, like this last example, hold just in virtue of the natures of various logical entities—the functions of conjunction, negation, disjunction, quantification,
Philosophia Scientiæ, 16-2 | 2012 108
identity, etc. These are the purely logical necessities. Other necessities depend upon the natures of non-logical entities—just as in my earlier examples, which depend upon the natures of certain mathematical entities. The essentialist theory is a kind of obvious generalisation of these claims. Things of all kinds have natures. Metaphysical necessities in general are just those necessities which hold in virtue of the nature of some things or other. That is, it is metaphysically necessary that p iff there are some
things X1,... ,Xn such that p is true in virtue of the natures of X1,Xn.
37 This is perhaps enough to give you an idea of the essentialist theory. A fuller explanation would need to say much more about the structure of the theory, and about the kind of explanation it provides. This would require a defence of the notion of essence or nature against the charge that these notions are unintelligible, or at least too unclear to be used for philosophical purposes. There need to be limits, or restrictions, upon what counts as belonging to the nature of a thing—if just any necessary truth about a thing counts as part of its nature, the theory becomes explanatorily vacuous. If the notion of essence is to have any explanatory use, there will need to be a distinction between those necessities which hold directly in virtue of a thing’s nature, and those which are more or less remote logical consequences of facts about its nature, along with the natures of other things. Among the questions that we shall need to answer are: Can the theory account for all metaphysical necessities? How does it account for metaphysical possibilities? Are all metaphysical necessities absolute? Canthetheory fully explain those necessities which are absolute, such as logical and mathematical necessities? I can’t discuss all these questions here. In my concluding section, I’ll outline my answer to the last of them.
6 Absolutely necessary beings
The first point to be clear about is that this question is distinct from the question whether the essentialist can explain all metaphysical necessities. It is plausible that all absolute necessities are metaphysical, so that an affirmative answer to the latter question requires an affirmative answer to our present question. But the converse does not hold. Metaphysical necessities—or at least what are commonly taken to be metaphysical necessities—may not all be absolute. Consider, for example, ‘Hesperus = Phosphorus’ or ‘Aristotle was a man’. According to post-Kripkean orthodoxy, these are metaphysical necessities. But they are surely not absolute. For there might have been no such planet as Venus, and in that case, it would not have been true that Hesperus = Phosphorus, i.e., ¬∀q(q □→ Hesperus = Phosphorus), and similarly in the case of Aristotle.26 An interesting question is whether other Kripkean a posteriori necessities,
such as that water is H2O, that light is a stream of photons, etc., are absolute. Kripke himself says they are necessary ‘in the highest degree—whatever that means’ [Kripke 1972, 99]. I am inclined to think they cannot be absolutely necessary— but I won’t go into this here.
38 If a necessity is to be absolute, it must not depend upon any matter of contingent fact. If an essentialist explanation is correct, the explanandum—the necessity to be explained— depends upon the explanans—the relevant facts about the nature of the entities involved. It follows that, if the necessity explained is to be absolute, the explanans must not itself be contingent—so that in particular, it must involve no commitment to any entity whose existence is a matter of contingency. Our question is, in part, whether
Philosophia Scientiæ, 16-2 | 2012 109
every absolute necessity can be given an essentialist explanation that meets this condition. Every essentialist explanation appeals to the nature of at least one entity, and so requires at the very least that certain natures exist. Thus if an essentialist necessity is to be absolute, the relevant nature(s) must exist of necessity. I hold that the nature of a thing is always a property,27 so we should begin by seeing how the existence of certain properties can be necessary.
39 According to the modest, deflationary theory of properties I think we should accept, it suffices for the existence of a property that there should be a suitably meaningful predicate—a predicate with a well-defined satisfaction-condition. To avoid complications afflicting predicates which involve reference to contingently existing objects, I shall focus on purely general predicates, by which I mean predicates entirely free of any devices of singular reference. Correspondingly, by a pure property or relation, I mean a property or relation which is or could be the semantic value of a purely general predicate. On the modest, deflationary theory of properties, the actual existence of a suitably meaningful purely general predicate suffices for that of a corresponding pure property or relation.28 But it is clear that this sufficient condition should not be taken to be necessary. For we should surely allow for the existence of properties and relations for which, as a matter of contingent fact, no actual language provides suitable predicates. The most that can properly be required, for the existence of a property or relation, is that there could be a suitable predicate—i.e., one which would express it, or have it as its semantic value. In particular, it is sufficient for the existence of a pure property or relation that there could be a suitably meaningful purely general predicate. But the possibility in question here—whether or not there could be a predicate with a certain meaning—is surely absolute. That is, if it is indeed possible that there should be a suitable predicate, that is itself necessarily so— i.e., it is necessarily possible. But if that is right, then the existence of any pure property or relation is always a matter of necessity. For let P be any pure property or relation. Necessarily, P exists iff there could be a predicate having P as its semantic value. But since the logic of absolute modality is S5, it is necessary that (there could be a predicate having P as its semantic value iff necessarily there could be such a predicate). It follows that if P exists, then necessarily P exists. 29
40 An essentialist explanation of a certain necessity may appeal to the nature of some entity whose definition identifies it as a pure property or relation, which— as we have just observed—exists as a matter of necessity. It is clear that if an essentialist explanation appeals only to pure properties and relations, there is no reason why the necessity explained should not be absolute. For there is, in the definition of the relevant entities, no presupposition of existence of any objects at all, and so no presupposition of any objects whose existence might be a contingent matter. However, it is plausible that there are absolute necessities which cannot be explained by appeal only to (the natures of things which are) pure properties or relations. For example, it is plausible that it is not only necessary, but absolutely necessary, that 1 < 2,andthat1 + 1 = 2. It seems quite clear that if these necessities can be explained on the essentialist theory at all, it must explain them, much as I have suggested already, by appeal to the nature of the numbers 1 and 2, the relation of being less than, and the operation of addition. But in that case, the essentialist explanation would not appeal only to pure properties and relations, for the definitions of these entities essentially involve
Philosophia Scientiæ, 16-2 | 2012 110
reference to particular objects. They presuppose the existence of the natural numbers, and in particular, of the number 0.
41 This does not mean that there are absolute necessities which cannot be explained by the essentialist theory. But it does bring to the fore a crucial question. For since these necessities require the existence of certain objects, they can be absolute only if the existence of those objects is itself absolutely necessary. The crucial question, therefore, is: How, if at all, can the essentialist theory explain the necessary existence of those objects?
42 It may seem that if the essentialist is to answer this question at all, he must be reduced to claiming that it is simply in the nature of certain objects to exist— that whereas the nature of aardvarks, say, leaves it open whether there are in fact any aardvarks, it belongs to the nature of natural numbers to exist—existing is part of what it is to be a natural number, in a way that it is not part of what it is to be an aardvark.30 Even if there is no outright incoherence in the idea that existence can be part of a thing’s essence, this is a desperate move—it amounts to an invitation to accept necessary existence as a brute, inexplicable fact. I shall argue that the essentialist can do better— that he can provide an explanation why the natural numbers, for example, exist as a matter of necessity. We start with the fact that pure properties and relations necessarily exist. I contend that this fact can be explained in essentialist terms. The essentialist does not claim that existence is simply and irreducibly part of what it is for something to be a pure property or relation. What he claims is that a pure property or relation just is one for the existence of which it is sufficient that there could be a suitable predicate—that is, in the case of a first-level property or relation, a predicate expressing the condition objects must meet, if they are to have that property or bear that relation to one another, and similarly for higher-levels. That is what is true, in virtue of the nature of a pure property or relation. The possibility involved here, of the existence of a suitable predicate, consists simply in its not being ruled out by any absolute necessities. Hence it is an absolute possibility. But what is absolutely possible is absolutely necessarily possible.31 And from this, as we’ve already seen, it follows that the existence of any pure property or relation is necessary.
43 This conclusion is quite general: whatever pure properties and relations there are, of whatever level, could not fail to exist—their existence is necessary. Since it is clear that there are indefinitely many meaningful purely general first-level predicates, this implies the existence, and indeed necessary existence, of a large range of pure first- level properties and relations. This includes many pure sort al properties—i.e., properties with which are associated not only satisfaction conditions, but also identity- conditions for their instances.
44 I want now to extend the argument just given to purely general functions— those functions which could be represented or expressed by functional expressions entirely devoid of singular terms. It might at first appear that no extension of the argument is required. For functions, as usually treated in set theory, are just a special subclass of relations.32 Since the argument already given applies to pure properties and relations quite generally, it may seem that it covers functions as a special case. But matters are not quite so straightforward.
45 A given relation’s being a function depends, of course, upon its meeting certain additional conditions—there must be, for every element of its domain, something to which that element bears the relation, and there must not be more than one such.33
Philosophia Scientiæ, 16-2 | 2012 111
Whether or not these conditions are met in a given case may be a matter of contingency. For example, in a society in which there are no single sex marriages, every adult is married, but no one has more than one spouse, the relation expressed by ‘x is married to y’ is functional, and is, indeed, not just many-one but one-one, so that the spouse of…’ stands for a function. This may be a matter of law, or it may be just a matter of chance. Either way, it is clearly a contingent matter—nothing in the notion of marriage as such precludes polygamy or enforces heterosexuality. My earlier argument does not, accordingly, establish the necessary existence of such a function. At most, it establishes the necessary existence of a certain binary relation—being married to—which may, but need not, be a function. And the point clearly generalises. That is, the general argument cannot, by itself, establish the necessary existence of any function; it may establish the necessary existence of a relation, but it cannot show that any relation is functional. How, then—if at all—can the necessary existence of any functions be established?
46 The obvious answer is that it may, in contrast with being married to, be part of the nature of a relation that it is many-one. As a simple illustration, consider the successor relation of addition among numbers, xSy. By the general argument given already, this relation necessarily exists. What we want to see is that it is, also as a matter of necessity, a functional relation. It will then follow that the existence of the successor function is necessary. I shall assume, with Frege, that a number34 is essentially the number of things of some kind. Where F is some kind of things, I’ll write NxFx to mean ‘the number of Fs’. We can define the successor relation among numbers—n follows directly after m—again with Frege,35 as follows:
nSm =def ∃F∃x(Fx ᐱ NuFu = n ᐱ Nu(Fu ᐱ u ≠ x)= m) —that is, n follows directly after m if n is the number of Fs and m is the number of all but one of the Fs. What we need to show is that if nSm and nSp,then m = p. To show this, we exploit the fact that the number of things of some kind F is the same as the number of things of some kind G if and only if there is a one-one correspondence between them. So suppose nSm and nSp. Thenfor some kind F and for some object a, Fa ᐱ NuFu = n ᐱ Nu(Fu ᐱ u ≠ a) = m and for some kind G and for some object b, Gb ᐱ NuGu = n ᐱ Nu(Gu ᐱ u ≠ b) = p. It follows from the two middle conjuncts that NuFu = NuGu, so that there must be a one-one correspondence between the Fs and the Gs. And it follows from this, together with the facts that Fa and Gb, that there must be a one-one correspondence between the 36 Fs other than a and the Gs other than b. Hence Nu(Fu ᐱ u ≠ a) = Nu(Gu ᐱ u ≠ b).But then m = p, as required.
47 The relation xSy is many-one, so we may write it using the standard functional notation: S(y)= x.
48 This illustrates one way in which we can establish the necessary existence of a function —there may be a relation which we can prove to be many-one. In such cases, we may think of the function as definable in terms of the relation. But not all functions can be defined in this way, on the basis of underlying relations which can be proved to be many-one. Inspection of our proof that the successor relation is many-one reveals why not. To carry out the proof, we have had to rely on the fact that numbers can be represented as themselves values of a certain function—the function represented by the number operator ‘Nu...u...’. Since this applies to predicates (which may be simple like ‘…is a horse’, or complex like ’... is a horse other than Bucephalus’), it stands for a function from properties to objects—it maps each property to the number of its
Philosophia Scientiæ, 16-2 | 2012 112
instances. This feature of our proof is no accident. Any proof of the functionality of some relation must rely upon some more basic function. Although many functions can be defined in terms of underlying relations which can be shown to be many-one, not all functions can be so defined. Those functions which cannot be defined in terms of underlying relations, but which can themselves be used to define relations and prove their functionality, might reasonably be viewed as basic or fundamental functions. I think that the number operator is best viewed as such a function.37
49 This gives rise to an obvious question: can the (necessary) existence of basic functions be proved, and if so, how? I want to defend an affirmative answer to the first part of this question, by way of a certain kind of answer to the second part.
50 How may expressions for basic functions be explained? To take a certain function f as basic is to take it that it cannot be explicitly defined by setting f (x) = y iff xRy, using some prior many-one relation R. But that does not mean that f cannot be defined at all. A now quite widely discussed proposal38 is that we can implicitly define functions by means of abstraction principles—that is, principles of the general shape: ∀a∀b(f (a) = f (b)⟷ aEb) where E is an equivalence relation on entities of the type over which a and b vary. The idea is that we may fix a function whose arguments are elements in the field of the equivalence relation (and whose values are objects) by giving, by means of that equivalence relation, a necessary and sufficient condition for the function’s value to be the same for any pair arguments. The proposal is, I need hardly say, controversial. If it is to be upheld, various objections must be answered and some hard problems solved. A full defence lies beyond the scope of this discussion, in which I shall largely take it for granted that that defence can be provided, and concentrate upon those aspects of the proposal which bear especially upon my present concerns. 39
51 We may, without serious loss of generality, focus on a definite example—the function invoked in our proof of the functionality of the successor relation. The abstractionist proposal here is that we may implicitly define a certain functional expression ‘the number of ...’ (Nu ...u...), where the gap is to be filled by a first-level sortal predicate, by means of: Hume’s Principle: ∀F∀G(NuFu = NuGu ⟷ F ≈ G) where F ≈ G abbreviates a second-order formula40 saying that there is a one-one correspondence between F and G. If all goes well, there is, corresponding to this second- level equivalence relation on properties, a second-level function from first-level properties to objects. The value of the function, for each such property as argument, is the number of objects having that property. The bare possibility that there could be a meaningful relational expression, such as ‘≈’, is sufficient for the existence of a corresponding relation, and the definition of this relation ensures that it is an equivalence.41 Thus the relation ≈ necessarily exists and it is necessarily an equivalence relation. Hume’s principle ensures the existence of the corresponding function, given the existence of the equivalence relation. Hence the function Nu ...u... necessarily exists.
52 The example is, in one way, quite special. For if, as Wright and I have argued, Hume’s principle can be laid down, with no significant epistemological cost, as an implicit definition of the number operator, it can usefully serve, given a suitable underlying logic, as an epistemological foundation for elementary arithmetic.42 Other functions definable from underlying equivalence relations are unlikely to be of much philosophical, or for that matter mathematical, interest or importance. But in another
Philosophia Scientiæ, 16-2 | 2012 113
way, the example is not at all special; wherever an acceptable abstraction principle can be formulated, there will be a function corresponding to its equivalence relation as Nu ...u... does to ≈,and wherever the relevant relation is provably and so necessarily an equivalence relation, the existence of the corresponding function will be necessary. There are many equivalence relations, and many of them are necessarily so. It follows that many functions exist as a matter of necessity.
53 We are now ready to give a simple and straightforward explanation of the necessary existence of certain objects, viz. cardinal numbers. The cardinal numbers exist necessarily because their existence is a consequence of the existence of a certain function and certain properties which themselves exist necessarily. They are the values of the purely general function Nu ...u... for a certain range of arguments—purely general first-level sortal properties—and both that function and those arguments to it exist necessarily.
54 This is not quite, yet, an explanation of the necessary existence of the natural numbers. But the extra steps needed to get such an explanation are simple. The natural numbers are just the finite cardinal numbers. The smallest finite cardinal number is 0. This certainly exists as a matter of necessity, since it is the value of Nu ...u... for any empty first-level property as argument, and there necessarily exists at least one empty first- level property, viz. the property an object x possesses if and only if it is self-distinct (i.e., x ≠ x). The remaining natural numbers can then be defined, following Frege, as those cardinal numbers which succeed 0—more precisely, those cardinals which bear the ancestral of the successor relation to 0.43 This definition ensures the validity of mathematical induction over the natural numbers, which can then be used to establish that each natural number has a new natural number as its successor, and hence that there are infinitely many natural numbers.44’ 45
Appendix 1 S4 and S5 principles
□p is true at w iff ∀q(q □→ p) is true at w
iff for every q, q □→ p is true at w
iff for every q and for every nearest q-possibility, w’,
accessible from w, p is true at w’
iff for every w’ accessible from w, p is true at w’.
The final equivalence is proved as follows:
55 Suppose that for every q and for every nearest q-possibility, w’, accessible from w, p is true at w’.Let w’ be any possibility accessible from w.Then for some q, w’ is a nearest q- possibility accessible from w.So p is true at w’.But w’ was arbitrary, so p is true at every possibility accessible from w.
56 Conversely, suppose p is true at every possibility accessible from w.Let q be any proposition. If there are any q-possibilities accessible from w, p is true at all of them,
Philosophia Scientiæ, 16-2 | 2012 114
and so true at all nearest q-possibilities accessible from w.Butq was arbitrary. So for every q and for every nearest q-possibility, w’, accessible from w, p is true at w’.
57 Expanded by our definition, the S4 principle in the form □p → □□p is: ∀q(q□→p) → ∀q(q□→∀r(r□→p)) 58 Proof. Suppose ∀q(q□→p) is true at w. Let w’ be any possibility. Then for some q, w’ is one of the nearest q-possibilities to w, so p is true at w’. Hence p is true at all possibilities.
59 Now let q be any proposition. If q is impossible, there are no nearest q-possibilities to w, so(vacuously) A is true at all nearest q-possibilities to w, for any proposition A. So in particular, ∀r(r□→p) is true at all nearest q-possibilities to w. So q □→ ∀r(r □ p) is true at w. But since q was arbitrary, ∀q(q □→∀r(r □→ p)) is true at w.
60 So suppose instead that q is possible. Let w’ be one of the nearest q-possibilities to w. We must show that ∀r(r □→ p) is true at w’. So we must show that p is true at the nearest r- possibilities to w’, for every r. But p is true at all possibilities whatever.46 A fortiori, p is true at the nearest r-possibilities to w’, no matter how r is chosen. Hence ∀r(r □→ p) is true at w’. So q □→ ∀r(r □→ p) is true at w. Clearly this reasoning does not depend on how q is chosen. Hence ∀q(q □→ ∀r(r □→ p)) is true at w. 61 Expanded by our definition, and using the equivalence of ◊ with ¬ □ ¬ the S5 principle in the form p □→ p is: ¬∀r(r □→¬∀q(q □→ p)) → ∀q(q □→ p). 62 Proof. Suppose that for some w, ¬∀r(r □→ ¬∀q(q □→ p)) is true at w, but ∀q(q □→ p) false at w. Then ∀r(r □→ ¬∀q(q □→ p)) is false at w, so that for some r, r ¬∀r(q □→ p) is false at w. Hence there is some w’ nearest to w at which r is true but ¬∀q(q □→ p) is false, and so at which ∀q(q □→ p) is true. Further, there is some w" nearest to w at which q is true but p is false. But47 for some s, w" is a nearest s-possibility to w’, and since ∀q(q □→ p) is true at w’, s p is true at w’ .But then p must be true at w", contradicting our earlier conclusion that p is false at w".So if -∀r(r □→ ¬∀q(q □→ p)) is true at w, ∀q(q □→ p) must be true there as well.
Appendix 2 Logical necessity, logical truth and a priority48
A problem for the essentialist theory
According to the essentialist theory, logical necessities are a (proper) subset of metaphysical necessities. The latter comprise those propositions which are true in virtue of the essences, or natures, of some things or other, and the logical necessities are then those propositions which are true specifically in virtue of the natures of logical entities—the various logical functions, including the truth-functions, the quantificational functions, the modal functions, and so on. Similarly, the mathematical necessities are those propositions which are true in virtue of the natures of just mathematical (and logical) entities.
63 The essentialist theory of necessity is, in a certain sense, epistemologically neutral—it does not imply any tight link between being necessary and being knowable apriori,but leaves room for necessities which may be knowable only a posteriori. Since it is very
Philosophia Scientiæ, 16-2 | 2012 115
plausible that at least some metaphysical necessities are only knowable a posteriori, this is just as well.
64 It may, however, seem that this feature of the essentialist theory has some unacceptable, or at least implausible, consequences. For logical and mathematical necessities, or so it may be thought, are always and by their very nature knowable apriori—we do not think that of the truths of logic and mathematics, there are some which can only be known a posteriori. And yet it seems that, according to the essentialist theory, some propositions which can be known only a posteriori must qualify as logically or mathematically necessary. Examples: (a) Let ‘Numerus’ rigidly designate the actual number of solar planets, i.e., 8, and consider:
65 (1) 8 > 7 ᑐ Numerus > 7 (1) is metaphysically necessary. And since (1) makes reference to no entity other than those to which reference is made in
66 (2) 8 > 7 ᑐ 8 > 7 the source of its truth must be the same. But (2) is logically necessary, since it is true just in virtue of the nature of truth-functional implication, which guarantees that any proposition whatever truth-functionally implies itself. So since the source of (1)’s truth is the same as that of (2)—indeed, according to one widely supported view, they are the same proposition in different guises49—(1) must likewise be logically necessary. But as against this, it may be claimed that (1) cannot be logically necessary, for it is surely logically possible that Numerus should not have been greater than 7. (b) 50 While it may not be absolutely necessary that Hesperus = Phophorus, because Hesperus/Phosphorus might never have existed, it surely is absolutely necessary that:
67 (3) Hesperus exists ᐱ Phosphorus exists ᑐ Hesperus = Phosphorus Similarly, it is surely absolutely necessary that:
68 (4) Hesperus exists ᑐ Hesperus = Hesperus. But now it may be argued that, since identity is a logical relation, and (4) is true just in virtue of the nature of identity, together with that of truth-functional implication, (4) must be reckoned logically necessary. And since (3) makes reference to no entities beyond those to which reference is made in (4), the source of its truth must be the same, so that it too must be reckoned logicallynecessary. But while it is perhaps metaphysically necessary that if Hesperus/Phosphorus exists, Hesperus = Phosphorus, the necessity of this identity is surely not a matter of logic.
A Two Dimensionalist response
69 One possible response to examples such as these is to concede that they bring out a defect in the essentialist account of logical necessity, but to argue that the defect can be remedied by combining the essentialist theory with a form of Two Dimensionalism about modality.51 More fully, it may be claimed that the difficulty stems from the fact that logical necessity is distinguished from other forms of metaphysical necessity not just by its source—in distinctively logical entities— but also by its being knowable priori. The essentialist theory captures the first distinguishing feature of logical necessity, but fails altogether to provide for the second. But, it may further be claimed, we can
Philosophia Scientiæ, 16-2 | 2012 116
respect the second feature of logical necessity, and block examples like those given above, by deploying the Two Dimensionalist distinction between two kinds of necessity. Putting the matter in terms of worlds, a statement, A,is superficially necessary iff the proposition A expresses (i.e., in the actual world) is true not only there, in the actual world, but also in every counterfactual alternative to the actual world; whereas A is deeply necessary iff, no matter which world is actual, the proposition A expresses in that world is true there. In terms ofthis distinction, it can be seen that while (1) is superficially necessary, it is deeply contingent, whereas (2) is deeply necessary.
70 Similarly, whereas (4) is deeply necessary, (3) is, while superficially necessary, deeply contingent. Thus the unwanted conclusion that (1) and (3) are logically necessary can be blocked by insisting that metaphysical necessity in general, and specific kinds of metaphysical necessity such as logical necessity, must be understood as forms of deep necessity. That is, for it to be metaphysically necessary that p, itisrequiredthatitbedeeply
necessary that p, and that there be some entities x1 ,x2such that p is true in virtue of the
nature(s) of x1 ,x2;and for it to be, additionally, logically necessary that p, it is
additionally required that x1,x2,... be logical entities. 71 Whilstitmaybetruethatitisonlyinthiswaythatonecancombineanes-sentialist account of the basis of logical necessity with the insistence that logical necessities are always knowable a priori, it must, I think, be allowed that this solution carries with it a heavy— and I would hold—unacceptable cost. For in Two Dimensionalist terms, many standard examples of metaphysical necessities will fail to qualify as such. What ensures that logical necessities are always knowable apriori, on this account, is the insistence that metaphysical necessities, including logical necessities, must always be deeply necessary. But since what is deeply necessary is always knowable apriori, this entails that there can be no a posteriori metaphysical necessities. Thus virtually all of the main examples of essentialist necessities discussed by Kripke in Naming and Necessity will fail to qualify as metaphysical necessities, on the present proposal—for necessities of origin, of substance or substantial composition, of kind membership and kind inclusion,
and what he terms ‘theoretical identifications’, such as ‘Water is H2O’, Heat is mean kinetic energy’, etc., are all, typically, knowable only a posteriori.
72 I think a quite different kind of response is called for—one which, crucially, leaves room for essentialist necessities which are knowable only a posteriori. But before I go into details, it will be useful to notice that the issue is not confined to specifically logical necessity. Essentially the same situation arises in regard, for example, to mathematical necessities. Examples:
73 (c) Let ‘Numerus’, as in example (a), rigidly designate the actual number of solar planets, and consider:
74 (5) Numerus > 7 Since (5) is true in virtue of the nature of the objects Numerus (i.e., 8) and 7, and the relation greater than among natural numbers, it is metaphysically necessary. And since (5) makes reference to no entity besides those mentioned in:
75 (6) 8 > 7 the source of its truth must be the same. But (6) is true solely in virtue of the natures of purely arithmetical entities and so is arithmetically necessary, so that (5) must be so as
Philosophia Scientiæ, 16-2 | 2012 117
well. Yet surely (5) is not a truth of arithmetic, so how can it be arithmetically necessary?
76 It should be clear that there is a general recipe for generating further examples.52 For wherever we have a species of metaphysical necessity concerning entities of some specific kind—schematically, Ф-necessity, such that Ф-necessary truths can be known a priori—it should be possible to introduce new terms as rigidly designating entities of that kind, fixing their reference to those entities by relying upon contingent facts of some sort, just as we fixed the reference of ‘Numerus’ as the number 8, by means of the description the number of solar planets’, which contingently applies to that number. Then, by substituting such terms in statements expressing Ф-necessities, we may obtain statements which we are unwilling to regard as Ф-necessary.
An alternative response
We must first dispose of a red herring. In stating the objection to the essentialist theory, it was suggested that, given a certain conception of how names work, (1) and (2) would express one and the same proposition. It would then follow immediately, given that (2) states a logical necessity, that (1) must likewise do so. If the objection depended upon the claim that (1) and (2) (and likewise (3) and (4)) express the same proposition, it would admit of a simple and obvious reply. For given that (2) and (4) express logically necessary propositions, the conclusion that (1) and (3) do so is unavoidable, since they express the very same propositions! And since it is undeniable that the propositions expressed by (2) and (4) are logically necessary, the objection is simply confused. The response can be put as a dilemma: Either the pair (1)/(2) express the same proposition (likewise (3)/(4)), or they don’t. If they do, the objection is incoherent, but if they don’t, it collapses (since it depends upon the claim that they do).
77 I don’t think we should be satisfied with this quick response. For the objection does not, contrary to what the response assumes, depend upon the identification of the propositions expressed by (1) and (2), or of those expressed by (3) and (4). It is enough for the objection that both of the propositions expressed by (1) and (2) are necessary, and that their truth has the same source. Given that the source of the truth of the proposition expressed by (2) is purely logical, it follows that that of the proposition expressed by (1) must be so as well. Thus a better response is called for.
78 The Two Dimensionalist response assumes that we should agree that, while it is necessary that if 8 > 7, then Numerus > 7, and necessary that if Hesperus/ Phosphorus exists, then Hesperus = Phosphorus, these necessities are not logical. It does so because it further assumes that logical necessities are, by their very nature, always knowable a priori. A radical response to the alleged difficulty is to reject these assumptions—i.e., to deny that logical necessities are, as such, knowable a priori, and to claim that the necessities expressed by (1) and (3) are, after all, logical. Similarly, one might deny that mathematical necessities are, by their very nature, knowable a priori, and claim that the necessity expressed by (5) is no less mathematical than that expressed by (6).
79 Obviously more needs to be said, lest this response should seem no more than a desperate exercise in bullet-chewing. In particular, something needs to be done to accommodate, or neutralise, the objection that now clamours for attention: Surely while it is a logical truth that if 8 > 7,then8 > 7,itisno truth of logic that if 8 > 7, then Numerus> 7. Likewise, it is logically true that if Hesperus exists, Hesperus = Hesperus,
Philosophia Scientiæ, 16-2 | 2012 118
but not a logical truth that if Hesperus and Phosphorus exist, Hesperus = Phosphorus. And similarly, while it is a mathematical truth that 8 > 7, it is no mathematical truth that Numerus > 7.
80 There is, it seems to me, no denying these last claims. (1), (3) do not express logical truths, and (5) does not express a truth of mathematics. But this gives trouble only if we make the further assumptions that only logical truths are logically necessary, and that only mathematical truths are mathematically necessary. And it seems to me that we can quite sensibly and reasonably reject these assumptions. Certainly all true logical propositions are logically necessary, and all true mathematical propositions are mathematically necessary. But it does not follow—and I think we should deny—that all logically necessary propositions are logical truths, and that all mathematically necessary propositions are truths of mathematics. A proposition may be true for purely logical reasons, or true on purely logical grounds (because true just in virtue of the nature of certain logical entities), without being a proposition of logic. Similarly, a proposition may be true on purely mathematical grounds (because true just in virtue of the nature of certain logical and mathematical entities), without being a proposition of mathematics. Putting the point another way, there is more to being a logical truth than being logically necessary, and more to being a mathematical truth than being mathematically necessary. What more there is can be seen by considering Quine’s well- known characterisation of logical truths as those statements which are true and remain so under all uniform replacements of non-logical vocabulary. It is clear from this that Quine is thinking of the truths of logic as a class of statements (or interpreted sentences). By contrast, I am viewing logical truths as a certain class of true propositions. Further, unlike Quine, I think we should take logical truths to be a subclass of necessary truths. Allowing for these divergences, we can characterise the logical truths as those logically necessary propositions which may be expressed using only logical vocabulary. Given the essentialist theory, this means that the logical truths are just those true propositions which are true solely in virtue of the nature of logical entities, and which can be expressed in purely logical terms. Similarly, the mathematical truths are those true propositions which are true solely in virtue of the nature of logical and mathematical entities, and which can be expressed in purely mathematical terms. On this account, being knowable a priori is indeed a mark of logical and mathematical truths, but it is not required for logical or mathematical necessity. The fact that expressibility in purely logical or mathematical terms is required for logical or mathematical truth obviously plays a part in explaining how it is that logical and mathematical truths may be known a priori—but that is not my present concern.
BIBLIOGRAPHIE
BOOLOS, GEORGE 1997 Is Hume’s Principle analytic? in Logic, Language, and Thought, edited by HECK,R., G. JR., Oxford:
Philosophia Scientiæ, 16-2 | 2012 119
Oxford University Press, 1997, reprinted in [Boolos 1998, 301-314]. 1998 Logic, Logic, and Logic, Cambridge (Mass.): Harvard UniversityPress.
BOOLOS, GEORGE & HECK, RICHARD, G.JR. 1997 Die Grundlagen der Arithmetik§§ 82-83, in Philosophy of Mathematics Today, edited by SCHIRN, M., Oxford: Clarendon Press, reprinted in [Boolos 1998, 315-338].
CHALMERS, DAVID, MANLEY, DAVID & WASSERMAN, RYAN (EDS.), 2009 Metametaphysics, Oxford: Clarendon Press.
EDGINGTON, DOROTHY 2004 Two kinds of possibility, in Proceedings of the Aristotelian Society, Supplementary volume 78, 1-22.
FINE, KIT 1994 Essence and modality, Philosophical Perspectives, 8, 1-16, edited by TOMBERLIN, J.. 1995 Ontological dependence, in Proceedings of the Aristotelian Society, vol. 95, 269-290.
FREGE, GOTTLOB 1879 Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Halle: Louis Nebert. 1884 Die Grundlagen der Arithmetik, Breslau: Wilhelm Koebner, translated into English by J.L. Austin as The Foundations of Arithmetic, Oxford: Blackwell 1959 (References are to this translation).
HALE, BOB 1987 Abstract Objects, Oxford: Basil Blackwell. 1994 Dummett’s critique of Wright’s attempt to resuscitate Frege, Philosophia Mathematica, 2(3), 122-147, reprinted in [Hale & Wright 2001, 189-213]. 1996 Absolute necessities, Philosophical Perspectives, 10, 93-117, edited by TOMBERLIN, J.. 1999 On some arguments for the necessity of necessity, Mind, 108(429), 23-52.
HALE, BOB & WRIGHT, CRISPIN 2001 The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, Oxford: Clarendon Press. 2008 Abstraction and additional nature, Philosophia Mathematica, III(16), 182-208. 2009a Focus Restored—Comments on John MacFarlane’s "Double Vision...", in The Bad Company Problem, edited by LINNEBO,Ø., Synthese, 170(3), 457-482.
2009b The metaontology of abstraction, in Metametaphysics, Oxford: Clarendon Press, 178-212.
HUMBERSTONE, LLOYD 1981 Relative necessity revisited, Reports on Mathematical Logic, 13, 33-42.
KRIPKE, SAUL 1971 Identity and necessity, in Meaning and Reference,edited by MOORE, A. W., Oxford: Oxford University Press, 162-191, 1993. 1972 Naming and necessity, in Semantics ofNatural Language, edited by DAVIDSON,D. & HARMAN, G., Dordrecht: Reidel, 253-355, reprinted as Naming and Necessity, Oxford: Basil Blackwell 1980 (Page references to this reprint).
LINNEBO,ØYSTEIN (ED.) 2009 The Bad Company Problem, Synthese, 170(3).
L0WE, E.J. 2008 Two notions of being: Entity and essence, in Being: Developments in Contemporary Metaphysics, edited by LE POIDEVIN, R., Cambridge: Cambridge University Press, 23-48.
Philosophia Scientiæ, 16-2 | 2012 120
MACFARLANE, JOHN 2009 Double vision: Two questions about the neo-Fregean program, in The Bad Company Problem, edited by LINNEBO, Ø., Synthese, 170(3), 443-456.
MCFETRIDGE, IAN 1990 Logical necessity: Some issues, in I.G. McFetridge: Logical Necessity & other essays, edited by HALDANE,J. & SCRUT0N,R. (EDS.), London: Aristotelian Society, vol. 11, 135-154.
QUINE, WILLARD VAN ORMAN 1953 From a Logical Point of View, Harvard: Harvard University Press, chap. Reference and Modality, essay 8, 139-159, reprinted by Harper & Row, Inc., New York and Evanston, 1963 (page references are to this reprint). 1956 The Ways of Paradox, New York: Random House.
RUSSELL, BERTRAND 1903 The Principles of Mathematics, London: George Allen & Unwin, 2nd ed., 8th Impression, 1964 (page references are to this impression).
SMILEY, TIMOTHY 1963 Relative necessity, The Journal of Symbolic Logic, 28(2), 113-134.
STALNAKER, ROBERT 1968 A theory of conditionals, Studies in Logical Theory American Philosophical Quarterly, Monograph Series No. 2, 98-112.
STRAWSON, PETER F. 1959 Individuals: An Essay in Descriptive Metaphysics, London: Methuen&Co Ltd.
WRIGHT, CRISPIN 1983 Frege’s Conception of Numbers as Objects, Aberdeen: Aberdeen University Press. 1998 On the (harmless) impredicativity of Hume’s principle, in The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, edited by HALE, B. & WRIGHT, C., Oxford: Clarendon Press, 229-255, 2001.
ZALTA, EDWARD 2006 Essence and modality, Mind, 115(459), 659-693.
NOTES
1. A full statement of my reasons for this view is beyond the scope of this paper. In brief, I take the most plausible versions of the opposing view—that modal facts can be reduced to facts about possible worlds—to be those advocated by David Lewis and David Armstrong. Both depend, in different ways, on a combinatorialist assumption to the effect that there is a possible world corresponding to every mathematically possible combination, or arrangement, of some specified collection of fundamental bits and pieces (mereological individuals or atoms in Lewis’s theory, thin’ particulars and sparse’ universals in Armstrong’s). In brief, I think this conception can avoid circularity—and thus constitute a genuine reduction—only if the combinatorialist assumption is understood in such a way that it begs fundamental questions against broadly essentialist views; questions which, in my view, ought to be settled by philosophical argument, not stipulation. Of course, both Lewis and Armstrong are perfectly well-aware of the anti- essentialist implications of their theories of worlds, and are untroubled by them, because they are in any case opposed to essentialism. If they had independently compelling arguments against essentialism, that might be some comfort—but they don’t, so it isn’t.
Philosophia Scientiæ, 16-2 | 2012 121
2. [Quine 1956, 174]. In ‘Reference and modality’, he writes: Being necessarily or possibly thus and so is in general not a trait of the object concerned, but depends on the manner of referring to the object… Necessary greaterness than 7 makes no sense as applied to a number x; necessity attaches only to the connection between ‘x > 7’ and the particular method ... of specifying x.’ [Quine 1953, 148-149]. 3. The terms can be misleading, because they suggest that the necessities so-called have their source in concepts or facts about meaning. I reject such views. I think talk of conceptual or analytic necessity is best understood in an epistemological sense—for it is plausible that such necessities can indeed be known a priori, on the basis of a grasp of the relevant concepts. 4. As it happens, I think there are compelling reasons to believe that some necessities are absolute (see fn. 9 below). But the interest and importance of the question what absolute necessity is does not depend on this belief—for one cannot even sensibly deny the existence of absolute necessity unless one is clear what it would be, for something to be absolutely necessary. 5. I use this fulsome term as conveniently ambiguous between set and (proper) class. 6. What, in general, makes a form of relative necessity interesting is a good question, but not one which I can pursue here. 7. Locus classicus—[Smiley 1963]. In this formulation, Ф is harmlessly identified with the conjunction of its members. 8. This is one reason for thinking that there must be some absolute necessities. I believe there are other, in some ways philosophically more important reasons. Some of these reasons are developed in [Hale 1999].
27 9. Here I quantify into operator position, with D0 varying over possibility-operators. 10. I am not sure that it is good enough. I think a modality is usually said to be alethic if it has somehow to do with the way or mode’ in which a proposition is true—as opposed to how it is known, believed, etc., or whether it ought to be true, etc. This is rather vague. A more precise statement is that a modality is alethic iff the strong modal operator is factive—but while that excludes doxastic and deontic modalities, it makes epistemic modalities alethic, so that one would need a separate stipulation to exclude them. 11. This idea is implicit in [McFetridge 1990]. It is discussed in [Hale 1996]. The idea of explaining □ in terms of the strong or counterfactual conditional goes back at least to Robert Stalnaker (see [Stalnaker 1968]). It is discussed in several recent publications by Timothy Williamson. One reader of this paper reminds me that one might distinguish different sorts of counterfactual— such as logical, metaphysical, and natural. In view of this, I should emphasise that I intend my counterfactual to be so understood as to make as strong a claim as possible. 12. This explanation assumes the standard Stalnaker-Lewis semantics for conditionals, under which strong conditionals with impossible antecedents are always automatically true. I am grateful to Sonia Roca Royes for discussion of this and several other points.
27 13. (LNC D0 ) asserts, in effect, the maximally-absolute necessity of the law of non-contradiction— there is no relevant sense of ‘possible’ in which it is possible that a contradiction is true. It may be supposed that this simply begs the question against those— dialetheists and paraconsistent logicians—who hold that some contradictions are or could be true. But matters are not quite so simple. ¬(A ᐱ¬A) is a thesis of Priest’s Logic of Paradox and likewise of the relevant logic R. One
27 would expect ¬ D0 (A ᐱ¬A) to hold. The real problem lies elsewhere. In contrast with the rest of us, a
27 27 dialetheist may hold that both ¬ D0 (A ᐱ¬A) and D0 (A ᐱ¬A) are true—and the truth of the latter is enough to spoil the claim of logical necessity to be maximally-absolute. But the vast majority of propositions are not dialetheia, so unless the dialetheist finds fault with the argument elsewhere, he should accept a qualified version of the claim, to the effect that if a non-dialetheic proposition is logically necessary, there is no competing sense in which its opposite is possible.
27 ( D0 -closure) is denied by Dororthy Edgington, who claims: [Hale’s] crucial assumption is this: if A logically entails B, and it is in any sense possible that A, it
Philosophia Scientiæ, 16-2 | 2012 122
is in that sense possible that B. But this assumption is question-begging. The opponent thinks that A&¬B is logically impossible, and so entails everything, yet A&¬B is possible in some other sense. But she does not accept that everything is possible in this other sense. [Edgington 2004, 14, fn. 9].
27 Two points in reply: First, it is hard to see how Edgington can reject ( D0 -closure)—if what follows
27 27 from D0 -possibilities need not be D0 -possible, how are we to reason about such things? Second, I think it is Edgington who begs the question—her argument requires ex falso quodlibet, but this does not hold in the minimal logic employed in my argument. There are good reasons to rely only on a weak logic in this context—in mounting an argument for the absoluteness of logical necessity, one should make one’s demands on logic as weak as possible, and in particular, avoid reliance on putative logical principles whose status as such is open to dispute. 14. In view of my rejection of any explanation of necessity and possibility in terms of worlds (see Preamble), it might reasonably be asked what, if anything, entitles me to deploy semantic arguments such as this one, in which I deal freely in terms of possible worlds or possibilities. At the very least, it might be supposed, such arguments ought, for me, to be mere shortcuts, replaceable by others which make no use of the apparatus of world semantics. I disagree. It is beyond the scope of this paper to give details, but I think it can be shown that we can reconstruct a version of world semantics (possibility semantics) within a general theory of properties which I believe can be shown to support a reasonable form of second-order logic. This theory of properties is irreducibly modal, so there is no reduction of modality—but it does, I think, entitle me to free use of semantic arguments such as the ones given in this paper. I am indebted to Professor Kazuyuki Nomoto, of Tokyo Metropolitan University, for helpful discussion of this point. 15. By a possibility, I mean a way things could be, or might have been. Possibilities are not assumed to be fully determinate or complete, so they are not possible worlds in the usual sense. I think we can and should dispense with worlds in favour of possibilities, but we need not consider how that might be done here. Nothing in the argument under discussion turns on the distinction between worlds and possibilities. 16. In my view, arithmetical necessities are a species of metaphysical necessities, so that if I am right, at least some metaphysical necessities are absolute. Whether all the examples of metaphysical necessity often discussed—such as those prominent in Kripke’s third lecture on Naming and Necessity—are absolutely necessary is a further question. 17. This assumes a space of possibilities, or possible worlds, which are taken to be complete or fully determinate ways things could be. I prefer a more modest version which avoids the assumption of completeness. This makes for some complications, but I need not trouble you with them here. 18. It is worth emphasising that I am not identifying what philosophers often call metaphysical necessity with absolute necessity, or assuming that metaphysical necessities are invariably absolute—although I hold that some are (see fn 16). So I am not claiming that the logic of metaphysical necessity is S5. On the contrary, it may be that while some metaphysical necessities are absolute, others are not, so that there is, properly speaking, no such thing as the logic of metaphysical necessity. 19. Here and hereafter, in the absence of explicit indication to the contrary, ‘absolute’ means absolute in the generalised counterfactual sense. 20. Perhaps most philosophers would accept this. But not all. It is denied by Dorothy Edgington (op. cit.), who identifies logical necessity with a priori knowability and thinks that while Leverrier knew a priori that if Neptune existed, it caused certain irregularities in the orbit of Uranus, that conditional is not metaphysically necessary—for Neptune might have existed but been knocked off course by an asteroid a million years ago, so that it would have been too far away to disturb the orbit of Uranus. I think we can and should reject her identification of logical necessity with a
Philosophia Scientiæ, 16-2 | 2012 123
priori knowability. We may agree that logical necessities are knowable a priori, but deny that everything knowable a priori is logically necessary. 21. This means that a description’s being free from explicit or implicit inconsistency does not guarantee that it represents a possibility—freedom from contradiction is a necessary, but not a sufficient condition. It may not be possible to give apriori acomplete characterisation of the space of possibilities. If there are any absolute necessities which can be known only a posteriori, then the space of (absolute) possibilities cannot be characterised a priori. I am inclined to the view that the usual Kripkean examples of a posteriori necessities are not absolute, and that, more generally, that no a posteriori necessities are absolute. But even if I am wrong about that, it does not necessarily mean that we cannot, for purely logical purposes, restrict our attention in doing model-theoretic semantics to what we might call logical possibilities. 22. According to the worlds approach, distinctions between different kinds of necessity and possibility are to be explained in terms of different classes of worlds throughout which the different kinds of modal proposition hold true—but, as we have seen, the relation between logical and metaphysical necessity cannot be satisfactorily explained in these terms. 23. Broadly similar or related ideas have been put forward by various others, including especially [Fine 1994, 1995], with whose view mine has some significant affinities; see also [Zalta 2006] and [Lowe 2008]. A comparative assessment is beyond the scope of this paper, and would, however illuminating, distract from my main purposes. 24. Thus my use of’ ‘thing’ maybe compared with Russell’s use of ‘term’ in [Russell 1903], where he writes: ‘Whatever may be an object of thought, or may occur in any true or false proposition, or can be counted as one, I call a term. This, then, is the widest word in the philosophical vocabulary’ [Russell 1903, 43]. 25. My definitions of circle and mammal leave it open what kinds of entity I take these things to be. I don’t believe anything of much importance turns on this, at least for my purposes—it would be easy enough to re-state the definitions as definitions of certain first-level properties. 26. This raises the question: in what sense, if any, are these propositions necessary? One might suggest (as Kripke does, cf. [Kripke 1993, 164] that they are weakly necessary, in the sense that they hold true at all the possibilities at which the relevant objects exist. One might, perhaps, agree that ¬◊Hesperus ≠ Phosphorus, and that ¬◊Aristotle was not a man, but deny that ¬◊¬p entails □p. That is, as in Prior’s system Q, ¬◊¬p is a weaker proposition than □p. One could then define a weak necessity operator by ⊡p =df¬◊¬p. An alternative, to which I am myself inclined, is to insist that only the conditionals ‘If Aristotle exists, he is a man’ and ‘If Venus exists, Hesperus = Phosphorus’ are absolutely necessary. One could then define the weak necessity operator ⊡ by
⊡p =df □(e ᑐ p),where e asserts the existence of the things which must exist, if p is to be true. 27. What kind of property depends on what kind of thing is in question. The nature of an individual object—what it is to be that object—is a first-level property, but the nature of a general property or relation is a higher-level property, and so on. 28. Readers familiar with Strawson’s Individuals may notice a close affinity between my claim and Strawson’s view that no more is required for the introduction’ of a universal (in contrast with particulars) than the existence of a suitably meaningful general term. See [Strawson 1959, 180ff]. 29. If we abbreviate ‘P exists’ by p and ‘there is a predicate having P as semantic value’ by q,our inference has the form: □(p⟷◊q)∴pᑐ□p. This is easily seen to be valid in S5. Suppose the premise true but the conclusion false at some world (or possibility) w0.Then p must be true but
□p false at w0,so that p must be false at some w1 accessible from w0.
But p ⟷ ◊q must be true at w1,so that ◊q must be false at w1. However, since p ⟷ ◊q must be true also at w0,where p is true, we must have ◊q true at w0.This requires q true at some w2 accessible from w0. But since the accessibility relation is both symmetric and transitive, w2 is accessible from w1,whence q must be false at w2 (since ◊q is false at w1). Contradiction! It follows that there can be no counter-model to the inference.
Philosophia Scientiæ, 16-2 | 2012 124
30. Of course, there couldn’t be aardvarks that don’t exist—the point is that there is such a thing as being an aardvark, whether or not the general property is actually instantiated. 31. This (i.e., ◊p 3□◊ p)is equivalent to the S5 law: ◊□p ᑐ □ p. The equivalence holds in intuitionistic as well as classical S5. 32. i.e., many-one relations, where a binary relation R is many-one if anything that bears R to anything bears it to at most one thing (i.e., ∀x∀y∀z((xRy ᐱ xRz)ᑐ y = z)), and likewise, with minor adjustments, for relations of more terms. 33. These are what are commonly called the existence and uniqueness requirements— for every thing that is a possible argument to the function, there must exist a value, and this must be unique. I am assuming the function is to be total—that is, defined for every element in its domain. A partial function, say from domain X to range Y, need not be defined for every element of X, i.e., have a value in Y for every argument in X;but its value for any argument must still be unique, wherever it is defined. 34. That is, a cardinal number—a number we can use to say how many things of some kind there are. 35. Cf. [Frege 1884, §76]. 36. Let ∅ be the given one-one correspondence between the Fs and the Gs.If a = b, ∅ itself is a one- one correspondence between the Fs other than a and the Gs other than b. If a ≠ b, ∅ (a) = c for some c such that Gc, and ∅(d)= b for some d such that Fd. Let ∅* be just like ∅ except that ∅*(d) = c.Then ∅* is a one-one correspondence between the Fs other than a and the Gs other than b. 37. It might be suggested that we could define the number operator in terms of an underlying relation, expressed by ‘x numbers F’, by stipulating that NuFu = the x such that x numbers F. This seems to be what [Boolos 1997, 306] and [MacFarlane 2009, 448] have in mind. But, of course, this just assumes that the numbering relation is many-one. Without a proof that it is so, we are no further forward. Stipulating that ‘x numbers F’ is to stand for a many-one relation (i.e., that if x numbers F and y numbers F, x = y) just begs the question: how do we know that such a stipulation is effective? (i.e., that there is such a many-one relation).
It might be suggested that we could define the number operator using class-abstraction: NuFu = df {x∣x ≈{u∣Fu}},where x ≈ y iff there is a one-one correspondence between the classes x and y. Perhaps, but only at the price of taking the class-abstraction operator as basic. I think we do best to define the number operator more directly in terms of one-one correspondence, without any detour through set theory. 38. This is a central plank in the neo-Fregean version of logicism originally put forward by Crispin Wright in [Wright 1983], supported in [Hale 1987], and defended by Wright and me in numerous papers, many of them collected together in [Hale & Wright 2001]. 39. Perhaps the main problems confronting the claim that functions may be implicitly defined by abstraction are the so-called Julius Caesar and Bad Company Problems. These are both discussed in [Hale & Wright 2001]—see the Introduction (especially pp.14—23) and Essays 5, 8, 9-14, and the Postscript. The Bad Company problem is the subject of a special number of Synthese edited by ∅ystein Linnebo [Linnebo 2009]. Some more recent defensive efforts are included in [Hale & Wright 2008, 2009a,b]. 40. Such as ∃R(∀x(Fx ᑐ ∃!y(Gy ᐱ xRy)) ᐱ ∀x(Gx ᑐ ∃!y(Fy ᐱ yRx)). 41. Proof : Let F ≈ G abbreviate the formula in the previous note. To see that ≈ is reflexive, observe that for any F,wehave ∀x(Fx ᑐ ∃!y(Fy ᐱ x = y)),so we can let R be identity. For symmetry, suppose that R is a relation which one-one correlates F with G. Then R’s converse—the relation which G bears to F exactly when F bears R to G— one-one correlates G with F. For transitivity, suppose that R one-one correlates F with G and S one-one correlates G with H. Then the composition of R and S —the relation which F bears to H just when there is some G such that F bears R to G and G bears S to H—one-one correlates F with H.
Philosophia Scientiæ, 16-2 | 2012 125
42. The underlying logic must be at least second-order, and if Hume’s principle is to subserve a proof of the infinity of the natural numbers, it must be understood so that properties of numbers themselves are among the possible values of the variables F and G. This requires that the first- level quantifiers involved in the expanded version of F ≈ G must be construed impredicatively, by allowing numbers—which are defined via Hume’s principle—to be possible values of the variables they bind. Some critics of the neo-Fregean programme view this as objectionable. For defence, see [Wright 1998] and [Hale 1994]. One must also, of course, defend the claim that higher-order logic really is logic, and not just—as Quine and others have complained—’set theory in sheep’s clothing’. 43. Following [Frege 1879], we say that x bears the ancestral of a binary relation R to y (briefly xR*y)iff y has every property P which belongs to x and belongs to anything to which anything that has P bears the relation R (i.e., xR*y iff ∀P ((Px ᐱ ∀u∀v((Pu ᐱ uRv)ᑐ Pv)) ᑐ Py). Then x is a natural number iff x = 0 ⋁ xS*0. 44. As Frege explains in [Frege 1884, §§82-83]. See also [Wright 1983, 154ff], and [Boolos & Heck 1997]. 45. This paper was written during my tenure of a Senior Leverhulme Research Fellowship. I should like to express my gratitude to the Trust for its generous support. The paper is a somewhat revised and expanded version of a talk given at a workshop on the semantics and epistemology of modality organised by the universities of Paris-Sorbonne, Rennes 1, Nantes and Nancy, and held in Nancy in December 2010. I am grateful to the organisers and the other participants, and especially Christian Nimtz, Sonia Roca Royes and Filipe Drapeau Vieira Contim, for very helpful discussion, and to two anonymous referees for useful comments which have led, I hope, to some improvements in my paper, even though I have not always felt able to follow their advice. 46. This is the crucial step, of course. Without the assumption that the accessibility relation is universal, we would have only that p is true at all possibilities w’ accessible from w, and could not get from here to the conclusion that p is true at the nearest r-possibilities to any such w’. For that step, the minimum assumption we would need is that the accessibility relation is transitive. 47. This is the crucial step, i.e., the point at which we rely upon the accessibility relation being symmetric, as well as transitive. 48. This appendix did not form part of my original paper, but resulted from a very useful exchange with Filipe Drapeau Contim, to whom I am deeply indebted. 49. I am thinking, of course, of a ‘direct reference’ theory of names, according to which a name directly contributes an object—the bearer of the name—to any proposition expressed by a sentence in which the name is used, without the mediation of any Fregean sense, and without otherwise contributing any information about the object. 50. (a) and (b) are slightly modified versions of examples suggested by Filipe Drapeau Contim, who suggested that the problem might best be solved by adopting a Two Dimensionalist treatment which allows one to hold that logical necessities are always knowable a priori by maintain that while (1) is superficially necessary, it is—in contrast with (2)—deeply contingent. 51. This is the response originally favoured by Filipe Drapeau Contim (see previous note)—he claims, and he may well be right, that it is the only way to preserve an essentialist account of logical necessity whilst accepting that such necessities are always knowable a priori. 52. I am not claiming that further examples can only be generated in this way.
Philosophia Scientiæ, 16-2 | 2012 126
RÉSUMÉS
On pourrait définir la nécessité absolue comme la vérité dans absolument tous les mondes possibles sans restriction. Mais nous devrions être capables de l’expliquer sans invoquer les mondes possibles. J’envisage trois definitions alternatives de : « Il est absolument nécessaire que p » et défends une définition contrefactuelle généralisée : ∀q(q□→p).Je montre que la nécessité absolue satisfait le principe S5 et soutiens que la nécessité logique est absolue. Je discute ensuite des relations entre la nécessité logique et la nécessité métaphysique, en expliquant comment il peut y avoir des nécessités absolues non logiques. J’esquisse également une théorie essentialiste selon laquelle la nécessité a son fondement dans la nature des choses. Je discute certaines de ses conséquences, y compris concernant l’existence nécessaire de certaines propriétés et celle de certains objets.
Absolute necessity might be defined as truth at absolutely all possible worlds without restriction. But we should be able to explain it without invoking possible worlds. I consider three alternative definitions of ’it is absolutely necessary that p’ and argue for a generalized counterfactual definition: ∀q(q□→p). I show that absolute necessity satisfies the S5 principle, and argue that logical necessity is absolute. I discuss the relations between logical and metaphysical necessity, explaining how there can be non-logical absolute necessities, and sketch an essentialist theory according to which necessity is grounded in the natures of things, and discuss some of its consequences, including the necessary existence of certain properties and objects.
AUTEUR
BOB HALE Department of Philosophy, University of Sheffield (UK)
Philosophia Scientiæ, 16-2 | 2012 127
Essentialist Blindness Would Not Preclude Counterfactual Knowledge
Sònia Roca-Royes
1 Introduction and aims
Understood as what it is—an existential claim—it is safe to assume that we have counterfactual knowledge. This claim would be true even if we only knew a few trivial counterfactuals like: If I were there, I would be there. It is also un-controversial that we have non-trivial counterfactual knowledge. I know that if I were a seven-year-old human, I would have blood. Although I haven’t flipped the £ 1 coin in my pocket, I know that if I had flipped it, it would most likely end up in tails or heads. I know that if I ate an Amanita phalloides, I would be severely poisoned. I know also that, in the scenario Williamson describes in [Williamson 2007, 142], if the bush hadn’t been there, the rock would have ended in the lake. When I say that it is uncontroversial that we know those counterfactuals, I intend to be understood as saying that, mostly, it’s those who are sceptic about counterfactual knowledge in general that would find their knowability controversial.
1 But there are counterfactuals whose knowledge (or knowability) is controversial even among the non-sceptics. I distinguish two sorts. First, there are counterfactuals the controversy around whose knowledge (or knowability) is inherited from local controversies elsewhere. Do we know the content of Goldbach’s Conjecture? Controversy here will translate into controversy as to whether we know the counterfactual: "If Humphrey had won the elections, every even integer greater than two could be expressed as the sum of two primes". Do we know whether humans are essentially so? Controversy here will translate into controversy as to whether we know the counterfactual: "If Wittgenstein and Betty Hutton had had a child in common, s/he would be essentially human". 1 Second, there are counterpossibles. The controversy around the knowledge (or knowability) of counterpossibles is the (socio- epistemological) consequence of a philosophical disagreement among epistemic peers. If Nicotine—the yucca plant in my office—were human, she would not have blood. Is this
Philosophia Scientiæ, 16-2 | 2012 128
so? Here— under the assumption that (it is agreed that) Nicotine cannot, metaphysically, be a human being—the controversy is served. Those who—for whichever theoretical reasons—think that all counterpossibles are vacuously true would say ‘yes’ whereas those who allow—also for whichever theoretical reasons—for false counterpossibles would most likely say no, Nicotine would have blood if she were human’.
2 I have two related goals in this paper. First, to motivate the negative answer to the following question: Would our (hypothetical) blindness to the essentiality of essential facts—‘essentialist blindness’ henceforth—preclude knowledge of all or most counterfactuals (including most uncontroversial ones)?2 The second aim is to assess a certain consequence of such negative answer. I’ll achieve my first aim by defending (i)over (¬i):
3 (i) Our epistemology of counterfactuals should not place the capacity for essentialist knowledge among the core capacities for counterfactual knowledge.
4 (¬i) Our epistemology of counterfactuals should place the capacity for essentialist knowledge among the core capacities for counterfactual knowledge.
5 I won’t offer a precise characterisation of the distinction between core capacities for counterfactual knowledge and counterfactual-specific capacities. Instead, a vague characterisation should suffice. A capacity for mathematical knowledge is deployed in acquiring (first hand) knowledge of: "If two men and two women had come to the party, four people would have come." If that capacity is deployed in acquiring knowledge of most counterfactuals—including most uncontroversial ones—it is a core capacity. If, for most counterfactuals, that capacity is not deployed in acquiring knowledge of them, it is instead a counterfactual-specific capacity. Similarly for any capacity that is deployed in acquiring knowledge of (at least) some counterfactual. These hints as to how to understand the distinction don’t provide a clear cut-off line. For current purposes, it won’t harm to leave things underdetermined.
6 It is none of my current aims to argue that there are core capacities for counterfactual knowledge. Instead, the paper is confined to doing the two things anticipated above. First, to argue for (i)—independently of what’s the case with other capacities—and, second, to assess a certain consequence of it.
7 Why, however, should one invest efforts in defending (i)? I intend this question to have two dimensions. First, why is it important to secure (i)? Second, who am I arguing against? I address them in turn.
8 The prospects of a satisfactory epistemology of essence are—we have reasons to believe —worse than those of a satisfactory epistemology of counterfactuals. The truth of (¬i), however, would make the epistemology of essence a constitutive part of a general epistemology of counterfactuals. It is desirable to have reasons against this dependence so that the possibility of progress in the epistemology of (the knowable) counterfactuals is justifiably believed to be immune to our failures in the epistemology of essence. In a similar vein, that we have essentialist knowledge is controversial. The truth of (¬i) would force us to transfer this controversy onto most claims to counterfactual knowledge. It is desirable to have reasons not to have to do this. In this context, it is of value to argue that the robustness of our claim to counterfactual knowledge is independent of the robustness (or else weakness) of our claim to essentialist knowledge.
Philosophia Scientiæ, 16-2 | 2012 129
9 But can’t we just take (i) for granted? This brings me to the second dimension of the question. I think that (i) is exceedingly plausible and that one should be allowed to take it as the default claim. Provided—and here comes an important qualification—that there are no threats to it. As it turns out, there are threats to it that one would do well, I think, not to overlook. These threats come in the form of a suspicion that (¬i) might be true and which arises from the works of Kment [Kment 2006] and Williamson [Williamson 2007]. To prevent misunderstanding, let me emphasize that I attribute (¬i) neither to Kment nor to Williamson. The claim is rather that their works provide grounds for thinking that (¬i) might be true. I want to undermine those grounds.
10 Even granting that Kment and Williamson do not (explicitly at least) endorse (¬i), would their views be somehow affected in the event that my post-threat vindication of (i) were persuasive? It is assessment of the consequences of (i)as far as this question is concerned that is my second goal. To anticipate: the reasons I shall offer to vindicate (i) will reveal what I believe to be argumentative gaps in each of their accounts on the relation between modality and counterfactuals.
11 The structure of the paper is as follows. In § 2, I construct the threat to ( i) that emerges from the works of Kment and Williamson. In § 3, I argue that the case does not survive scrutiny and vindicate (i). In §4, I articulate the argumentative gaps in Kment’s and Williamson’s accounts that the discussion in § 3 appears to reveal.
12 In what follows, I make heuristic use of worlds and scenarios (whether possible or impossible). I also assume that we have (at least) uncontroversial non-trivial counterfactual knowledge.
2 The two-horn case against (i)
In this section, I present the two-horn (prima facie) case for (¬i). The structure of the case is as follows. Assuming that there are false counterpossibles—the first horn—I formulate (emr-1); a general rule for counterfactual reasoning that would be very reliable on this horn’s assumption. Assuming that all counter-possibles are vacuously true—the second horn—I formulate (emr-2); a general rule for counterfactual reasoning that would be very reliable on this horn’s assumption. Kment endorses the content of the first assumption and Williamson that of the second. Partly on the basis of their views, both (emr-1) and (emr-2) could easily be thought to require, if we are to follow them in an informed manner, (the proper exercise of) a capacity for essentialist knowledge in evaluating most counterfactuals. Either there are false counterpossibles or there aren’t. The two-horn (prima facie) case that emerges from here is that, whether or not there are false counterpossibles, a capacity for essentialist knowledge would be a core capacity.
13 I begin with some preliminary remarks on the relation between counterfactual truth and counterfactual knowledge.
14 According to (the thinnest expression of) the minimality requirement at the level of truth- conditions, the worlds that are relevant to the truth or falsity of (P □→ Q) are the closest P-worlds.3 Disagreements arise, however, as to what exactly the extension of the closeness relation is; that is, on which differences among worlds contribute more to overall similarity than which others. It is widely agreed that, given two worlds, w and w , a draw in the number of same facts that w and w share with the actual world need
Philosophia Scientiæ, 16-2 | 2012 130
not mean a draw in their overall similarity. Instead, which are the same facts can make a difference. And once one is in the business of weighting similarities, the options are several as to which (kinds of) facts are (thought to be) heavier than which others. I shall not commit myself to any detailed weighting system. I will only assume that (kinds of) worlds are ordered as follows: 4
Graphic 1
15 My assuming Graphic 1 does not beg the question against those who (would) believe in fewer kinds of worlds than represented here. One just needs to delete as many circles as necessary until one is left with a representation that mentions only those kinds of worlds one believes in. Someone like Lewis would only keep the two smallest circles, whereas someone like Nolan would arguably keep them all. The assumption does not rule out conflation of circles either. All the assumption rules out is this: the order- inversion of any two rings that represent worlds one would believe in. So understood, this is not an uncommon thing to assume and, at any rate, it is something Kment endorses 5 [Kment 2006, 258-259] and Williamson gives us no reason to think he denies.
16 Now, the minimality requirement at the level of truth-conditions involves a consistency bit and a maximal similarity bit. It amounts to the claim that the closest worlds are those consistent worlds (provided the antecedent is consistent) that are as similar to the actual world as the truth of the antecedent of the counter factual at hand allows. What the counterfactual facts are depends on what the similarity order is. And how capable we are of counterfactual knowledge depends on how capable we are of tracking the similarity order. The existence of non-trivial counterfactual knowledge implies that, in hypothetical reasoning, and to some extent, we operate constrained by an epistemic counterpart of the minimality requirement which, in evaluating (P □→ Q), sufficiently reliably leads us to consider what in fact are the closest P-worlds. In agreement with Kment, "hypothetical reasoning needs to be based on rules that permit us to determine which propositions are cotenable with a given antecedent" [Kment 2006, 288].
17 Which, then, are these rules? First, how they should not look like. A rule that simply asked "consider consistent P-scenarios" would be a very unreliable guide to counterfactual knowledge. For, for most true counterfactuals, (P □ → Q), there are different ways of preserving consistency some of which do not satisfy the minimal alteration bit and falsify Q. The Amanita phalloides counterfactual illustrates this, and other examples are not difficult to come by. And a rule that didn’t go beyond "consider
Philosophia Scientiæ, 16-2 | 2012 131
consistent P-scenarios maximally similar to the actual world" would not be operationally effective unless it came with an indication as to what counts as a maximally similar world (i.e., as to what counts as a minimal change). How, then, would a reliable and operationally effective rule look like? There are two most natural answers to this question, depending on whether or not one believes that there are false counterpossibles. And, as anticipated, each of them allows for the construction of a case against (i), which is what generates the two-horn case against it. Let me consider them in turn.
18 Assume first that some counterpossibles are false—and that there are impossible worlds. Counterpossible (1) is a plausible candidate to be false under these assumptions:
(1) If Nicotine were human [P], she would not have blood [Q].
19 Arguably, there are impossible worlds that are nonetheless logically consistent. Among them, some are P&¬Q-worlds and some are P&Q-worlds. It is safe to assume that all P&Q-worlds are further away from actuality than some P&-Q-world, which renders (1) false. Initial Reason: Since we are to preserve consistency, Nicotine being human (i.e., P) makes "Nicotine is not human" non-cotenable. The law-like fact that all humans have blood, however, remains cotenable. So it must stay—by the minimality bit. So human- Nicotine has blood and (1) is false. Complaint: In fact, therefore, Nicotine being human makes non-cotenable "Nicotine is not human" and "Nicotine has no blood". That’s two items. Why should these two items go away as opposed to these other two: "Nicotine is not human" and "All humans have blood"? The assumption that worlds are ordered as in Graphic 1, together with some further views of Kment, provides an answer to this complainer.
20 By looking at that graphic, we can see that, at the level of truth-conditions, and other things being equal, 6 sameness of conceptual truths is the heaviest— i.e., any world that violates as few as one of them is automatically placed at the furthest shell—followed by sameness of metaphysical necessities, followed by sameness of laws of nature, and followed by sameness of non-mathematical particular facts. 7 The metaphysical necessities, according to Kment, are whatever is implied by the conceptual truths, the mathematical truths and the conditionalized essential truths. A conditionalized essential truth about x is an essential truth about x conditionalized on x’s existence. For 8 instance, if water exists, it is composed of H20. (The reason why Kment speaks of conditionalized essential truths is to allow for essential yet contingent truths—e.g. water
is composed of H2 O—whose contingency would be inherited from the contingency of the entities they are about—e.g. water.) Now, the two options that the complainer puts on the table are different as to whether to delete "Nicotine has no blood" or "All humans have blood". Assuming that the latter is a biological necessity, it is the former that should go, since it is a (non-mathematical) particular fact.9 This is the rejoinder that we can construct assuming Graphic 1 and the other views of Kment involved.
21 On these assumptions, the following epistemic minimality requirement— which closely mimics (a thicker expression of) the minimality requirement at the level of truth- conditions—is, among the reliable and operationally effective guides to counterfactual knowledge, ideally informative:
Philosophia Scientiæ, 16-2 | 2012 132
22 (emr-1) When evaluating (P □→ Q), imagine away as few truths as possible compatibly with complying with:
(a) Preserve consistency;10 and
(b) Imagine away p1 over p2 whenever:
pi is a non mathematical particular fact and p2 is a nomic or a mathematical (b.1) or a conditionalized essential or a conceptual fact;
pi is a nomic fact and p2 is a mathematical or a conditionalized essential or a (b.2) conceptual fact;
pi is a mathematical or a conditionalized essential fact and p2 is a conceptual (b.3) fact. 11 If p1 and p2 are of the same kind, it won’t make a difference to overall similarity which one you imagine away.
23 Kment—who believes in false counterpossibles—comes very close to endorsing (emr-1) explicitly. As mentioned above, he thinks that hypothetical reasoning needs to be based on rules that permit us to determine which propositions are cotenable with a given
antecedent. He adds to this that "(RM ) is such a rule" [Kment 2006, 288]. Consistency
permitting, (RM) requires us to hold fixed all mathematical and conditionalized essential truths:
Analytically consistent worlds in which all actual mathematical and conditionalized (R ) M essential truths hold are closer to the actual world than all other worlds. [Kment 2006, 269]
Similarly, (RN)—consistency permitting—requires us to hold fixed all nomic factsaswell:
Analytically consistent worlds in which all actual mathematical and conditionalized
(RN) essential truths hold, and which have the same laws of nature as the actual world, are closer to the actual world than all other worlds. [Kment 2006, 269]
And an analogous rule, (RC)—though Kment does not formulate it explicitly— would require us to hold fixed all conceptual truths too:
(RC) Analytically consistent worlds are closer to the actual world than all other worlds.
24 (R The difference between (emr-1) and A) + (RM) + (RC)—when taken as rules that govern hypothetical reasoning—virtually reduces to a difference in form. Let us grant for now that our counterfactual reasoning is based on a rule akin to this.
25 How does it bear on (¬i)? Kment thinks, first, that "applications of (RM) in hypothetical reasoning are very common" [Kment 2006, 289, my emphasis] and, second, that, when
one wants to apply (RM) when evaluating (P □→ Q), one needs to proceed in two steps: (1) to determine whether P is metaphysically possible and, if it is, (2) to determine which
Philosophia Scientiæ, 16-2 | 2012 133
propositions are the metaphysically necessary truths in order to (knowledgably) hold them all fixed. He concludes that: Determining whether a given antecedent [is metaphysically possible] is thus a
routine task that speakers face when applying (RM). [...] Determining whether a proposition [is metaphysically necessary] is therefore a routine task in evaluating counterfactuals. [Kment 2006, 289, my emphasis]
26 One might wonder why Kment thinks that determining whether something is
metaphysically possible [or necessary] is a step in our applications of (RM); for the former
involves the properties of metaphysical necessity and possibility while (RM) mentions mathematical and conditionalized-essential truths instead. Given what he takes the necessary truths to be, the short answer is that determining whether an analytically consistent proposition is metaphysically necessary just is determining whether it is implied by the mathematical and the conditionalized essential truths; and determining whether an analytically consistent proposition is metaphysically possible just is determining whether it is compatible with the mathematical and the conditionalized essential truths plus their corresponding minor premises. (See [Kment 2006, 288-289] for the details.) Equallyroutinely, therefore, we would need to deploy a capacity for essentialist knowledge in counterfactual reasoning.
27 Now, I’m not in a position to say that ’routinely’, in the context of Kment’s views, implies ’often enough as to imply (¬i)’, and this is why I don’t attribute (¬i) to him. Yet, his ’routine’-claim certainly provides enough grounds for a prima facie case against (i) that no one who believes in false counterpossibles and grants Graphic 1 should overlook. In § 3, I will provide the reasons on which I believe this case can be undermined. Before that, I turn next to the second horn; the one that, relying on Williamson’s work, can be constructed under the assumption that all counterpossibles are vacuously true.
28 (emr-1) encodes a cotenability priority order that only those committed to false counterpossibles—and to impossible worlds if to worlds at all—could be happy with. Let me explain why this is so, and then identify an alternative cotenability priority order that someone who believes that all counterpossibles are vacuously true could be happy with. Consider (1) again: (1) If Nicotine were human [P], she would not have blood [Q].
29 And consider a semantics for counterfactuals with only metaphysically possible worlds. Graphic 2 in the next page illustrates this case.
30 According to one such semantics, (1) is vacuously true: there is no (possible) world where Nicotine is human (and has blood). Yet, if, in hypothetical reasoning, we followed (emr-1), we would judge (1) to be false. On the basis of clause (a), we would preserve consistency; and, on the basis of (b.1), we would imagine away: "Nicotine does not have blood" (p1) in favour of keeping "all humans have blood" (p2). On one such semantics, therefore, (emr-1) is a highly unreliable guide to counterpossible knowledge.12 If, by contrast: "Nicotine is human"
Philosophia Scientiæ, 16-2 | 2012 134
Graphic 2
31 (the antecedent of (1)) and "Nicotine is a plant (and therefore not human)"— which, let us assume, is an actual and essential truth—were both deemed cotenable, their being jointly inconsistent could provide (access to) the vacuous truth of (1); her not having blood would trivially follow.
32 Let me generalize. Every counterpossible—by definition, a counterfac-tual with metaphysically impossible antecedent—contradicts some (non-conditionalized) essential fact. On this basis, the easiest way to secure our sensitivity to the vacuous truth of counterpossibles would be by means of a rule that, in hypothetical reasoning, requires us to always hold essential facts fixed (conditionalized or not) irrespective of the antecedent. Not surprisingly, this is what Williamson—who thinks that all counterpossibles are vacuously true— thinks about the way we reason counterfactually: part of the general way we develop counterfactual suppositions is to hold such constitutive [i.e., essential] facts fixed. [Williamson 2007, 164] It is on these grounds that he thinks that we are sensitive to, for instance, the vacuous truth of (2): (2) ¬(Gold has atomic number 79) □→⊥. 33 If all counterpossibles are vacuously true, therefore, (emr-2) is, among the reliable—on the current horn’s assumption—and operationally effective rules, ideally informative:
When evaluating (P □→ Q), imagine away as few truths as (emr-2) possible compatibly with complying with:
Preserve consistency13 so long as doing so does not require you to (c) imagine away any essential fact (conditionalized or not, and particular or not); and
If all the essential facts are consistent with P, then, imagine away p1 (d) over p2 whenever:
p1 is a (non-essential) particular fact and p2 is a (d.1) nomic or a mathematical or an essential or a conceptual fact. 14
p1 is a nomic fact and p2 is a mathematical or an (d.2) essential or a conceptual fact.
Philosophia Scientiæ, 16-2 | 2012 135
p1 is a mathematical fact and p2 is a conceptual fact. 15 If p1 and p2 are of the same kind, it won’t make a (d.3) difference to overall similarity which one you imagine away.
34 (When the antecedent of (P □→ Q) is metaphysically impossible, therefore, all actual truths are cotenable.)
35 How does this bear on (¬i)? As an advocate of the vacuous truth of all counterpossibles, Williamson endorses the following equivalences:
36 (□) □A≡¬A□→⊥ 37 (◊) ◊ A≡¬(A□→⊥)
38 (emr-2) constrains what we can imagine away or must hold fixed in hypothetical reasoning. Suppose that (¬A □→ i) is true; so ¬A is metaphysically impossible and the counterfactual, therefore, a counterpossible. For the sake of specificity (and without loss of generality), suppose that it is (2) above.
39 Suppose—as Williamson thinks—that we have the capacity to know that (2) is vacuously true. This implies that, in evaluating (2), we would hold fixed "Gold has atomic number 79" despite the fact that it contradicts the antecedent of (2). Looking back at (emr-2), and especially at clause (c), the suggested explanation of why, in acquiring knowledge of (2), we hold that fixed is that we are sensitive to the essentiality of "Gold has atomic number 79". Generalizing, the suggested explanation is that we have the capacity to know about the truth of vacuously true counterpossibles and to know that the negations of their antecedents are metaphysically necessary because we have a capacity for essentialist knowledge.
40 Indeed, according to Williamson, the judgement that something is metaphysically necessary is the output of evaluating counterpossibles together with the fact that holding fixed essential facts "is part of our general way of assessing counterfactuals" [Williamson 2007, 170]. (Note an additional disagreement between Kment and Williamson: Only according to Williamson are all particular essential facts necessary; in line with his necessitist views.)
41 Now, even if the suggested explanation were correct, it being so falls admittedly short of supporting (¬i). Allitsupports isthatthe knowability of at least some counterfactuals depends on our essentialist vision. But (¬i)requires it to be so for at least most counterfactuals. How, then, could Williamson’s work provide grounds for thinking that (¬i) might be true? Not only does Williamson think that (some) counterpossibles, like (2), are accessible to us but also that, in evaluating counterfactuals of the form of (2), our reasoning is: subject to the same constraints, whatever they are, as counterfactual conditionals in general, concerning which parts of our background information are held fixed. [Williamson 2007, 163-164]
42 No matter whether the counterfactual at hand is a counterpossible or not, or of the form of (2) or not, therefore, one same rule—encoding the relevant cotenability priority order—governs our hypothetical reasoning in general. Williamson is particularly explicit about this in [Williamson 2007, 171]. There, he considers the objection that a capacity to know ordinary counterfactuals— typically not counterpossibles and typically
Philosophia Scientiæ, 16-2 | 2012 136
with consistent consequent—need not amount to a capacity to know counterfactuals of the form (A □→ i). The response he offers is to the effect that it does amount to it. For the reasons above, if we are sensitive—as we are according to Williamson—to the vacuous truth of counterpossibles like (2)—which is of the form (A □→ i)—those general constraints must be akin to (emr-2). Since one same rule governs hypothetical reasoning, then, independently of whether the counterfactual at hand is a counterpossible or not, or has consistent consequent or not, (emr-2), or a rule equivalent to it, is the rule that constrains our hypothetical reasoning also when we evaluate ordinary counterfactuals.
43 When applying (emr-2) in counterfactual reasoning, we have to proceed in two steps: (1) determine whether the negation of the antecedent is (or is metaphysically implied by) an essential fact, (2) only if it is, hold it fixed. Paralleling Kment’s reasoning above, therefore, the belief that this might induce is that we routinely deploy our capacity for essentialist knowledge in evaluating counter-factuals (whether ordinary or not); contra (i). This is a prima facie case against (i) that no one who believes in the vacuous truth of all counterpossibles should overlook. Also in this case, I want to resist it in § 3.
44 This concludes my prima facie two-horn case against (i).
3 Reinstating (i)
In this section, and granting that either (emr-1) or (emr-2) encode the correct cotenability priority order (i.e., granting Graphic 1), I argue that (i)should be reinstated. The conclusion I’m after is correspondingly two-horn: whether or not one believes in false counterpossibles, (i) is in good standing. I’ll achieve this conclusion by arguing that: (ii) (Granted Graphic 1) Essentialist blindness would preclude the knowa-bility of some counterfactuals but not most—for a substantial body of counterfactuals, it would not preclude their knowability. (i) follows from (ii). For (i) says that a capacity for essentialist knowledge is not a core capacity for counterfactual knowledge and (ii) says that too and, in addition, that our essentialist vision—if we have it—is a counterfactual-specific capacity. Arguing for (ii), therefore, will be my vindication-strategy. The extra content of (ii) will be used in § 4.
45 The argument to follow is somehow complex, because I aim at an argument that can be found persuasive irrespective of one’s views on the truth-value of counterpossibles. (emr-1) and (emr-2) are statements of the two ideally informative rules for counterfactual reasoning that, respectively, a believer and a disbeliever in false counterpossibles can reasonably endorse. The reason for this is that (emr-1) would make us track the sometimes truth and sometimes falsity—under the first horn’s assumption—of counterpossibles, and (emr-2) would make us track their always being vacuously true—under the second horn’s assumption. For the reasons in § 2, I grant that, in order to acquire knowledge of a given counterfactual, the evaluator has to behave according to (emr-1) [or else ( emr-2)] in an informed manner. The main idea in the argument below is that, even if we suffered from essentialist blindness, we could still informedly behave according to (emr-1) [or else (emr-2)] when evaluating many counterfactuals; enough of them as to undermine (¬i).
46 There are two sources of essentialist blindness—the phenomenon of being blind to the essentiality of essential facts—relevant for current purposes:
Philosophia Scientiæ, 16-2 | 2012 137
Due to conceptual impoverishment; suffered by those who lack essen-tialist notions, thereby (Con) being not even enabled to grasp essentialist thoughts—let alone to acquire essentialist knowledge.
Due to cognitive impoverishment (broadly understood); suffered by those who, while (Cog) conceptually equipped to grasp a true essential-ist thought (like ⌐a essentially ∅’s¬) are nonetheless not cognitively equipped to know that it is true. 16
Given these two potential sources, and given what kind of argument I aim at, this is its structure:
3.1 The case for those who believe that all counterpossibles are true; the (emr-2) horn
Suppose that all counterpossibles are vacuously true. Suppose also—borrowing one of Williamson’s everyday examples—that in our world a rock falls down a slope and, instead of ending in the lake at the bottom, it rolls into a bush. Suppose further that (3) is true: (3) If the bush had not been there [P], the rock would have ended in the lake [Q]. The (emr-2) + (Con) case. Could, in evaluating (3), a (Con)-evaluator behave according to (emr-2) in a knowledge-conferring manner? I think she could (assuming minimal logical skills). One lacking essentialist notions is compatible with one being guided (in hypothetical reasoning) by the non-crossed-out portion of (emr-2):17
When evaluating (P □→ Q), imagine away as few truths as (emr-2) possible compatibly with complying with:
Preserve consistenc∣y so long as doing so docs not require you to imagine (c) away any essential fact (conditionalized or not, and particular or not); and
If all the essential facts arc consistent with P, then, imagine away pi over (d) p2 whenever:
p1 is a non-essential particular fact and p2 is a (d.1) nomic or a mathematical or an essential or a conceptual fact.
p1 is a nomic fact and p2 is a mathematical or an (d.2) essential or a conceptual fact
Philosophia Scientiæ, 16-2 | 2012 138
p1 is a mathematical fact and p2 is a conceptual fact. If p1 and p2 are of the same kind, it won’t (d.3) make a difference to overall similarity which one you imagine away.
P is the negation of the—by assumption—actual truth ‘the bush is there’ (¬P). Can the conceptually-impoverished evaluator imagine ‘¬P’ away? Yes, because "¬P" contradicts the antecedent and—we theorists know—it is not an essential fact. But would she imagine it away? Yes, because "¬P" contradicts the antecedent and, despite her lacking essentialist notions, she is following a portion of (c) that asks her to do so. Next: Where would the rock end? If she knew that "the rock ends there" is a particular fact, and if she knew also that "rocks slide down sufficiently steep slopes like this unless there’s something on their way to stop them" is a nomic fact, she would (be in a position to) knowledgeably follow (d.1), thereby imagining away "the rock ends there" and imagining in "the rock ends in the lake". This blind evaluator would therefore act according to (emr-2) despite her (Con)-blindness.
47 I conditionalized twice with ’If she knew’; once, on her knowing that certain facts are particular facts; the other, on her knowing about nomic tendencies. Those antecedents might not be true on occasions. For my argument to go through, however, I don t need the antecedents to be true. If the conditionals are true—as I intend them to be so- recognized—then, as far as evaluating (3) is concerned, informedly acting according to the seen portion of(emr-2) does not require essentialist notions. In addition, the evaluator’sbehaviour amounts to acting according to (emr-2).
48 Similar conclusions apply in the cases of other uncontroversial counterfactuals— typically not counterpossibles and with consistent consequent. I omit the statement of analogous treatments but one might want to explore other cases like, for instance:
49 (4) If I were there, I would be there.
50 (5) If I were a seven-year-old human, I would have blood
51 (6) If I had flipped the coin, it would most likely end up in tails or heads
52 (7) If I ate an Amanita Phalloides I would be severely poisoned.
53 Consequently, the impoverished rule that the conceptually impoverished evalu-ator follows is, for a big enough body of counterfactuals, a sufficiently reliable guide to counterfactual truth. Provided that she responsibly acts according to the portion of (emr-2) she has conceptual resources to see, the output of so doing will be a true and informed judgement. If my belief that I have hands counts as knowledge, those counterfactual judgments should count as knowledge too.
54 So far, of (ii), I’ve motivated this much (for the (emr-2) + (Con) case): for a substantial body of counterfactuals, essentialist blindness would not preclude their knowability. I will next argue that: it would nonetheless preclude the knowability of some.
55 Our conceptual impoverishment would block—in the current case—the knowability of at least some counterpossibles as well as that of some non-counterpossibles. Consider first counterpossible (2):
56 (2) ¬ (Gold has atomic number 79) [¬P] □→⊥[Q] Could, in evaluating (2), a conceptually impoverished evaluator behave according to (emr-2) in a knowledge-conferring manner? I think this time she could not. ¬P is the
Philosophia Scientiæ, 16-2 | 2012 139
negation of the—by assumption—actual and essential truth ’Gold has atomic number 79’. Can the conceptually-impoverished evaluator imagine ‘P’ away? No, because it is an essential fact and, as per (c), it must stay. But would a responsible such evaluator imagine it away? Yes, because it contradicts the antecedent and, according to the bit of (c) she sees, it must be imagined away. The conceptually-impoverished evaluator would therefore preserve consistency, thereby judging (2) to be false. However, (2) is true—all counterpossibles are true in the current case. The evaluator would therefore arrive at a false judgement.18 Similar conclusions apply in the case of many other counterpossibles. 19
57 If Kment’s treatment of (8) below is correct [Kment 2006, 289], there are also counterfactuals that are not counterpossibles and that are also epistemically inaccessible for a conceptually-impoverished evaluator: (8) People use a certain colourless, odourless, tasteless liquid that is not composed of hydrogen and oxygen to quench their thirst, etc. □→. People use a liquid other than water Kment thinks that, in evaluating (8), we—as a matter of fact—behave as follows: we imagine away the actual and non-essential truth that ‘water is the colourless, odourless, tasteless liquid that people usually use to quench their thirst, brush their teeth, etc.’ and we hold fixed instead the actual and essential—or so let us grant—truth ’if water exists, it is composed of hydrogen and oxygen’. (Note that they are individually consistent yet jointly inconsistent with the antecedent, so exactly one must go.) He then explains why we—as a matter of fact—behave as we do by appealing to our essentialist vision; in particular, to our knowledge that ’if water exists, it is composed of hydrogen and oxygen is an essential truth. The knowability of this Putnam-style example would be precluded too if we suffered from (Con)-blindness.
58 We can sum up as follows. Examples (2) and (8)—granting Kment’s diagnosis of the latter—show that, sometimes, the conceptually impoverished evaluator might have a dilemma as to whether or not to imagine a given fact away that would critically require (the proper exercise of) her essentialist vision to solve it in a knowledge-conferring manner. Example (3)—and, by extrapolation, (4)-(7)—suggests, however, that many (ordinary) counterfactuals will not generate such critical dilemmas. This concludes my argument for (ii) for the (emr-2)+(Con) case.
59 The (emr-2)+(Cog) case. The (Cog)-type counterfactual evaluator sees—let us assume, so that the case is interestingly different from the previous one— the whole of (emr-2) but is cognitively impoverished. Now, knowledge that X is not an essential fact is compatible with (Cog)-type essentialist blindness.20 Therefore, there are non-counterpossibles such that, when evaluating them, one can knowledgeably follow (c) compatibly with being blind to the essentiality of essential facts. Let me elaborate on this by focusing on (3). A (Cog)-type evaluator can know that the presence here ofthis bush is essential neither to the bush nor to the place without knowing, of any essential fact, that it is an essential fact. "The bush is there" would therefore be imagined away. Next: Where would the rock end? If she knew that "the rock ends there" is a non-essential particular fact, and if she knew that "rocks slide down sufficiently steep slopes like this unless there’s something on their way to stop them" is a nomic fact, she would (be in a position to) knowledgeably follow (d.1), thereby imagining away "the rock ends there" and imagining in "the rock ends in the lake". The counterfactual would correctly be judged to be true. As above, I intend this example to be generalizable to a substantial body of
Philosophia Scientiæ, 16-2 | 2012 140
non-counterpossibles, among which (4)-(7). For reliability reasons as above, these informed true judgements should count as knowledge.
60 Things are otherwise with (this time: all) counterpossibles. If "Gold has atomic number 79" is an essential fact, one cannot know that it is not (by facticity of knowledge). And a (Cog)-evaluator cannot know either that it is essential. Under these circumstances, any behaviour according to (c)—the whole of which is now seen—when evaluating (2) would be knowledge-undermining. The discussion of (8) above applies in the (Cog)-case too.
61 By now, therefore, we have enough reasons for (ii) also in the (emr-2) + (Cog) case. Nonetheless, it will be helpful to discuss here (9) as well: (9) If Wittgenstein and Betty Hutton had had a child [P], s/he would be essentially human [Q]. Compared to (2) and (8), its distinctive feature is that it overtly involves essentialist notions. As a result, it would be ungraspable by a (Con)-evaluator but not by a (Cog)-one. Even if graspable, it remains unknowable. If S knew that ‘¬P’ is a non-essential particular fact, she would act according to clause (c) and imagine it away. Next: Would the child be essentially human? The child is essentially human in the closest P-worlds if and only if’All humans are essentially so is an actual truth. The epistemic priority here lies on the right-hand side: unless S knows whether ’all humans are essentially so is actually true, she won t know whether the child is essentially human in the closest P- worlds.
62 This concludes the first half of the argument.
3.2 The case for those who believe that there are false counterpossibles; the (emr-1) horn
Suppose that there are false counterpossibles. Consider (3) again:
63 (3) If the bush had not been there [P], the rock would have ended in the lake [Q]. The (emr-1) + (Con) case. Could, in evaluating (3), a conceptually-impoverished evaluator behave according to (emr-1) in a knowledge-conferring manner? I think she could. As above, conceptual impoverishment of the kind at issue is compatible with one being nonetheless sensitive to the non-crossed-out portion of (emr-1):
When evaluating (P □→ Q), imagine away as few truths as (emr-1) possible compatibly with complying with:
(a) Preserve consistency; and
(b) Imagine away p1 over p2 whenever:
p1 is a non-mathematical particular fact and p2 is a (b.1) nomic or a mathematical or a conditionalized- cssential or a conceptual fact;
pi is a nomic fact and p2 is a mathematical or a (b.2) conditionalized-essential or a conceptual fact;
p1 is a mathematical or a conditionalizced-cssential (b.3) fact and p2 is a conceptual fact.
Philosophia Scientiæ, 16-2 | 2012 141
If p1 and p2 are of the same kind, it won t make a difference to overall similarity which one
you imagine away.
64 Except for ’non-mathematical’—which makes no significance difference—the remaining bit is identical to what remained in the case of (emr-2). Consequently, the conceptually- impoverished yet responsible evaluator would behave exactly as above: she would imagine away (¬P) and "the rock ends there". But should she behave like that? Yes. (¬P) should be imagined away according to clause (a) and "the rock ends there" should be imagined away according to (b.1). Similar conclusions apply in the case of many other everyday counterfactuals like (4)-(7). Also in this case, therefore, the output will be a true and informed judgement that should count as knowledge.
65 This case differs from the previous (Con)-case in that, according to clause (a)—but not according to clause (c)—the negation of a given antecedent should be imagined away irrespective of whether it is an essential fact. As far as counterpossibles are concerned, therefore, there are even fewer chances for the conceptually-impoverished evaluator to deviate from the demands of (emr-1). A current assumption is that there are false counterpossibles, and (2) is a best candidate to be an instance of the (content of the) assumption. By the reasons in the previous (Con)-case, it will be judged to be false by the conceptually-impoverished evaluator, provided she is responsibly acting according to the part of the rule she sees. So it will be known to be false.
66 In relation to (ii), therefore, and for the current (Con)-case, we have enough material to conclude that, for a substantial body of counterfactuals (now including some counterpossibles), essentialist blindness would not preclude their knowability. To conclude my argument for (ii) for this case, I should next argue that it would nonetheless block the knowability of some of them. To this effect, it suffices to note that the reflections above on counterfactual (8)— granting Kment’s diagnosis— apply here as well.
67 The (emr-1) + (Cog) case. This is the fourth and final case. Ordinary counterfactuals like (3)-(7) will be knowable also by this (Cog)-evaluator that sees the whole of (emr-1). This is even more straightforward in this case than in the (emr-2) + (Cog) one, since (emr-1) leaves less space for what we referred to above as critical dilemmas (i.e., dilemmas that require essentialist vision to solve them knowledgeably). One can see this by comparing clauses (a) and (c). By parity of reasoning, therefore, also in this case we get that for a substantial body of counterfactuals (also including some counterpossibles now), essentialist blindness would not preclude their knowability.
68 For reasons strictly analogous to those in the previous (Cog)-case, counter-factuals along the lines of (8) and (9) are epistemically inaccessible to (Cog)-evaluators also under the (emr-1)-assumption. Therefore, (Cog)-essentialist blindness would block the knowabilityofsome counterfactuals.
69 This concludes the second half of the argument.
70 If the argument in this section is persuasive, then, irrespective of whether we are sympathetic to the cotenability priority order encoded in (emr-1) or to the one encoded in (emr-2), we have no good reason to think that (i) is false. This concludes my two-horn defence of it.
Philosophia Scientiæ, 16-2 | 2012 142
4 Consequences for Kment’s and Williamson’s views on the relation between modality and counterfactuals
It emerges from § 3 that no view on the truth-value of counterpossibles by itself incurs commitment to (¬i). This is good news; especially if (i) is agreed to be the default claim. The discussion there, however, puts us in a position to realize—or so I wish to motivate next—that certain evolutionary explanations that Kment and Williamson provide are unsatisfactory.
71 Kment and Williamson appeal to the evolutionary usefulness of counterfactual knowledge with a view to achieving several explanatory goals. Among them (see [Williamson 2007, 134-136] and [Kment 2006, 243, and 288-290]):
(EG. Explaining the emergence of our metaphysical modal notions and thought. (Kment and
1) Williamson)
(EG. Explaining the existence of our capacity for metaphysical modal knowledge. (Kment and
2) Williamson)
(EG. Subsuming the epistemology of metaphysical modality under the epistemology of
3) counterfactuals. (Williamson)
Consider now these similar goals one could have:
(EG.4) Explaining the emergence of our essentialist notions and thought.
(EG.5) Explaining the existence of our capacity for essentialist knowledge.
(EG.6) Subsuming the epistemology of essence under the epistemology of counterfactuals.
And consider these two tasks:
72 (*) Meeting (EG.4)-(EG.6) without having (¬i)available
73 (**) Meeting (EG.4)-(EG.6) by appealing to (¬i). In order to identify what I believe to be argumentative gaps in Williamson’sand Kment’s ways of achieving (EG.1)-(EG.3), I’ll proceed as follows. First, I’ll show that (**) is considerably easier than (*). Second, I’ll show how that bears on (EG.1)-(EG.3) in the context of Kment’s and Williamsons’ accounts.
74 (**) is easier than (*). Knowledge of ordinary (and uncontroversial) counterfactuals like (7): "If I ate an Amanita Phalloides I would be severely poisoned" have a very good claim to be evolutionarily useful. If (¬i) were true, knowledge of most ordinary counterfactuals like (7) would already require a capacity for essentialist knowledge. Consequently, the fact that knowledge of them is evolutionarily advantageous would suffice to, on those grounds, meet the goals
75 (EG.4)-(EG.6) by means of an evolutionary explanation. But if (i) is true—and thereby (¬i) unavailable—considerably more needs to be done to meet those goals by those means. Let me elaborate.
Philosophia Scientiæ, 16-2 | 2012 143
76 As noticed in § 3, (ii) implies not only (i) but also that a capacity for essentialist knowledge—if we have it—is a counterfactual-specific capacity. Suppose— as engagement in (EG.4)-(EG.6) presupposes—that we enjoy essentialist vision. Let C be the set of all counterfactuals that we are conceptually enabled to know (and therefore have conceptual resources to entertain). The claim that our capacity for essentialist knowledge is counterfactual-specific implies that there is a non-empty proper subset of C—let’s call it ’(DepEss)’—that is exactly the set of counterfactuals from C whose knowability depends on us not being blind to the essentiality of essential facts. Let us call the complementary subset ’(NotDepEss) . Consider now the following claim:
Our (hypothetical) essentialist blindness would have (had) no negative effect on our survival or reproduction chances because epistemic access to the elements in (DepEss) is (iii) evolutionarily irrelevant (or, at any rate, redundant). Rather, it is epistemic access to (some of) the elements of (NotDepEss) that makes the evolutionary difference in view (or, at any rate, that suffices for it).
In the absence of (¬i), and in order to meet (EG.4)-(EG.6) by means of an evolutionary explanation, one must argue that (iii) is false. Now, belief on what the elements of (DepEss) are depends on whether one believes in false counterpossibles or not. As we saw in § 3, if one disbelieves in false counterpossibles, (DepEss) should be believed to include virtually all non-trivial counterpossibles, Putnam-style counterfactuals like (8) —granting Kment’s diagnosis—and counterfactuals like (9). If one believes in false counterpossibles, those (false) counterpossibles are arguably excluded from (DepEss). But in each case, (DepEss) contains elements whose knowability is independently controversial—let alone their evolutionary usefulness. Many ordinary counterfactuals like (7)—with possible antecedent—are plausibly known and plausibly evolutionarily useful. But these counterfactuals fall, in all cases, under (NotDepEss). 21 To successfully argue against (iii), one would need to argue that we (the species) know some elements in (DepEss)— enough of them to ground evolutionary explanations—and that knowledge of them is (or has been) evolutionarily useful. Given what—on the basis of § 3—we can expect the elements of (DepEss) to be—on each of the two (Cog)-horns—this is a very difficult task; certainly considerably harder than (**), especially given that everyday counterfactuals like (3)-(7) are not in (DepEss).
77 How does this bear on (EG.1)-(EG.3)? Each of (EG.1)-(EG.3) speaks of metaphysical modality. Here, I need to separate the case of metaphysical necessity from that of metaphysical possibility. I begin with the former. The conditionalized-essential facts that (emr-1) mentions are metaphysically necessary according to Kment, and so are, according to Williamson, the essential facts that (emr-2) mentions. With this in mind, one can now retrospectively check that, mutatis mutandis, and by their respective lights, the arguments in § 3 apply to the property of metaphysical necessity as well. As a result, by their lights (especially: by what each takes the metaphysical necessities to be):
(Granted Graphic 1) Blindness to the metaphysical necessity of meta-physically necessary facts (iv) would preclude the knowability of some counterfactuals but not most—for a substantial body of counterfactuals, it would not preclude their knowability.
Philosophia Scientiæ, 16-2 | 2012 144
To satisfactorily achieve (EG.1)-(EG.3) by means of an evolutionary explanation for the case of metaphysical necessity, therefore, Kment and Williamson would need to argue that we (the species) know some elements in (DepEss)—enough of them to ground evolutionary explanations—and that knowledge of them is (or has been) evolutionarily useful. That difficult task, however, as far as I’ve been able to see, has been carried out by none of them. This reveals what I believe to be a considerable argumentative gap in their respective accounts.
78 Provided that my arguments in relation to metaphysical necessity are persuasive, we now got to a dialectical point where I think that it wouldn’t add much to unfold the case of metaphysical possibility.For—that proviso in place— Kment’sand Williamson’saccounts, as they (seem to) stand, support, at most, a counterfactual-based evolutionary explanation for the case of metaphysical possibility only. This, for some (and I believe Kment and Williamson to be included here), would be a disappointingly less philosophically significant result.
79 Despite not needing to elaborate much on this: I think that similar conclusions as above apply in the case of metaphysical possibility all the same. I shall just offer a hint as why I think so: None of the arguments in § 3 that were aimed at showing that—whichever the case—ordinary counterfactuals like (3)-(7) belong to (NotDepEss) exploited at any point the evaluator’ssensitivity to the metaphysical possibility of metaphysically possible facts either.
80 On the basis of §§ 3-4, therefore, and as far as we’ve been given reasons to believe, it might still be that essentialist and metaphysical modal thought can be "removed from our conceptual scheme without collateral damage", contrary to what Williamson argues [Williamson 2007, 136] and Kment suggests [Kment 2006, §7].22,23
BIBLIOGRAPHY
FINE, KIT 1994 Essence and modality, in Philosophical Perspectives 8: Logic and Language, Atascadera, CA: Ridgeview, 1-16.
HALE, BOB 2002 Knowledge of possibility and of necessity, in Proceedings of the Aristotelian Society, 103(1), 1-20.
ICHIKAWA, JONATHAN ms. Modals and modal epistemology. http://jonathanichikawa.net/papers/mme.pdf,version of 9 May 2011, accessed 17 December 2011.
KMENT, BORIS 2006 Counterfactuals and the analysis of necessity, Philosophical Perspectives, 20(1), 237-302.
LEWIS, DAVID 1973 Counterfactuals, Oxford and Cambridge: Blackwell Publishers, and Harvard University Press.
Philosophia Scientiæ, 16-2 | 2012 145
NOLAN, DANIEL 1997 Impossible worlds: A modest approach, Notre Dame Journal of Formal Logic, 38, 535-572. 2011 Modal knowledge and counterfactual knowledge, Logique et Analyse, 54(216), 537-552.
WILLIAMSON, TIMOTHY 2007 The Philosophy of Philosophy, Oxford: Blackwell.
NOTES
1. The existence of this sort of controversial counterfactuals is one consequence of the fact that, as Williamson says: "In general, our capacity to evaluate counterfactuals recruits all our cognitive capacities to evaluate sentences" [Williamson 2007, 152]. 2. By ‘uncontroversial counterfactual’ I mean counterfactual whose knowability is uncontroversial. 3. I assume, for simplicity and pace some doubts to the contrary expressed by Lewis [Lewis 1973, § 1.4], that there always are closest worlds. 4. As the graphic suggests, a (non-empty) class of metaphysically impossible worlds that nonetheless satisfy all the actual laws of nature should be recognized. A world where Stuart Mill is a satisfied pig but that is qualitatively exactly like the actual world belongs to this category. I am calling these worlds ’metaphysically impossible yet nomically possible’. Kment—who takes the nomically possible worlds to be "just those metaphysically possible worlds that have the same laws of nature as the actual world’’ [2006, 261; my emphasis]—would need to call them something else. But he presumably would not neglect the existence of such (non-empty) category. To that extent, the disagreement here is merely terminological. 5. Though not fully explicitly, since—terminological discrepancies aside (see previous footnote)— he does not explicitly distinguish between the two shells within the shell of the metaphysically impossible (but conceptually possible) worlds. 6. In Kment’s case: "other explanatory facts being equal". 7. I include the qualification ‘non-mathematical’ here partly to follow Kment as closely as possible (see (RM) below in the main text). But also for independently good reasons: While some mathematical facts are particular, they are (agreed to be) necessary and, as such, heavier than particular facts about contingent entities. What to do with particular facts about other abstract entities (like, perhaps, fictional characters) arguably depends on whether these entities are contingent or necessary. For the sake of attempting to start making progress at all with the current discussion, I leave this debate at one side. I believe that the arguments can be adapted if other qualifications are believed to be necessary.
8. N.B.: An essential truth—e.g., (allegedly) water is composed of H2O—should not be confused with an essentialist truth—e.g. water is essentially composed of H2O. 9. Despite being arguably essential, it is a non-mathematical particular fact and, therefore, it is less heavy than a natural law. 10. Doable only when P is not logically contradictory itself. 11. This clause must (and can) be included only if mathematical and essential truths are believed not to be conceptual truths. 12. Sometimes—as in: "If Nicotine were human, she would have blood"—the judgement could be judged to be correct (if we charitably ignore what are perhaps relevant differences between judging x to be true and judging it to be vacuously true) but the rule is still highly unreliable. In don’t need to enter this debate here. 13. Doable only when P is not logically contradictory itself. 14. If mathematical or conceptual facts are essential—as one might plausibly endorse— there is redundancy in (d.1) and (d.2). But redundancy won’t do any harm here (and the intensional
Philosophia Scientiæ, 16-2 | 2012 146
differences might be serviceable, as §3 will put us in a position to see). In addition, for the reasons in fn.7, if mathematical facts were believed to be necessary yet not essential, (d.1) should begin with ’p1 is a non-essential and non-mathematical, particular fact’. 15. This clause must (and can) be included only if mathematical facts are believed not to be essential. 16. Equivalently: suffered by those who, while conceptually equipped to entertain es-sentialist thoughts, are not cognitively equipped to know, of an essential truth—like (allegedly) water is composed of H2O—that it is an essential truth. 17. In relation to fn. 14, this is why the intensional differences might be useful despite a potential redundancy. 18. Any behaviour according to (c) under the illusion that one has to behave according to the seen portion of (c) would be blame-worthy in the case of (2) and, as such, knowledge-destroying. 19. Sometimes—as in "¬(Gold has atomic number 79) □→ 2 + 2 = 4"—the judgement that a counterpossible is true might be argued to amount to knowledge; provided one is charitably not too picky about that judgment not (possibly) taking into account its being vacuously true. Whether those judgements amount to knowledge is controversial, but I don t need to decide these cases here. If they do, they provide additional support for the previous bit of (ii) I argued for. And to argue for the bit of (ii) I’m currently arguing for, it suffices that sometimes—as in (2)— the judgement be uncontroversially incorrect. 20. Knowledge that I’m not an essentially standing being (e.g., on the basis of my being sitting or having sat) is compatible with blindness as to which the essential facts are. 21. Let me say in passing: My explanation why the knowability of ordinary counterfac-tuals like (3)-(7) is not controversial is two-fold. First, they are epistemically accessible even when guided by some impoverished rule and, second, they are counterfactuals on which (emr-1) and (emr-2) agree. They are, therefore, among the agreed data. To rest one’scase on controversial counterfactuals is a more demanding task. (See [Roca-Royes 2011] for a related point.) 22. Jonathan Ichikawa [ms.] argues that, rather than by appealing to the evolutionary usefulness of counterfactuals, one can meet (EG.1) by appealing to the evolutionary usefulness of our capacity to reason modally in general—as opposed to metaphysically modally in particular. I am very sympathetic to his case for this. It remains to be seen, however, how that could contribute towards (EG.2)-(EG.3). The following seems to me to be a plausible, open possibility: That we have the conceptual resources to formulate questions about metaphysical necessity and essence which we do not have the capacity to knowledgeably answer. Elaborating on this, however, falls beyond the scope of the present paper. 23. Thanks to the audiences in Barcelona (Logos Seminar), Lisbon (Research(es) in Epistemology Workshop), London (London Logic and Metaphysics Forum), Nancy (Modalities: Semantics and Epistemology Workshop), Nottingham (VSS), Oxford (Jowett Society) and Sheffield (VSS) for valuable discussions on the topic. Thanks also to my colleagues in Stirling, and to Bob Hale, Jonathan Ichikawa, Margot Strohminger, Tuomas Tahko and Anand Vaidya. Finally, I’m enormously grateful to two anonymous referees for this journal for extremely penetrating comments and helpful suggestions on previous drafts, as well as to the guest editors of this issue, Filipe Drapeau Contim and Sebastien Motta.
Philosophia Scientiæ, 16-2 | 2012 147
ABSTRACTS
This paper does two things. First, it defends, against a potential threat to it, the claim that a capacity for essentialist knowledge should not be placed among the core capacities for counterfactual knowledge. Second, it assesses a consequence of that claim—or better: of the discussion by means of which I defend it—in relation to Kment’s and Williamson’s views on the relation between modality and counterfactuals.
L’objectif de cet article est double. Il défend d’abord, contre une menace potentielle, la thèse selon laquelle une capacité pour la connaissance essentialiste ne doit pas figurer parmi les capacités fondamentales pour la connaissance des contrefactuels. Il évalue ensuite une conséquence de cette thèse, ou du moins de la défense que j’en fais qui s’appuie sur une discussion des théories de Kment et de Williamson portant sur le lien entre la modalité et les contrefactuels.
AUTHOR
SÒNIA ROCA-ROYES University of Stirling (Scotland, UK)
Philosophia Scientiæ, 16-2 | 2012 148
Représentations de soi et modalités
Manuel Rebuschi
1 Introduction
Les représentations physiques comme les portraits ou les statues ont soulevé un problème intéressant en sémantique des langues naturelles. Une photo visible sur Internet montre la chanteuse Rihanna embrassant sa propre statue de cire au musée Tussauds1. Dans un tel contexte, la phrase
(1) Rihanna kisses herself.
Rihannas’embrasse (elle-même).
peut être utilisée pour dire que Rihanna embrasse sa propre statue. Cela signifie que la phrase en tant que telle est ambiguë entre plusieurs significations, qui dépendent du contexte : s’il n’y a pas de statue dans l’environnement immédiat alors la phrase possède son sens littéral, tandis que s’il y a une statue la phrase peut être employée comme on vient de le mentionner.
1 Cette ambiguïté est localisée dans le pronom personnel « s(e) » ou « herself ». Elle pourrait apparaître de façon similaire avec le nom propre « Rihanna », utilisé pour faire référence à la statue, comme par exemple dans :
(2) Rihanna a les cheveux blonds.
2 Dans cet article je me concentre cependant sur les pronoms personnels, particulièrement sur les cas où ils sont employés comme des anaphoriques. D’après les traitements classiques d’anaphore comme la théorie du gouvernement et du liage (government and binding theory) de Chomsky, un anaphorique comme « herself » et son antécédent « Rihanna » sont supposés partager la même référence2. Bien entendu,
Philosophia Scientiæ, 16-2 | 2012 149
comme il y a une lecture possible en termes de représentants (proxy reading) pour le pronom personnel, l’approche standard doit être révisée3.
3 Pour la phrase (1) interprétée en contexte comme signifiant que Rihanna embrasse la statue qui la représente, trois possibilités semblent se présenter4. On peut considérer (i) que le sujet, « Rihanna », ne fait pas référence à Rihanna (mais à une entité plus large incluant sa statue), ou (ii) que le pronom « se » n’est pas coréférentiel avec son antécédent « Rihanna », ou encore (iii) que le prédicat « embrasser » n’a pas sa signification habituelle.
4 Dans un article récent, Reuland et Winter choisissent l’option (ii) en proposant d’assouplir l’exigence d’identité. Selon leur critère alternatif, on exigerait du référent de « herself » dans (1) qu’il soit l’un des proxies de Rihanna [Reuland & Winter 2009]. Dans cet article, je critique la proposition de Reuland et Winter. Je montre qu’elle ne peut pas rendre compte de la spécificité des attitudes dites de se, c’est-à-dire des attitudes en première personne. Pourtant, la distinction entre attitudes de re et attitudes de se est tout à fait pertinente même dans les situations impliquant les proxies.
5 Je défends une autre conception, suivant laquelle les supports physiques des représentations d’une personne sont considérés comme des fenêtres modales, i.e. comme les moyens concrets permettant de voir comment cette personne serait dans telle ou telle situation possible (et souvent contrefactuelle). Ma conception s’inscrit dans l’option (iii) puisqu’elle conduit à une réinterprétation des prédicats habituels.
6 L’article s’organise comme suit. Dans la prochaine section, j’expose très succinctement l’explication de Reuland et Winter et je présente le problème posé par les attitudes de se. Dans la section 3 je donne une sémantique alternative basée sur la notion de fenêtre modale. Dans la section 4, je discute les implications ontologiques et métaphysiques de cette nouvelle sémantique. Les résultats sont brièvement récapitulés dans la conclusion.
2 Proxies et attitudes de se
L’approche en termes de proxies L’approche que j’expose ici très succinctement avant de la critiquer plus loin vise à rendre compte de cas de pseudo-coréférence comme celui de l’exemple (1), en faisant porter la charge de la variation sémantique au pronom anaphorique « se » (« herself »). C’est en tant qu’illustration de cette stratégie — l’option (ii) de la section précédente — que je m’intéresse à la théorie des proxies de [Reuland & Winter 2009] ; l’argument que je lui oppose porte sur la stratégie elle-même, i.e. sur le renoncement à l’identité (ou à la coréférence) comme fondement de l’anaphore.
7 Reuland et Winter considèrent plusieurs exemples notamment celui de [Jackendoff 1992] (analogue à (1), ci-après (3a)), et d’autres qui impliquent une quantification universelle comme dans (3b) :
(3) a. [Dans un musée de cire]
Soudainement, Ringo commença à se déshabiller.
b. Soudainement, chaque pop star commença à retirer la chemise qu’elle portait.
Philosophia Scientiæ, 16-2 | 2012 150
Dans ces deux exemples, on est confronté à une sous-spécification des pronoms anaphoriques qui peuvent faire référence aux statues respectives plutôt qu’aux personnes elles-mêmes : Ringo déshabille sa statue, de même que chaque star retire la chemise de sa propre statue. Tandis que l’approche de la théorie du liage implique la coréférence (i.e. l’identité des références) d’un pronom anophorique et de son antécédent, Reuland et Winter proposent qu’un pronom anaphorique puisse faire référence à l’un des proxies du référent de son antécédent.
8 Les deux auteurs introduisent une relation appelée proxy relation, notée PR, qui lie chaque entité à ses proxies. Cette relation est apportée par le contexte : elle peut impliquer n’importe quelle représentation physique d’une personne, comme des images, des statues, des acteurs jouant le rôle de cette personne, etc. PR est une relation réflexive, autrement dit chaque entité est l’un de ses propres proxies.
9 Pour analyser les énoncés quantifiés, la théorie utilise la notion de fonction de Skolem5 : c’est une fonction qui envoie des (n-uplets d’)entités sur des entités : f : Dn → n D, i.e. ∀(x1,... ,xn)—∈ D ,f(x1,... ,xn)∈ D, éventuellement selon un paramètre relationnel.
Une fonction de Skolem unaire fR avec un paramètre relationnel R est telle que pour
toute entité x, on ait : R(x, fR(x)).La dénotation d’un pronom réfléchi comme « herself »
est alors définie comme une fonction de Skolem de paramètre PR, fPR : à chaque entité x 6 elle attribue l’un de ses proxies, fPR(x), qui est tel que PR(x, fPR(x)) . Les phrases (1), (3a) et (3b) seront ainsi respectivement représentées par :
(4) a. embrasse (rihanna, fPR(rihanna))
b. déshabille (ringo, fPR(ringo))
c. ∀x(pop_star(x) — retire(x, la_chemise_que_fPR(x)_porte))
qui autorise l’interprétation en termes de proxies, à condition que la relation PR ne soit pas contextuellement réduite à l’identité — i.e., si on considère l’exemple (4a), à condition qu’il y ait dans le contexte des proxies de Rihanna autres que Rihanna elle- même. La spécificité des attitudes de se Lewis, Castaneda, Perry et d’autres auteurs ont montré que les comptes-rendus d’attitudes de se (en première personne) sont irréductibles à des comptes-rendus d’attitudes de re. L’irréductibilité se manifeste par le fait que partant d’une phrase employant le pronom personnel « je » (ou l’adjectif possessif « mon », ou toute autre expression à la première personne), on ne peut pas trouver de formulation équivalente qui éliminerait ce pronom (ou cette expression) et qui en préserverait le sens. Cette spécificité des attitudes de se est particulièrement bien illustrée dans l’extrait suivant d’Ernst Mach : Il y a quelque temps, après un éprouvant voyage en train de nuit, alors que j’étais très fatigué je suis monté dans un omnibus quand un autre homme est apparu à l’autre bout. « Quel pédagogue défraîchi ! », ai-je pensé. C’était moi-même : il y avait en face de moi un grand miroir. Je connaissais assurément mieux la physionomie de ma classe que ma propre physionomie.7
10 La situation évoquée dans l’extrait peut être résumée ainsi. Avant de réaliser qu’il s’observait lui-même comme après sa découverte, Mach croit ou pense de re de lui- même (i.e. de Mach) qu’il est un pédagogue défraîchi (a shabby pedagogue). Autrement
Philosophia Scientiæ, 16-2 | 2012 151
dit, avant comme après sa découverte, la croyance de Mach a un contenu identique, qui est une proposition singulière au sujet d’un individu donné (le même prédicat est prédiqué du même individu qui se trouve être Mach lui-même). Quand il réalise son erreur, Mach ne croit pas quelque chose de neuf à propos du monde, mais à propos de lui-même : il acquiert une nouvelle croyance au sujet de sa propre localisation dans le monde. Quand il découvre qu’il est celui qu’il observe dans le miroir, le sujet s’identifie à l’objet de son attitude : d’une attitude de re, sa pensée devient une attitude de se.
11 Le contraste entre les deux attitudes peut être éclairé par la formalisation. Considérons tout d’abord, même si ce n’est pas usuel, l’expression des croyances en première personne. Si Mach croit que Boltzmann est un pédagogue défraîchi, il pourra l’exprimer en énonçant la phrase suivante qui donne lieu à deux interprétations et formalisations :
(5) a. Boltzmann est un pédagogue défraîchi
b. de dicto : PédagogueDéfraîchi(b)
c. de re : R(xs,b) ᐱ PédagogueDéfraîchi(b)).
La constante b représente Boltzmann8. L’interprétation de dicto correspond au cas où Mach ne sait pas nécessairement qui est Boltzmann, tandis que l’interprétation de re exige une relation d’accointance (ou directe) entre le sujet (Mach) et l’objet (Boltzmann) de l’attitude9. J’emprunte à [Maier 2009] la mention explicite de la relation d’accointance R dans la formalisation : ici elle permet de distinguer entre les deux interprétations de la phrase (5a), i.e. entre les deux types de croyances pouvant être exprimées par cette phrase. La formalisation de la croyance de re introduit en outre la
variable xs qui représente le pronom à la première personne, « je ». L’évaluation sémantique de ce type de formules, suggérée par [Lewis 1979] (voir aussi [Ninan 2010]), se fait non pas simplement relativement à un monde, mais relativement à un monde centré (ω,α), c’est-à-dire à une paire composée d’un monde et d’un agent (cf. Annexe). Le fait de considérer des mondes centrés permet d’attribuer une valeur aux indexicaux
comme « je », « ici », « ce », etc. Ici la valeur de xs sera donc α, le« centre »du monde (le locuteur), quel que soit le monde ω considéré.
12 Revenons à la situation de Mach dans l’omnibus. S’il exprimait sa croyance en voyant l’image du pédagogue dans le miroir, on aurait avant et après sa découverte l’énoncé de deux phrases distinctes :
(6) a. C’est un pédagogue défraîchi
b. de re : R(xs,y) ᐱ PédagogueDéfraîchi(y).
(7) a. Je suis un pédagogue défraîchi
b. de se : (xs = y) ᐱ PédagogueDéfraîchi(y)
⇒ PédagogueDéfraîchi(xs).
Philosophia Scientiæ, 16-2 | 2012 152
Avant sa découverte, la croyance de Mach repose sur une relation d’accointance (la perception visuelle) entre Mach et un individu (lui-même) ici représenté par la variable y (qui prend une valeur dans le domaine d’objets de manière standard, i.e. selon l’assignation considérée). Après sa découverte, la croyance de Mach repose sur l’identité entre le sujet et l’objet de l’attitude. On est ainsi passé d’une attitude de re à une attitude de se.
13 Le contraste est également visible à partir des rapports d’attitudes à la troisième personne. Considérons tout d’abord le cas général du compte-rendu d’une croyance de re :
(8) a. Mach croit que Boltzmann est un pédagogue défraîchi
b. de dicto : Bm PédagogueDéfraîchi(b).
(9) a. Mach croit de Boltzmann qu’il est un pédagogue défraîchi
b. de re : R(m,b) ᐱ Bm (R(ys,b) ᐱ PédagogueDéfraîchi(b)).
14 Les constantes m et b représentent respectivement Ernst Mach et Ludwig Boltzmann,
l’opérateur doxastique Bm se lit « Mach croit que... », et R est la relation d’accointance entre le sujet et l’objet de la croyance. Suivant Maier, il est requis que le symbole R ait deux occurrences puisque la relation doit être saillante (vivid) pour le sujet (seconde occurrence), mais elle doit aussi effectivement lier le sujet et l’objet (première occurrence, hors de la portée de l’opérateur doxastique)10.
15 La formalisation introduit une nouvelle variable distinguée, ys, qui correspond au « soi » (au oneself, ou au he* de Castañeda) spécifique des attitudes de se11. Dans la
formule (9b) la variable ys étant dans la portée de l’opérateur Bm, elle prendra pour valeur celle de m. La sémantique suppose ici d’introduire un second centre, donc d’évaluer la formule relativement à un monde doublement centré (ω, α, β) et de faire varier ce centre selon les opérateurs d’attitudes introduits12 (se reporter à l’Annexe pour plus de détails).
16 Si nous nous tournons maintenant vers les attitudes de re et de se,nous pouvons contraster les deux interprétations à partir d’une seule phrase :
(10) a. Mach croit de lui-même qu’il est un pédagogue défraîchi
b. de re : R(m,m) ᐱ Bm(R(ys,m) ᐱ PédagogueDéfraîchi(m))
c. de se : (m = rn) ᐱ Bm(ys = m ᐱ PédagogueDéfraîchi (m))
⇒ Bm PédagogueDéfraîchi (ys).
Pour l’attitude de re, on a donc l’assertion de la croyance par Mach (m)quelui-même (en
tant que lui-même, ys) entretient une relation d’accointance R avec l’individu m, et que cet individu est un pédagogue défraîchi ; cet individu se trouve être identique à lui- même, mais Mach ne le sait pas ni même ne le croit. Dans le cas de l’attitude de se, la
Philosophia Scientiæ, 16-2 | 2012 153
relation R dans la portée de l’opérateur Bm a été remplacée par l’identité, si bien que Mach croit de lui-même en tant que lui-même, et non plus d’un individu qu’il ne parvient pas à identifier, qu’il est un pédagogue défraîchi. Un problème pour les proxies Considérons la situation où Ernst Mach, plutôt que de se contempler dans un miroir, regarde une photo de lui-même. On distingue alors trois composants : le sujet (Mach), le support (la photo) et le contenu (qui est un contenu objectuel : Mach sur la photo). L’exemple de la photo est préférable à celui du miroir (où la différence entre le sujet et le contenu n’est pas évidente, j’y reviens plus bas) ou à celui de la statue (où le support n’est pas dissocié du contenu). Le contraste entre attitudes de re et attitudes de se se manifeste également ici puisque Mach peut manquer de se reconnaître sur la photo. Comment la théorie des proxies de Reuland et Winter rendrait-elle compte d’un tel cas ? Outre une relation d’accointance comme dans le cas du miroir, la formalisation ferait intervenir ici la proxy relation PR en lieu et place de l’identité. Pour un compte-rendu en troisième personne, nous aurions donc :
(11) a. Mach croit de lui-même qu’il est un pédagogue joyeux
PR(m,n) ᐱ R(m,n) ᐱ B (R(y ,n)A PédagogueJoyeux b. de re : m s (n))
c. de se :
(i) PR(m,n) ᐱ Bm(PR(ys,n) ᐱ PédagogueJoyeux (n))
(ii) PR(m,n) ᐱ Bm(ys = n ᐱ PédagogueJoyeux (n))
⇒ PR(m, n) ᐱ Bm (PédagogueJoyeux (ys)).
Je vais argumenter qu’aucune des deux propositions (i) ou (ii) ne convient pour formaliser l’attitude de se. Le défaut fondamental de l’approche de Reuland et Winter réside dans le fait que la distinction entre support et contenu disparaît puisque les deux sont en quelque sorte « fondus » dans le proxy. Cela peut conduire à attribuer faussement des attitudes contradictoires à un sujet. Ainsi Mach peut-il détester sa photo (par exemple parce qu’elle est compromettante), sans se détester sur la photo : il détesterait le support sans détester le contenu. Selon la théorie des proxies, Mach détesterait et ne détesterait pas son proxy. L’anomalie n’est donc pas spécialement liée aux attitudes de se, mais comme la théorie vise à rendre compte de certains usages des pronoms réfléchis, elle prend une acuité particulière sur ce type d’attitudes.
17 Venons-en à l’interprétation des formules (i) et (ii). Le proxy est généralement un objet du contexte auquel le sujet est lié par diverses relations autres que l’identité, dont PR (et éventuellement d’autres relations, le sujet pouvant être conduit par exemple à voir, embrasser ou déshabiller son proxy). Le proxy paraît ainsi envisagé en tant que support plutôt qu’en tant que contenu. Mais concevoir l’attitude de Mach comme orientée vers le support (la photo) est inadéquat. Quand en observant la photo Mach pense qu’il est un pédagogue joyeux, ce n’est pas à la photo qu’il attribue cette qualité mais bien à la personne (qu’il reconnaît être lui-même) sur la photo.
Philosophia Scientiæ, 16-2 | 2012 154
18 L’autre interprétation consiste donc à considérer le symbole n comme dénotant non pas le support mais le contenu objectuel. La formule (i) exprimerait ainsi le cas où Mach croirait de son propre proxy (au sens de : Mach selon la photo) qu’il est un pédagogue joyeux. Mais la relation PR a été spécialement introduite pour rendre compte d’usages de pronoms réfléchis dans des situations où le proxy n’est pas identique au sujet. Mach peut-il reconnaître son propre proxy (i.e. Mach selon la photo) comme tel, croire de ce proxy qu’il est un pédagogue joyeux, sans croire de se de lui-même qu’il est un
pédagogue joyeux (selon la photo) ? Autrement dit, peut-on avoir PR(ys,n) sans avoir ys = n dans la portée de l’opérateur de croyance ? Ce serait contre-intuitif car on ne voit pas ce qu’il faudrait ajouter à la croyance de Mach pour qu’elle soit plus directement à propos de lui-même. Si Mach pense de se à lui-même tel qu’il est représenté sur la photo (i.e. à son proxy), alors il pense de se à lui-même. Il semble bien que la formule (i) implique la formule (ii).
19 Mais si croire quelque chose de se de son propre proxy revient à s’identifier à son propre proxy, cela ne signifie pas que l’identité se prolonge dans le monde actuel. Mach n’est pas actuellement identique au Mach selon la photo (l’un peut être joyeux et l’autre pas), même si Mach s’identifie intentionnellement au Mach selon la photo. La formule (ii) qui convient pour la croyance cesserait alors de fonctionner pour toute attitude factive (i.e. impliquant la vérité de son contenu) comme savoir ou voir. En effet, Mach ne pourrait pas savoir ou voir qu’il est identique à son proxy (n) si actuellement il ne l’est pas. La formule (ii) manque ainsi de généralité, et elle conduit à attribuer à Mach des croyances de se systématiquement fausses car impliquant une identité erronée.
20 L’échec de la théorie des proxies à rendre compte des attitudes de se résulte de son incapacité à distinguer le proxy en tant que support (auquel le sujet est actuellement lié par diverses relations autres que l’identité) du proxy en tant que contenu objectuel (auquel le sujet s’identifie intentionnellement). L’approche que je vais développer dans la section suivante repose sur l’introduction d’opérateurs correspondant aux photos, portraits et autres représentations physiques des agents, et elle permet de maintenir la distinction entre support et contenu.
3 Les fenêtres modales
Idée générale Je vais développer dans cette section une proposition alternative à celle de Reuland et Winter, qui préserve l’identité et évite la proxy relation dans la résolution des anaphores.
21 L’idée est que les statues, les photos, les miroirs, etc. sont des fenêtres modales : ce sont des dispositifs physiques qui nous permettent de voir comment serait un individu dans d’autres circonstances — i.e. dans un autre monde possible, ou dans une autre paire monde-instant. Pour des attitudes focalisées sur des personnes, le contraste entre attitude de re et de se est alors naturellement rendu puisque ce sont les personnes elles- mêmes, et pas leurs proxies, qui sont visées.
22 Ainsi quand Rihanna observe sa propre statue de cire, elle peut avoir des attitudes à propos d’elle-même si elle avait été blonde13, c’est-à-dire à propos d’elle-même dans les mondes possibles (contrefactuels) où elle est blonde. Ces attitudes (admirations, dégoûts, désirs, etc.) peuvent être de se ou simplement de re, selon que Rihanna s’identifie ou non à la statue. D’autres personnes que Rihanna peuvent aussi avoir des
Philosophia Scientiæ, 16-2 | 2012 155
attitudes (de re) à l’égard de la statue, comme à l’égard de Rihanna au travers de sa statue.
23 De la même manière, quand il regarde sa propre photo, Mach peut avoir des attitudes à propos de lui-même tel qu’il était quand la photo a été prise, c’est-à-dire dans les mondes et indices temporels où lui-même était tel qu’il est représenté par la photographie. Mais le cas du miroir doit également être envisagé avec cette approche : en s’observant dans le miroir, Mach peut avoir des attitudes à propos de lui-même si la droite et la gauche étaient inversées, autrement dit dans des mondes possibles qui sont comme le monde actuel à ceci près que la gauche et la droite sont inversées. Le fait que les miroirs (non déformants) représentent un monde très proche du monde actuel, au point que l’on peut faire intellectuellement la correction assez facilement pour reconstituer le monde actuel14 peut contribuer à expliquer pourquoi la dimension modale du miroir est restée inaperçue.
24 L’hypothèse que je veux défendre est donc que les pronoms réfléchis comme « lui- même », « elle-même », de même que d’autres pronoms et indexicaux, doivent être interprétés relativement aux fenêtres modales disponibles dans le contexte de leur assertion. La présence d’une fenêtre modale dans un contexte peut alors déclencher l’introduction d’un opérateur modal dans la forme logique des phrases assertées dans ce contexte.
25 La conséquence de cette hypothèse est que les prédicats qui nous lient aux individus au travers des fenêtres modales ont une interprétation non standard. En effet, ils dénotent des relations inter-mondaines, dont la sémantique peut être précisément définie mais dont le statut métaphysique est discutable. Je propose de considérer que ces relations sont fondamentalement des relations intentionnelles, même dans les cas où on a affaire à autre chose qu’à des verbes d’attitudes (comme « désirer » ou « haïr »). Des prédicats comme « embrasser » ou « déshabiller » auront ainsi deux extensions, l’une standard et intra-mondaine, l’autre non standard, intentionnelle et inter-mondaine. Retour aux représentations de Mach Considérons à nouveau les exemples d’Ernst Mach, sa photographie et son image dans le miroir. La présence de la photographie dans le contexte provoque l’introduction d’un opérateur modal, que l’on notera [photo],
défini sémantiquement à l’aide d’une relation d’accessibilité Rphoto qui relie les mondes compatibles avec le contenu de la photo. Par exemple si une photo représente le buste de Mach, on comptera parmi les mondes possibles compatibles avec la photo ceux où le buste de Mach est tel qu’il est représenté, mais où les choses peuvent varier « hors cadre » : dans un monde il aura un chat sur les genoux, dans un autre il n’aura pas de chat sur les genoux ; dans un monde il aura les pieds dans une bassine, dans un autre non ; et bien entendu les mondes possibles accessibles vont combiner ces différentes possibilités15. On aura finalement une définition tout à fait standard de la vérité d’une formule précédée de ce nouvel opérateur :
(12) ❬ω,α❭⊨ [photo]∅ ⇔ pour tout w’ tel que wRphotow’ : (ω ’, α) ⊨ ∅
26 Les cas envisagés plus haut en (10) et (11) peuvent ainsi être formalisés à nouveau :
(13) a. C’est un pédagogue joyeux
Philosophia Scientiæ, 16-2 | 2012 156
is b. de re : ❬ω,α❭⊨g [photo](R (xs,y) ᐱ PédagogueJoyeux (y))
(14) a. Je suis un pédagogue joyeux
b. de se : ❬ω,α❭⊨g [photo] ((xs = y) ᐱ PédagogueJoyeux (y))
❬ω,α❭⊨g [photo] PédagogueJoyeux (xs).
27 Il faut noter ici que la transition du cas de re au cas de se est à nouveau tout à fait
standard : elle réside dans le passage d’une relation d’accointance R entre le sujet xs et l’objet y de l’attitude, à l’identité. La sémantique est définie de telle sorte que la
variable xs, qui représente « je », fonctionne comme un désignateur rigide et renvoie au
centre a quel que soit le monde considéré ; autrement dit, xs désigne a, que son occurrence figure dans la portée d’un opérateur modal comme [photo] ou en dehors.
28 L’interprétation de R, qui représente la relation d’accointance,est en revanche non standard. L’exposant is qui suit le symbole R est emprunté à [Wehmeier 2011]. Il indique que le symbole est interprété sur un mode que l’on pourrait qualifier d’indicatif- subjonctif, où le premier terme prend sa valeur dans le monde actuel et le second dans le monde courant, éventuellement distinct du monde actuel16. Selon la formalisation proposée, la relation d’accointance lie donc le sujet du monde actuel à un individu dans un autre monde possible. Je reviendrai dans la section (4) sur cette interprétation spéciale des symboles de relations. Le lecteur intéressé peut en outre se reporter à l’Annexe où la sémantique est explicitement définie.
29 On peut également considérer des cas proches de l’exemple ci-dessus, où le sujet ne parle pas d’individus perçus à travers la fenêtre modale, mais de la fenêtre elle-même. Ainsi dans les deux exemples suivants :
(15) a. C’est une photo joyeuse
b. de re : ❬ω,α❭⊨g R(xs,y) ᐱ PhotoJoyeuse (y)
(16) a. *Je suis une photo joyeuse
b. de se : ❬ω,α❭⊨g PhotoJoyeuse (xs)
l’opérateur modal a disparu, ce qui signifie que les formules sont évaluées relativement au monde actuel. Évidemment dans ce cas, en observant une photographie, on peut avoir des attitudes de re (le sujet peut croire, voir, désirer certaines choses à propos de la photo), mais en apparence, sauf cas tirés par les cheveux, on ne peut pas véritablement avoir d’attitude de se.
30 Les exemples (13) et (15) ci-dessus montrent qu’à la différence de la théorie des proxies la sémantique des fenêtres modales permet de distinguer le sujet représenté de sa représentation. On peut attribuer des prédicats à la représentation (dans le monde actuel) et d’autres prédicats à ce qu’elle représente (dans des mondes contrefactuels). Un sujet peut ainsi reconnaître qu’ un objet actuel est sa propre représentation et entretenir des attitudes de re à l’égard de cet objet ; ces dernières ne seront pas
Philosophia Scientiæ, 16-2 | 2012 157
identiques aux attitudes de se qu’ il pourra entretenir vis-à-vis de lui-même, au travers de cet objet. Uneambiguïté généraliséedes indexicaux Si nous considérons maintenant le cas du miroir, il est traité de manière analogue tout en laissant voir un aspect intéressant. Un opérateur modal [miroir] est défini exactement sur le modèle de l’opérateur [photo], et on peut également contraster les deux types d’attitudes ((7) et (8) plus haut) :
(17) a. C’est un pédagogue défraîchi
is b. de re : ❬ω,α❭⊨g [miroir](R (xs,y) ᐱ PédagogueDéfraîchi (y))
(18) a. Je suis un pédagogue défraîchi
b. de se :
(i) ❬ω,α❭⊨g [miroir] PédagogueDéfraîchi (xs)
(ii) ❬ω,α❭⊨g PédagogueDéfraîchi (xs).
La phrase (18a) est ambiguë entre les deux sens exprimés par les formules (i) et (ii). Mais il faut noter que dans le cas d’un miroir non déformant l’ambiguïté en jeu est innocente : que le sujet se considère lui-même de se à travers un miroir ou directement dans le monde actuel fait très peu de différence, si ce n’est l’inversion gauche-droite mentionnée plus haut. Il semble donc que le cas du miroir ait conduit à ne considérer que l’interprétation non modale (ii), qui a du coup laissé dans l’ombre l’ interprétation modale (i). Et de façon analogue pour (17a), qui la plupart du temps est interprétée comme (17b) sans la modalité [miroir].
31 D’autres cas d’ambiguïté entre les deux interprétations sont plus riches en contenu. Ainsi, Rihanna observant sa statue et constatant la différence de teintures pourrait parfaitement s’écrier :
(19) a. Regarde, ici j’ai les cheveux blonds mais en fait j’ai les cheveux rouges !
b. de se :
❬ω,α❭⊨g [statue] CheveuxBlonds (xs) ᐱ CheveuxRouges( xs).
Ce qui se manifeste, c’est l’ambiguïté de l’indexical « je » (xs), qui conduit à le mettre dans la portée de l’opérateur modal ou en dehors : c’est le contexte qui permet de trancher entre l’une et l’autre interprétations.
32 Ce mécanisme peut être décrit en général de la manière suivante. Ce qui est pertinent pour l’interprétation de « je » comme d’autres indexicaux, c’est la classe, déterminée par le contexte, des fenêtres modales, Ω. Chaque membre ω de la classe des fenêtres détermine un opérateur modal (world-shifting), [ω], et introduit une lecture possible de « je ». Ainsi, « Je suis un F » se formalise en :
Philosophia Scientiæ, 16-2 | 2012 158
(20) OF(xs),avec O ∈{[ ω] : ω ∈ Ω }ᑌ{-}
i.e., O étant soit l’un des opérateurs contextuellement disponibles, soit la modalité nulle (• ∅⇔∅). Cette ambiguïté n’est évidemment pas le propre des attitudes en première personne et elle vaut pour tous les indexicaux, notamment pour « ceci », « ce », etc. Si l’on considère à nouveau la phrase (6a), prononcée par Mach ou par l’un de ses élèves, on disposera de plusieurs lectures dépendant du contexte :
is (21) a. ❬ω,α❭⊨g •(R (xs ,y) ᐱ PédagogueDéfraîchi (y))
is b. ❬ω,α❭⊨g [miroir](R (xs,y) ᐱ PédagogueDéfraîchi (y))
is c. ❬ω,α❭⊨g [statue](R (xs,y) ᐱ PédagogueDéfraîchi (y))
d. …
33 De façon générale, on formalisera « Ceci est un F »par :
is (22) O(R (xs,y) ᐱ F(y)),avec O ∈{[ω] : ω ∈ Ω}ᑌ{-}.
4 Portée ontologique et métaphysique
Retour sur les anaphoriques Les pronoms anaphoriques qui étaient le point de départ de la théorie des proxies peuvent être appréhendés suivant la même stratégie. Si nous considérons à nouveau les comptes-rendus d’attitudes à la troisième personne de Mach face au miroir, soit l’exemple (10) plus haut, on pourra contraster les deux types d’attitudes de la manière suivante :
(23) a. Mach croit de lui-même qu’il est un pédagogue défraîchi
is b. de re : Bm [miroir ](R (ys,m) ᐱ PédagogueDéfraîchi (m))
c. de se : Bm[miroir](ys = m ᐱ PédagogueDéfraîchi(m))
⇒ Bm[miroir]( PédagogueDéfraîchi (ys)).
Autrement dit, l’usage de se du pronom anaphorique « il », ou de « lui-même » entraîne l’identité d’avec l’antécédent, et non une relation spéciale avec un proxy. Du point de vue ontologique, les fenêtres modales offrent une sérieuse économie : quand Mach s’observe dans le miroir, il y a Mach lui-même, le miroir (l’objet physique), et rien d’autre. Chez Reuland et Winter, si Mach et Boltzmann s’observent côte à côte dans un miroir, il y a non seulement Mach, Boltzmann, le miroir, mais en outre les deux proxies (et des proxies pour tous les individus qui se reflètent dans le miroir). Le point, qui peut sembler anodin dans le cas de la statue (car le proxy et son support se confondent), devient explosif dès que l’ on aborde d’ autres supports comme les miroirs, les photos,
Philosophia Scientiæ, 16-2 | 2012 159
etc. : le moindre miroir se voit doté d’un pouvoir ontologique exorbitant puisqu’il engendre un proxy pour chacun des individus qui vient se refléter en lui. Une telle inflation ontologique doit être si possible évitée. Quel statut pour les relations inter-mondaines ? D’autres cas tels celui mentionné en introduction soulèvent un problème que je n’ai fait qu’effleurer jusqu’ici, à savoir celui du statut des relations inter-mondaines. On a vu que ces dernières sont mobilisées dans la formalisation à l’aide de l’exposant is, suivant une sémantique parfaitement définie (cf. Annexe). Si les relations de ce type paraissent envisageables quand elles sont abstraites, comme la comparaison de grandeurs (plus grand que dans « Paul aurait pu être plus grand que Marie (n est grande) »), cela semble plus délicat pour des relations concrètes, notamment les relations causales [Wehmeier 2011]. Or la relation située dans la portée des opérateurs générés par les fenêtres modales dans les exemples cités jusqu’ici est supposée être une relation d’accointance, comme la perception visuelle. Comment comprendre qu’un sujet dans un monde puisse percevoir un individu dans un autre monde possible ?
34 Le cas de Rihanna embrassant sa statue pose le même type de difficulté. Pour clarifier la situation et dissocier la supposée représentation de Rihanna de son support, je vais considérer l’exemple du miroir plutôt que celui de la statue, et contraster différents cas. On peut considérer l’ensemble des quatre exemples suivants :
(24) a. Rihanna (r) embrasse (K) Britney Spears (b).
b. ❬ω,α❭⊨g Krb
(25) a. Rihanna s’embrasse (elle-même).
b. ❬ω,α❭⊨g Krr
(26) a. Rihanna s’embrasse (elle-même) [dans le miroir (m)].
is b. ❬ω,α❭⊨g [m] K rr
c. ❬ω,α❭⊨g [m] K rr
(27) a. Rihanna embrasse le miroir.
b. ❬ω,α❭⊨g Krm.
Le cas (25) se distingue de (24) uniquement du fait qu’on envisage l’identité de l’agent et du patient : (25) correspond au cas où Rihanna s’embrasserait la main. Avec (26), la présence du miroir introduit une fenêtre modale. Dans chacune des deux interprétations (26b) et (26c), il faut relever que le pronom personnel est supposé désigner Rihanna elle-même et pas un autre individu : l’identité est ici encore impliquée par l’anaphore. Le cas (26c) est analogue au précédent (25), mais la scène (où Rihanna s’embrasse la main) est vue dans un miroir : la relation K est encore intra- mondaine. Un cas plus intéressant et délicat est (26b) où Rihanna s’embrasse à travers la fenêtre modale, et où la relation K devient inter-mondaine. L’ambiguïté de la phrase « Rihanna s embrasse elle-même » se manifeste donc par l’ambiguïté du prédicat K entre ses deux interprétations, intra-mondaine ((25b) et (26c)) ou inter-mondaine (26b).
Philosophia Scientiæ, 16-2 | 2012 160
Dans la situation du miroir on peut enfin distinguer (27) de (26b), par exemple si Rihanna embrasse le miroir dans le noir donc sans voir que c’est un miroir, alors que comme je l’ai signalé la situation est difficile à démêler dans le cas de la statue.
35 Est-il métaphysiquement possible que Rihanna interagisse causalement avec elle-même (ou avec d’autres individus) dans d’ autres mondes possibles ? Si c’était le cas, cela serait une conséquence tellement forte de l’approche en termes de fenêtres modales qu’on ne serait pas loin d’une réfutation par l’absurde. On peut fort heureusement y échapper. Il suffit en effet d’interpréter l’extension inter-mondaine des symboles de relations comme constituant des relations intentionnelles (ou mentales). Pour reprendre l’exemple du symbole K,tandis que son extension intra-mondaine est la relation physique d’embrasser,l extension inter-mondaine dénotée par Kis n’est pas cette relation physique mais une autre relation, intentionnelle, qui prend appui sur et étend cette relation au-delà de son extension physique.
36 La lecture intentionnelle des relations inter-mondaines vaut naturellement pour l’extension des relations d’accointance mobilisées dans les comptes-rendus d’attitudes propositionnelles de se ou de re. Lorsque Mach se voit dans le miroir et qu’il croit de lui- même, sur la base de ce qu’il voit, qu’il est un pédagogue défraîchi, ce qui permet de parler d’une attitude minimalement de re et maximalement de se est son apparente accointance avec lui-même à travers le miroir. Mais il n’y a pas plus de relation d’accointance entre Mach et son alter ego dans le miroir qu’entre Rihanna et le sien : il y a tout au plus une accointance (donc une relation physique) avec la fenêtre, et une extension intentionnelle de l’accointance vers les individus appréhendés à travers la fenêtre. Peut-on indéfiniment multiplier les fenêtres modales ? Les fenêtres modales permettent d’expliquer comment on peut avoir des attitudes à l’égard d’individus actuellement existants, y compris à l’égard de soi-même, dans des situations contrefactuelles. Au-delà du cas des miroirs ou de celui des photographies, il semble que dans bon nombre de situations, à commencer par celles impliquant des statues, la possibilité d’entretenir une attitude focalisée sur un individu existant via une représentation repose essentiellement sur un travail d’interprétation du sujet de l’attitude.
37 Les trois exemples imaginaires d’attitudes de se ci-après17 permettent de voir que les fenêtres modales vont se multiplier à l’égal des situations dans lesquelles un sujet se pense représenté :
(28) a. [Dans la réalité virtuelle :]
Je suis un beau pédagogue.
b ❬ω,α❭⊨g [VR] BeauPédagogue(xs)
(29) a. [En admirant une statue de Picasso :]
Je suis un pédagogue étrange.
b. ❬ω,α❭⊨g [Picasso] EtrangePédagogue(xs)
Philosophia Scientiæ, 16-2 | 2012 161
(30) a. [En découvrant le Professeur Tournesol :]
Je suis un pédagogue fou.
b. ❬ω,α❭⊨g [Tintin] FouPédagogue(xs).
Le cas de la réalité virtuelle peut être considéré comme n’étant pas trop éloigné de celui du miroir ou de la photographie au sens où il suppose une interaction causale entre le sujet et le support physique de la représentation18.Une situation similaire est offerte par les jeux dont les joueurs sont projetés sur une pièce de manière purement conventionnelle, et où un énoncé comme : « Attention, je vais te manger » ne trouve son sens qu’au travers de la convention en question19. En revanche, qu’un sujet se projette dans une statue de Picasso (qui n’a pas été réalisée dans l’idée de le représenter) ou dans une fiction20, cela paraît reposer sur sa seule capacité interprétative.
38 Je ne fais ici que souligner une caractéristique bien connue des représentations en général, et la théorie des proxies y serait également confrontée (avec la nécessaire extension de la classe contextuelle des proxies, et par voie de conséquence de la proxy relation). La dimension interprétative des représentations prend cependant une coloration particulière dans la conception défendue ici, puisqu’elle paraît se refléter directement dans le caractère purement intentionnel des relations inter-mondaines. Un paradigme pour les relations intentionnelles ? Avant de clore cette section, je voudrais tenter d’appréhender la réciproque de la lecture intentionnelle des relations inter-mondaines. Peut-on considérer que les relations intentionnelles en général sont, et ne sont rien de plus que des relations inter-mondaines ?
39 Reprenons le cas de Rihanna et la statue. Comme la fenêtre modale (la statue de cire) est en un certain sens entièrement remplie par la représentation de Rihanna, à la différence des cas de photographies ou d’images dans le miroir, on doit pouvoir distinguer deux manières pour Rihanna d’embrasser sa statue (s) :
(31) a. ❬ω,α❭⊨g Krs
is b ❬ω,α❭⊨g [s]K rr.
40 La première formule indique que Rihanna embrasse la statue comme objet matériel (le support de la représentation d’elle-même), et la seconde qu’elle s’embrasse elle-même à travers la statue21. D’un point de vue physicaliste ou béhavioriste, rien ne permet de distinguer un événement de l’autre. On peut lire les deux formules comme exprimant deux aspects de l’action de Rihanna : (31a) en décrit la dimension physicaliste, dans le monde actuel, et (31b) la dimension intentionnelle, dans les mondes possibles ouverts par la statue.
41 On pourrait appréhender sur ce modèle l’ensemble des relations intentionnelles, certaines ayant une contrepartie physicaliste (comme K), d’autres non. Faire cela suppose d’introduire des fenêtres modales à volonté, et en fait à chaque projection intentionnelle, c’est-à-dire en chaque occasion où la capacité interprétative d’un sujet est éprouvée. Ainsi, admirer, désirer, adorer, haïr, etc. seraient autant de prédicats dont l’extension pertinente est inter-mondaine, à la différence des prédicats physicalistes
Philosophia Scientiæ, 16-2 | 2012 162
qui sont intra-mondains. Ce qui n’implique absolument pas que les objets de nos admirations, désirs, adorations, haines, etc. n’existent pas dans le monde actuel, ni que nous ne puissions nous-mêmes pas être parmi les objets de nos propres attitudes.
5 Conclusion
Dans cet article, j’ai proposé une analyse des représentations physiques des individus comme les statues, les photographies ou les images dans les miroirs, en termes de fenêtres modales. L’idée est relativement intuitive puisque les attitudes à l’égard de ces représentations s’expriment naturellement en termes d’attitudes à l’égard d’individus actuels représentés dans des situations possibles non actuelles (contrefactuelles, passées ou autres).
42 Cette approche permet de rendre compte de la spécificité des attitudes de se même dans les cas où celles-ci passent par l’intermédiaire de représentations, à la différence de la conception en termes de proxies. Autre avantage de ma proposition : elle préserve le rôle central de l’identité pour la résolution des anaphores, et par voie de conséquence, elle évite l’inflation ontologique inhérente à la théorie des proxies.
43 La sémantique avancée dans cet article conduit à considérer les modalités comme étant d’un usage bien plus répandu que ce que l’on admet habituellement. En outre, elle implique que nous entretenions des relations avec des individus possibles non-actuels. Cela pourrait être perçu comme une difficulté pour le réalisme modal (du moins dans la version de [Lewis 1986] qui exclut les relations inter-mondaines). On l’interprète ici directement dans la perspective d’un anti-réalisme modal. Les fenêtres qui nous donnent à voir d’autres situations possibles sont essentiellement dans nos têtes, et ces situations sont autant de projections intentionnelles sur les individus actuellement existants (et parfois sur d’autres, inexistants22).
44 La conception fictionnaliste des modalités introduites avec les fenêtres modales paraît défendable dans les cas d’interprétation radicale, mais elle soulève des difficultés pour les cas de l’image dans un miroir, de la photographie ou de la réalité virtuelle, dont on peut considérer à bon droit qu’elles représentent objectivement, et pas seulement dans nos têtes, celles et ceux qu’elles donnent à voir. Ces difficultés n’ont pas été abordées dans l’article et elles mériteraient une étude approfondie. On peut entrevoir l’idée qu’une relation intentionnelle peut être plus ou moins objective si elle est ancrée dans, donc contrainte par une relation intra-mondaine ou non — autrement dit si elle est l’extension inter-mondaine d’une relation par ailleurs présente dans le monde actuel, ou si à l’inverse elle est « librement flottante ». Mais cela ne serait que le début d’une explication, sauf à considérer que l’objectivité se réduit à la physicalité.
45 L’approche sémantique en termes de fenêtres modales suggère d’analyser en retour les relations intentionnelles comme des relations inter-mondaines. Le champ des modalités en serait encore étendu, puisque chaque relation intentionnelle entre un sujet et un objet supposerait alors qu’un ensemble de mondes soit constitué et rendu accessible pour le sujet, mondes dans lesquels le sujet trouverait l’objet (parfois actuellement existant, et parfois lui-même) auquel se relier. Ce qui mérite d’être noté ici, c’est, outre le fait que les objets d’une relation intentionnelle peuvent être des objets actuels, la possibilité que la relation intentionnelle soit doublée d’une ou plusieurs autres relations physiques, causales ou non mais actuelles, entre le sujet de l’attitude et son objet. Mais à l’opposé de certaines conceptions, jamais la relation
Philosophia Scientiæ, 16-2 | 2012 163
intentionnelle (inter-mondaine) ne pourra être simplement réduite à la relation physique (intra-mondaine) à laquelle elle est éventuellement corrélée. Je tiens à remercier, pour leurs commentaires, critiques et suggestions très utiles, Maxime Amblard, Gregory Bochner, Franck Lihoreau, Christian Nimtz, Shahid Rahman, Sonia Roca Royes, Luc Schneider et Tero Tulenheimo. Je suis très fortement redevable à plusieurs rapporteurs anonymes, particulièrement à l’un d’ entre eux dont la critique acérée m’a permis de clarifier sensiblement le propos de l’article, ainsi qu’aux éditeurs de ce cahier thématique. Je reste évidemment seul responsable des erreurs et insuffisances du résultat.
BIBLIOGRAPHIE
CHOMSKY, NOAM 1991 Théorie du Gouvernement et du Liage. Les Conférences de Pise,Paris, Éditions du Seuil.
JACKENDOFF, RAY 1992 Mme Tussaud meets the Binding Theory, Natural Language and Linguistic Theory 10, 1-31.
LEWIS, DAVID 1979 Attitudes De Dicto and De Se, The Philosophical Review, 88, 513-543.
LEWIS, DAVID 1986 On the Plurality of Worlds, Oxford: Basil Blackwell.
MAIER, EMAR 2009 Presupposing Acquaintance: A Unified Semantics for De Dicto, De Re and De Se Belief Reports, Linguistics and Philosophy, 32, 429-474.
NINAN, DILIP 2010 De Se Attitudes: Ascription and Communication, Philosophy Compass, 5(7), 551-567.
Perry, John 1990 Self-Notions, Logos, xi, 17-31. Rebuschi, Manuel & Tulenheimo, Tero 2011 Between De Dicto and De Re: De Objecto Attitudes, The Philosophical Quarterly, 61(245), 2011, 828-838.
REULAND, ERIC & WINTER, YOAD 2009 Binding Without Identity: Towards a Unified Semantics for Bound and Exempt Anaphors, Lecture Notes in Computer Science, 5847, 69-79.
TAVINOR, GRANT 2010 Virtual Worlds and Interactive Fictions, dans Truth in Fiction, édité par LIHOREAU, F., Ontos Verlag, 223-244.
WEHMEIER, KAI 2011 Subjunctivity and cross-world predication, Philosophical Studies, doi: 10.1007/ s11098-010-9692-z
Philosophia Scientiæ, 16-2 | 2012 164
ANNEXES
Sémantique pour les fenêtres modales C étant un ensemble de constantes individuelles, P un ensemble de symboles de relations (prédicats), et Ω un ensemble non vide de symboles (que l’on appellera les fenêtres modales), le langage à fenêtres modales Lmw (C, P, O) est un langage multi-modal du premier ordre.
Syntaxe Les termes et les formules du langage Lmw (C, P, Ω) sont définis comme suit :
Termes : t ∷ = a ∣ x ∣ xs
is Formules : φ ∷ = ⊤ ∣ t1 = t2 ∣ Pt1 ...tn ∣ R t1 t2 ∣ ∃xφ ∣ ¬ φ (φ ᐱ φ)[ω]φ
où a est une constante individuelle de C, x une variable individuelle, xs une variable distinguée, P un symbole de relation (prédicat) n-aire de P, R un symbole de relation binaire de P,et w une fenêtre modale de Ω.
Modèles Un modèle de Kripke pour un langage Lmw (C, P, Ω) est un sextuplet
M = W, @, {R } , {D } ,I,Iis ,où : ❬ ω ω∈Ω ω ω∈W ❭ 1. W est un ensemble non vide (l’ensemble des mondes possibles) ;
2. @ ∈ W est un monde distingué (le monde actuel) ;
3. Rω ⊆ W x W est la relation d’accessibilité entre mondes possibles correspondant à la modalité [ω] (donc à la fenêtre modale ω) ;
4. Dω est un ensemble non vide (le domaine des individus existant dans ω) ; on note D . = D la réunion de tous les domaines (le domaine du modèle) ; ᑌω∈W ω 5. I est une fonction d’interprétation (standard) qui assigne :
-un individu I (a)∈ D à chaque constante individuelle a ;
n -une extension intra-mondaine : un sous-ensemble I (P,ω) de D ω à chaque prédicat n-aire P ∈ P et monde possible ω ∈ W ; 6. Iis est une fonction d’interprétation inter-mondaine qui assigne : -une extension inter- is mondaine : un sous-ensemble I (R, ω) de D@ x Dω à chaque prédicat binaire R ∈ P et monde possible ω e W, tel que Iis(R,@) = I(R, @). Commentaire : La seule originalité des modèles réside dans l’extension intermondaine empruntée à [Wehmeier 2011]. Cette extension permet d’étendre (minimalement) les relations aux paires constituées d’un individu du monde actuel et d’un individu d’un monde possible ω23. Interprétation L’évaluation des termes et des formules est relative à un modèle de Kripke M,un monde pointé ❬ω,α❭ (α étant un individu du domaine D), et une assignation g . Var → D. Dans ce qui suit, on omet la référence au modèle M. Valeur des termes
Philosophia Scientiæ, 16-2 | 2012 165
[x] = g(x), où x est une variable ; ❬ω,α❭,g
[a] = I(a), où a est une constante individuelle ; ❬ω,α❭,g
[x ] = . s ❬ω,α❭,g α
Interprétation des formules
ω,α Pt ...t ssi [t ] ,...,[t ] I(P,ω) ❬ ❭⊨g 1 n ❬ 1 ❬ω,α❭,g n ❬ω,α❭,g❭∈
ω,α Rist t ssi [t ] , [t ]( , ), ) Iis(R,ω) ❬ ❭⊨g 1 2 ❬ 1 ❬@,α❭,g 2 ω α g ∈
, g (t = t ) ssi [t ] = [t ]( , ), ❬ω α❭⊨g 1 2 1 ❬ω,α❭,g 2 ω a g
, (t =is t ) ssi [t ] = [t ]( , ), ❬ω α❭⊨g 1 2 1 ❬@,α❭,g 2 ω a g
❬ω,α❭⊨g ¬φ ssi ❬ω,α❭⊭g φ
❬ω,α❭⊨g φᐱψ ssi ❬ω,α❭⊨g φ et ❬ω,α❭⊨g ψ
❬ω,α❭⊨g ∃x φ ssi il existe δ ∈ Dw tel que : ❬ω,α❭⊨g[x/δ]φ
R ❬ω,α❭⊨g [ω] φ ssi pour tout ω’ ∈ W, si ω ωω’ alors {ω’,α)⊨gφ
Commentaires : • La seconde ligne permet d’évaluer le symbole de relation binaire R sur le mode is indicatif-subjonctif :la formule R tlt2 est satisfaite si et seulement si la paire formée
de la valeur du premier terme tl dans le monde actuel @ et de celle du second
terme t2 dans le monde courant ω, est dans l’extension inter-mondaine (sur D@ x
Dw ) du symbole de relation R. • La quatrième ligne assure que le symbole = est toujours interprété comme l’identité (sur D), même quand il est évalué sur le mode indicatif-subjonctif : on peut donc en pratique se dispenser de l’exposant is, l’identité inter-mondaine n’étant rien d’autre que l’identité habituelle (intra-mondaine). Extension Une version étendue du langage permet de formaliser les rapports de croyances à la troisième personne. Il faut ajouter à la syntaxe le terme ys qui correspond au pronom réfléchi, et les formules de la forme Bcφ (c étant une constante individuelle d’ un sous-ensemble fini Cagents de C) pour représenter « c croit que φ ». Les modèles sont enrichis d’une relation d’accessibilité Rc pour chaque nom d’ agent c e
Cagents, avec une condition d’unicité de la relation par agent : si C C, C’ ∈ agents et I(c) = I(c’), alors Rc = Rc’. Les termes et formules sont évalués relativement à un modèle M, un monde avec deux centres {ω,α,β), et une assignation g. Les valeurs des variables ordinaires et des constantes individuelles restent indépendantes des deux centres, celle de xs est le premier centre (α) et celle de ys le second (β).
Philosophia Scientiæ, 16-2 | 2012 166
L’interprétation des formules est semblable à celle définie plus haut, avec cette définition supplémentaire :
R ❬ω,α,β❭⊨g Bcφ ssi pour tout ω’ ∈ W,si ω c ω’ alors ❬ω’, α, I(c)❭ =g φ.
Commentaire : À la différence du premier, le second centre n’est pas un élément du contexte puisqu il est totalement indépendant des énonciations de la phrase représentée par la formule Bcφ.L’opérateur Bc modifie donc deux paramètres de l’ indice (ω et β) sans toucher au contexte.
NOTES
1. Par exemple sur le site du Daily Telegraph, dans un article daté du 1erseptembre 2010 : "Rihanna Twitters picture of her kissing her wax sculpture at Madame Tussauds". Cet exemple actualise celui présenté par [Jackendoff 1992], cf. section 2. 2. D'après la théorie du liage, l'explication est entièrement syntaxique. Dans une phrase comme (1), le nom propre « Rihanna » c-commande l'anaphorique « herself », donc le premier lie le second; le liage impliquant la co-référence, les deux expressions sont alors censées référer au même objet. Voir [Chomsky 1991]. 3. Le terme de « proxy » se traduit habituellement en « mandataire » ou « fondé de pouvoir », mais il sert ici à faire référence aux diverses représentations physiques d’un individu donné ; je vais conserver le terme original en anglais dans la suite de l’article. 4. Je dois à un rapporteur anonyme cet exposé systématique. 5. La suite de l'article se cantonne aux relations PR. L'exposé des fonctions de Skolem qui clot cette sous-section vise uniquement à compléter la présentation succincte de la théorie de Reuland et Winter. 6. Quand plusieurs proxies d'un individu donné sont présents dans le contexte, plusieurs fonctions de Skolem fPR sont corrélativement définissables. 7. "Not long ago, after a trying railway journey by night, when I was very tired, I got into an omnibus, just as another man appeared at the other end. 'What a shabby pedagogue that is, that has just entered, thought I. It was myself : opposite me hung a large mirror. The physiognomy of my class, accordingly, was better known to me than my own." (Ernst Mach 1885, cité par [Perry 1990]). 8. Mon propos n’étant pas centré sur l’analyse des noms propres je me contente de formaliser le nom par une constante, ici interprétée comme un désignateur non rigide. Cette présentation serait donc rejetée par un partisan de la théorie de la référence directe. 9. Une croyance de re à propos de Boltzmann n’exige pas du sujet qu’il emploie le nom propre « Boltzmann ». Une expression de cette croyance qui évite l’usage du nom pourrait être : « C est un pédagogue défraîchi », où l’objet de l’attitude est symbolisé par une variable (voir plus bas la formalisation (6)).
10. Chez Maier l'occurrence du symbole R en dehors de la portée de l'opérateur Bm n’apparaît pas dans une expression conjointe, mais dans une présupposition, voir [Maier 2009, 447 sq]. 11. Dans sa formalisation, [Maier 2009] utilise une variable ordinaire et introduit un prédicat
Center dans la portée de Bm ; la sémantique est analogue à celle proposée ici. 12. On trouve chez [Ninan 2010] l'idée d'une suite de centres pour évaluer des phrases comme « Je t'appellerai demain quand je saurai si Ernst veut venir », où le locuteur n'est que l’un des centres du contexte.
Philosophia Scientiæ, 16-2 | 2012 167
13. Sur la photo médiatisée de la rencontre entre la chanteuse et sa statue, la première a les cheveux rouges et la seconde les cheveux blonds. 14. Par exemple, si je m observe dans le miroir écrivant de la main gauche, je corrige immédiatement et je me vois bien écrivant de la main droite ; mais si je ne me reconnais pas et pense observer quelqu un d’autre à travers une vitre, je peux alors croire voir un gaucher. 15. On peut éviter ici de considérer tous les mondes logiquement possibles et se restreindre aux mondes les plus proches du monde actuel (au sens de Lewis), de manière à écarter les mondes où Mach a six jambes, où il a des pattes de canard, etc. 16. Pour donner une idée de ce qui motive la terminologie et la notation (i et s)de [Wehmeier 2011], l'indicatif i est employé quand on dit ce qu'un individu est (actuellement), et le subjonctif s quand on exprime ce qu'il serait ou aurait pu être (dans une situation contrefactuelle). 17. Le fait qu’on ait ici affaire à des cas d’attitudes de se n’est pas essentiel et le même point aurait pu être illustré avec des attitudes de re de sujets projetant des individus autres qu'eux-mêmes dans les trois exemples. 18. Pour un traitement de la réalité virtuelle en termes de modalités, au même titre que les fictions mais sans les réduire aux fictions, voir [Tavinor 2010]. 19. Cet exemple de projection sur la pièce d’un jeu m a été suggéré par un rapporteur. Il peut être traité à l'aide de fenêtres modales comme les autres, l'identification du sujet à sa pièce ou plus généralement à son rôle ne pouvant être réalisée qu’à travers la fenêtre. 20. L'approche de la sémantique des fictions en termes de modalités comme dans l’exemple est relativement standard. Mon propos n’est pas ici de réduire l’interprétation des statues ou des fictions à celle desfenêtresmodales, maisd'indiquer que ces œuvres peuvent aussi être interprétées comme telles, lorsqu'un sujet s'identifie en se projetant en elles. 21. Ce qu'elle peut exécuter de se ou de re, selon qu'elle se reconnaît ou pas. L'important est qu’en (b) Rihanna embrasse une personne à travers la statue, tandis qu’en (a) elle ne fait qu’embrasser un morceau de cire. 22. Les attitudes focalisées sur des objets inexistants peuvent être formalisées moyennant une nouvelle extension de la logique modale du premier ordre, l’extension IF (independence-friendly). Pour une présentation et une discussion de cas de ce type, se reporter à [Rebuschi & Tulenheimo 2011]. 23. L’extension est minimale à plus d’un titre : elle se cantonne aux prédicats binaires appliqués à des paires ordonnées comprenant comme premier terme un individu du monde actuel. On pourrait en principe envisager des relations inter-mondaines impliquant un individu actuel comme second terme, reliant des individus appartenant à différents mondes possibles sans inclure le monde actuel, mais aussi des relations d'arités supérieures à 2. Élargir ainsi la classe des relations inter-mondaines permettrait d'enrichir considérablement le cadre proposé dans cet article.
RÉSUMÉS
Les pronoms personnels peuvent faire référence à la représentation physique (comme une statue ou une photographie) d’une personne plutôt qu’à cette personne elle-même. L’article présente une explication de ce liage sans identité apparente. Une objection est adressée à la théorie des proxies de Reuland et Winter, fondée sur la distinction entre attitudes de re et attitudes de se. La
Philosophia Scientiæ, 16-2 | 2012 168
stratégie proposée ici consiste à introduire une nouvelle modalité pour chaque nouveau support d’une représentation physique, ce qui permet d’éviter les proxies et de restaurer l’identité à la base de la résolution des anaphores. Les modalités correspondent à des fenêtres modales au travers desquelles le sujet peut appréhender des objets, existants ou non, y compris lui-même. La sémantique proposée suppose de réinterpréter certains prédicats. Elle emprunte à Wehmeier l’idée de relation inter-mondaine, qui soulève en tant que telle des questions métaphysiques. L’article aborde ces questions, pour proposer finalement d’étendre la théorie des fenêtres modales à l’ensemble des relations intentionnelles.
Personal pronouns can refer to some physical representation (like a statue or a photograph) of a person rather than to the person herself. The paper presents an account of such binding without apparent identity. An objection is made to Reuland and Winter’s theory of proxies, based on the distinction between de re and de se attitudes. The strategy proposed here is to introduce a new modality for each new physical representation. This avoids proxies and restores the identity at the base of anaphora resolution. The new modal operators correspond to modal windows through which the subject can grasp objects, existing or not, including herself. The proposed semantics entails a reinterpretation of predicates. It borrows from Wehmeier the idea of cross-world relations, which in itself raises metaphysical questions. The article addresses these issues and finally suggests to extend the theory of modal windows to all intentional relations.
AUTEUR
MANUEL REBUSCHI Laboratoire d’Histoire des Sciences et de Philosophie, Archives H. Poincaré (UMR 7117), Université de Lorraine (France)
Philosophia Scientiæ, 16-2 | 2012 169
Varia
Philosophia Scientiæ, 16-2 | 2012 170
Sources et nature de la philosophie de la physique d’Henri Poincaré
Joâo Principe
Introduction
Cette étude est consacrée aux réflexions épistémologiques élaborées par Henri Poincaré à propos de la physique du XIXe siècle. Après avoir montré comment ses thèses épistémologiques émergèrent dans le cadre de ses cours et de ses recherches scientifiques, nous analysons l’ensemble des réflexions de Poincaré sur la nature et l’évolution des théories physiques jusqu’à la physique des principes. D une part, nous établissons la prégnance des thèses de Helmholtz et de Maxwell. D autre part, nous montrons la possibilité d’une lecture kantienne dans laquelle le plan transcendantal est constitué par des principes constitutifs et par des principes régulateurs. Le but n’est cependant pas d’élaborer un système philosophique rigoureux à partir d’idées que Poincaré n’a souvent fait qu’esquisser d’une manière heuristique.
1 La méthode des comparaisons et le Treatise de Maxwell
En août 1886, Poincaré succède à Gabriel Lippmann sur la chaire de physique mathématique et de calcul des probabilités de la Faculté des Sciences de Paris. Le cours du premier semestre 1887-1888 traite des théories mathématiques de la lumière. L’alternative entre éther moléculaire et éther continu était connue dès les années 1830, en raison de la compatibilité de la théorie de George Green avec un éther continu. Poincaré montre l’équivalence mathématique de six théories concurrentes, malgré les différentes hypothèses physiques de départ. Les théories mathématiques ne nous révèlent pas la « véritable nature des choses » ; elles sont des instruments dont le « but unique est de coordonner les lois physiques que l’expérience nous fait connaître » ; ces lois se traduisent analytiquement dans des équations, lesquelles « resteront vraies, au moins comme première approximation ». L’éther n’est qu’une hypothèse commode,
Philosophia Scientiæ, 16-2 | 2012 171
comme l’est aussi celle de l’existence des objets matériels ; la dernière étant une hypothèse qui restera toujours commode. Les diverses théories de l’éther mécanique sont toutes « également plausibles ». Se borner à l’une d’entre elles produirait une confiance aveugle ; le plus instructif, c est de les comparer. Il note que les hypothèses moléculaires, typiques des théories françaises, ne « jouent qu’un rôle secondaire [...] C est ce qui explique pourquoi la plupart des conclusions de Fresnel subsistent sans changement quand on adopte la théorie électromagnétique de la lumière [celle de Maxwell] » [Poincaré 1889, I-III, 398-400]1.
1 Le cours du second semestre 1888 est dédié aux théories électrodynamiques et à la théorie électromagnétique de la lumière de Maxwell. En 1890, Poincaré s’occupera de la théorie de Helmholtz et des expériences de Hertz et au premier semestre 1891-1892, il comparera la théorie de Maxwell avec celles de l’éther élastique : « J ai donc été conduit à traduire dans ce nouveau langage ce qu’avaient dit en d’autres termes les fondateurs de la théorie ondulatoire. » Il y exprime son engagement pluraliste : « J’ai voulu mettre le lecteur à même de manier avec la même facilité deux instruments qui peuvent être également utiles pour coordonner convenablement la multitude des faits observés » [Poincaré 1892b, VI]. En 1899, il présentera les théories électrodynamiques de Lorentz et de Larmor.
2 De toutes ces lectures de Poincaré, celle de Maxwell a été la plus stimulante sur le plan philosophique. L’ensemble des mémoires de Maxwell sur l’électromagnétisme montre un pluralisme de fait, accompagné de réflexions épistémologiques. La méthode de l’analogie physique est théorisée dans "On Faradays lines of force" (1855). Il s’agit d’une méthode intermédiaire entre deux pôles, celui des théories purement mathématiques et celui des théories qui partent des hypothèses physiques, à accent ontologique. L’analogie est comprise comme correspondance entre relations de systèmes différents. Elle est, en général, partielle car les deux systèmes ont des composantes (relations) qui ne sont pas similaires. La méthode a des avantages psychologiques nets : elle suscite l’attention et l’imagination et évite l’encombrement de la mémoire par l’excès de mathématiques difficiles. Dans "On physical lines of force" (1861-1862), Maxwell propose un modèle mécanique des interactions électromagnétiques. Il fait ici une hypothèse physique sur la nature tourbillonnaire du magnétisme, alors que justement il n’en faisait pas dans son mémoire précédent. En développant sa théorie dynamique du champ électromagnétique (1864), il remarque toutefois que son éther tourbillonnaire de 1861 n’est que « a demonstration that mechanism maybe imagined capable of producing a connexion mechanically equivalent to the actual connexion of the parts of the electromagnetic field2 » [Maxwell 1890, 452].
3 Dans "A dynamical theory of the electromagnetic field" (1864) et dans le Treatise on Electricity and Magnetism, Maxwell utilise la mécanique analytique de Lagrange, laquelle lui permet d’élaborer une théorie sans concrétiser le mécanisme du milieu qui permet les échanges énergétiques entre les corps. Le champ magnétique y est décrit comme un système mécanique à liaisons dont les mouvements sont cachés. Maxwell est convaincu de la supériorité de son approche, ce qui l’amène à considérer que cette méthode analytique correspond à la vraie méthode du raisonnement physique, qui évite les hypothèses non justifiées (qui abondaient dans les modèles mécaniques de l’éther optique). Dans le Treatise, Maxwell note qu’en principe il y a un nombre infini de modèles mécaniques capables de représenter le champ électromagnétique [Maxwell 1873, II, § 831]3.
Philosophia Scientiæ, 16-2 | 2012 172
4 En 1888, Poincaré affirme que le Treatise contient une idée fondamentale conduisant à un bouleversement du concept de réduction mécaniste des phénomènes : Maxwell ne donne pas une explication mécanique de l’électricité et du magnétisme ; il se borne à démontrer que cette explication est possible […] Si donc un phénomène comporte une explication mécanique complète, il en comportera une infinité d’autres. [Poincaré 1890, IV, VIII]4
5 Ce théorème de Maxwell, valable toutes les fois que les principes de l’énergie et de moindre action sont satisfaits, est démontré en détail par Poincaré. Les coordonnées généralisées correspondent à des paramètres observables. Ceux-ci peuvent être mis en rapport avec une myriade de systèmes de coordonnées moléculaires inobservables conduisant à la même fonction de Hamilton. Ce théorème justifie l’attitude de ceux qui trouvent inutiles les spéculations sur la structure ultime de l’éther. Aussi, le théorème met en valeur la dynamique abstraite, préférée par Maxwell. Selon Poincaré, l’idée fondamentale de Maxwell évacue les préoccupations ontologiques : « Le lecteur se trouve ainsi en présence d’une forme presque vide de matière qu’il est d’abord tenté de prendre pour une ombre fugitive et insaisissable » [Poincaré 1890, VXI]. Ce nonobstant, Poincaré constate que la tradition de la physique laplacienne, basée sur l’hypothèse de forces intermoléculaires qui deviennent insensibles à des distances sensibles, est encore très vivante en France et que son ontologie inconsciente constitue un obstacle épistémologique dans l’acceptation de nouvelles approches. Poincaré donne un cas concret d’application du théorème de Maxwell dans lequel il rejette la prétention des expériences d’Otto Wiener, faites en 1891, à décider entre les théories de Neumann et de Fresnel sur la polarisation de la lumière [Poincaré 1891b]5.
6 Dans ses leçons sur l’électrodynamique et l’optique, Poincaré adopte une présentation inductive, tout en fournissant des analogies expressives, notamment pour les propositions les plus difficiles. Il reconnaît la valeur didactique et heuristique des analogies mécaniques et les utilise de concert avec « l idée fondamentale » de Maxwell. C est aussi le cas dans La théorie de Maxwell et les oscillations hertziennes. Il commence par noter l’évolution des idées de Maxwell, de la construction d’un éther particulier jusqu’ à l’idée de la suffisance de la possibilité d’une explication mécanique. Il note que Maxwell s’est éloigné de la tradition britannique de construction de modèles d’« apparence concrète » et il note que par, « ce chemin détourné », Maxwell a été conduit « aux plus grandes découvertes ». Poincaré montre comment on peut donner des phénomènes électriques une explication mécanique « sans déployer tout l’appareil de l’analyse mathématique » [Poincaré 1899a, 6]. Il fournit plusieurs images mécaniques pour les phénomènes électrostatiques, la résistance des conducteurs, l’induction et les attractions électrodynamiques, ce qui démontre que, malgré sa préférence pour la vision définitive de Maxwell, Poincaré concède aux analogies mécaniques et aux modèles concrets un important rôle heuristique et didactique6.
2 Méthode et structure des théories physiques
Dans des textes écrits vers 1900 et destinés à des audiences disparates (allocutions prononcées lors de congrès internationaux, articles philosophiques) Poincaré présente d’une manière plus systématique, bien que très brève, ses réflexions sur la méthode, la structure et l’évolution des théories physiques jusqu’à la physique des principes. Je me limite aux textes où il parle de la physique du XIXe siècle car les bouleversements des théories physiques au tournant du siècle (nouvelles radiations, quanta, relativité)
Philosophia Scientiæ, 16-2 | 2012 173
l’amèneront à réfléchir sur un terrain bien différent de celui sur lequel Maxwell a vécu. En 1904, Poincaré juge que la physique des principes, dont Maxwell était l’un des pionniers, est en danger. Considérant l’état actuel de la physique mathématique, il parle d’une « débâcle générale des principes » [Poincaré 1904, 318], d’une seconde crise amenant à une troisième phase de la physique mathématique (les deux premières phases sont la physique des forces centrales et la physique des principes).
2.1 Généralisation et analogie
Pour Poincaré, la capacité de généraliser est une faculté de notre esprit qui est la condition de possibilité de la science [Poincaré 1892a, VI]. C est l’intuition, la faculté qui est l’instrument de l’invention, qui produit le passage du particulier au général. L’intuition permet de saisir l’unité d’un tout (d une démonstration, par exemple) et de trouver des rapports nouveaux en guidant l’esprit : Pour comprendre un plan, il faut en apercevoir à la fois toutes les parties, et le moyen de tout embrasser dans un coup d’œil d’ensemble, c est l’intuition seule qui peut nous le donner […] Il nous faut une faculté qui nous fasse voir le but de loin […] [Poincaré 1900b, 125]
7 L’intuition a plusieurs espèces : la généralisation par induction, celle qui fait appel au sens et à l’imagination et l’intuition du nombre pur (celle d’où sort le principe de l’induction mathématique qui engendre, par une voie synthétique, le raisonnement mathématique) [Poincaré 1902a, 127-128]. Cette dernière est celle des analystes et la deuxième est celle des géomètres. Ce nonobstant, Poincaré reconnaît que « l intuition sensible est en mathématiques l’instrument le plus ordinaire de l’invention » [Poincaré 1900b, 129] ; il note aussi que l’élaboration logique des concepts est précédée par celle de notions plus intuitives.
8 Poincaré note que c est la physique mathématique « qui doit guider la généralisation [en physique] de façon à augmenter [...] le rendement de la science » [Poincaré 1900a, 1164]. La Physique mathématique et l’Analyse partagent le même esprit et Poincaré en arrive à dire que les mathématiques sont la seule langue que le physicien puisse parler ; il note que ce langage permet de saisir les analogies intimes des choses [Poincaré 1897b, 858]. Maxwell, en 1855, avait déjà associé l’analogie au caractère constitutif et nécessaire des mathématiques dans les sciences physiques ; pour lui « the most universal ofall analogies », c’est que « all the mathematical sciences are founded on relations between physical laws and laws of numbers » [Maxwell 1890, I, 156]. Parmi les processus intuitifs permettant le guidage de l’esprit du savant dans son travail de généralisation, Poincaré accorde un rôle majeur à l’analogie et aux principes architectoniques (unité, simplicité, continuité)7.
9 L’analogie guide le raisonnement car elle permet de deviner, de pressentir les généralisations, les hypothèses. Elle est donc omniprésente. Et cela dès l’induction la plus élémentaire : en 1900, Poincaré note que la répétition est fondamentale pour qu’un fait soit considéré intéressant (en physique) ; mais les circonstances qui produisent un fait donné ne se reproduiront jamais à nouveau ; on peut seulement dire que dans des circonstances analogues un fait analogue aura lieu. Considérant l’élaboration théorique, il note que pour résoudre une nouvelle question on établit une analogie avec une autre dont la méthode de résolution est connue ; il faut ensuite s’apercevoir « en quoi cette nouvelle question diffère des autres » et déduire « les modifications qu’il est nécessaire d’apporter à la méthode » [Poincaré 1900b, 128]. Il distingue deux types
Philosophia Scientiæ, 16-2 | 2012 174
d’analogie, lesquelles sont en correspondance avec les deux dernières espèces d’intuition : les analogies mathématiques font deviner les analogies physiques et, en Analyse, ces dernières aident l’analyste ; c est-à-dire que l’intuition sensible a autant d’importance heuristique que celle des analystes, plus pure8.
10 Un exemple d’analogie est celui de « l analogie véritable » (mathématique) consistant « à nommer du même nom des êtres qui ne diffèrent que par la matière, à nommer du même nom par exemple la multiplication des quaternions et celle des nombres entiers » [Poincaré 1897b, 858] ; celui-ci est aussi mentionné par Maxwell en 1870, dans son allocution à la British Association, quand il note que des quantités de nature physique différente ont le même caractère vectoriel [Maxwell 1890, II, 218]. Un autre exemple est l’invention du courant de déplacement par Maxwell qui, selon Poincaré, « était profondément imprégné du sentiment de la symétrie mathématique ». Ce sentiment résulte du fait « que Maxwell était habitué à penser en vecteurs ». Pour Poincaré, « Maxwell n’était peut-être pas un habile analyste […] mais il avait au plus haut degré le sens intime des analogies mathématiques ». Si sur cet exemple l’analogie mathématique fait pressentir l’ analogie physique, un autre exemple — celui où la même équation aux dérivées partielles (celle de Laplace) « se rencontre dans la théorie de l’attraction newtonienne, dans celle du mouvement des liquides, dans celle du potentiel électrique, dans celle du magnétisme, dans celle de la propagation de la chaleur » [Poincaré 1897b, 859] — montre que l’analogie mathématique fournit des méthodes de résolution des équations et permet un transfert de vocabulaire qui aide à bâtir des concepts intuitifs. Ce dernier exemple ne s’inspire pas seulement de Maxwell et de Kelvin (analogie entre l’équation de la chaleur et celle du potentiel électrostatique), mais aussi des travaux de Poincaré sur les équations aux dérivées partielles de la physique mathématique9.
11 L’allocution de 1897 partage avec celle de Maxwell de 1870 le thème du rapport entre physique et mathématiques. Maxwell note qu’une des principales caractéristiques du mathématicien est sa sensibilité à la symétrie et sa capacité d’exprimer la même chose de différentes manières, et de transformer « aperplexing expression into another which explains its meaning in more intelligible language » [Maxwell 1890, II, 217]. Mais si le mathématicien montre au physicien que les quantités qu’il mesure sont liées par des rapports nécessaires, ce dernier révèle au premier l’existence de formes de quantités qu’il ne pouvait point imaginer. Maxwell met en rapport la méthode des illustrations (analogies) avec ce qu’il nomme la classification systématique des quantités. Cette classification est motivée par la perception des ressemblances entre les processus et formes de raisonnement mathématiques utilisés dans deux sciences différentes, dont la raison ultime est l’identité des rapports mathématiques. Les deux auteurs distinguent les analogies physiques des analogies mathématiques (formelles/vraies) et valorisent le rôle et le statut des dernières. Maxwell note que les analogies mathématiques permettent de juger de la justesse et de la vérité d’une illustration ou analogie physique10.
12 Kant, dans sa Logique, distingue entre « jugement déterminant » et « jugement réfléchissant ». Le premier détermine un cas au moyen d’un concept général. Le second part du ou des cas tels qu’ils sont donnés et recherche le concept général capable de les subsumer. Les raisonnements par induction et par analogie sont les deux moyens dont se sert le jugement réfléchissant pour trouver le concept général en question. Poincaré considère l’induction et l’analogie comme fondamentales pour la généralisation, mais,
Philosophia Scientiæ, 16-2 | 2012 175
contrairement à Kant, il semble assimiler l’induction à un type d’analogie. Les analogies sont donc des instruments omniprésents et à portée variable : elles sont présentes dans toute généralisation, fût-elle élémentaire ou correspondant à un grand changement théorique. L’établissement d’analogies entre théories permet leur éclaircissement mutuel et permet l’extension d’une théorie à un nouveau domaine de phénomènes. Poincaré reconnaît dans l’intuition sensible et dans les analogies physiques un rôle important dans l’élaboration des théories, mais il valorise davantage les analogies mathématiques. En 1897, Poincaré considère l’avènement de la mécanique de Newton comme un exemple majeur de « changement de langage », lié à l’introduction de l’analyse mathématique [Poincaré 1897b, 858]. Poincaré n’essaie pas de réduire ce processus de généralisation de haute portée à des analogies.
2.2 Le plan transcendantal : principes heuristiques et constitutifs
Dans cette section, orientée par des distinctions kantiennes, je m’occupe du méta- niveau des principes ayant des fonctions régulatrices et/ou constitutives.
13 Dans la préface de sa Thermodynamique, Poincaré note que les lois se formulent « après des expériences relativement peu nombreuses et qui présentent certaines divergences ». Toute proposition pouvant « être généralisée d’une infinité de manières », le choix de la loi générale se fait d’après un critère de simplicité [Poincaré 1892a, VI-VII]. En 1900, Poincaré amplifie ses réflexions sur le besoin d’ordre, d’harmonie et de simplicité, lequel correspond à une nécessité, un instinct ou une habitude de l’esprit ; il note que « toute généralisation suppose […] la croyance à l’unité et à la simplicité de la nature ». Il considère les rapports entre le simple et le complexe, montrant comment le progrès des théories présente des niveaux successifs d’organisation où le simple cache le complexe et inversement. Il affirme : « Il faut bien s’arrêter quelque part, et, pour que la Science soit possible, il faut s’arrêter quand on a trouvé la simplicité » [Poincaré 1900a, 1164-1167].
14 Dans l’article « Sur les hypothèses fondamentales de la géométrie », Poincaré, inspiré par Riemann et par Helmholtz, s’interroge sur l’origine du postulat des parallèles d’Euclide et sur la présence de jugements synthétiques a priori en mathématiques. Il établit le caractère conventionnel des postulats de la géométrie, soulignant qu’ils sont des conventions de langage, résultant de la décision libre de l’esprit mais motivées par l’expérience. En 1891, considérant les géométries non-euclidiennes et leur usage structurant dans la physique, il note que le test utilisant la parallaxe des étoiles admet que les rayons lumineux sont des lignes droites ; mais un résultat en apparence contraire à la géométrie euclidienne pourrait être interprété en modifiant les lois de l’optique et « tout le monde regarderait cette solution comme plus avantageuse » [Poincaré 1887, 213-214]. Poincaré croit donc que « la géométrie euclidienne est et restera la plus commode » [Poincaré 1891a, 774]11.
15 Poincaré considère le cas hypothétique où les astronomes découvrent « que les astres n’obéissent pas exactement à la loi de Newton [gravitation universelle] » ; alors, soit on change la loi, soit on postule « que la gravitation n’est pas la seule force qui agisse », en gardant la loi de Newton comme une définition de la gravitation : Dans le second cas ce sera l’attitude nominaliste. Le choix entre les deux attitudes reste libre, et se fait d’après des considérations de commodité, quoique ces considérations soient le plus souvent tellement puissantes qu’il ne reste pratiquement peu de chose de cette liberté. [Poincaré 1902a, 276]
Philosophia Scientiæ, 16-2 | 2012 176
16 L’attitude nominaliste est souvent inconsciente (voir plus-bas p. 209) ; c est la critique qui peut la dégager. Elle est essentielle pour bâtir une Physique des principes. Avec celle-ci on obtient une unité supérieure : « [Les principes] sont peu nombreux, parce que chacun d’eux remplace à peu près un grand nombre de lois. On n’a donc pas intérêt à les multiplier » [Poincaré 1902a, 278] , [Poincaré 1900a, 1166]. Cet effort d’économie et de systématisation des lois en les hiérarchisant par subsomption (l’ intégration de l’ individu dans l’espèce, ou de l’espèce dans le genre est obtenue par voie mathématique) est guidé par le besoin d’unité, simplicité, ordre et harmonie12.
17 Les règles ou principes généraux de la méthode associés à ce besoin peuvent être compris au sens kantien de « principes de convenance »que Kant définit comme des « règles de jugement auxquelles nous nous soumettons volontiers et adhérons comme à des axiomes, pour cette seule raison que, si nous nous en écartions, notre entendement ne pourrait presque jamais émettre un jugement sur un objet donné ». Ces principes « s’appuient sur des raisons subjectives, non point cependant sur les lois de la connaissance sensible, mais sur les lois de la connaissance intellectuelle elle-même, à savoir sur les conditions par lesquelles il paraît facile et rapide à cette connaissance d’user de sa propre perspicacité » [Kant 1770, § 30, II, 418]. Ces considérations, présentes à la fin de Dissertation de 1770, s’approfondissent avec la distinction constitutif/régulateur, développée dans les première et troisième Critiques13. Dans l’Analytique transcendantale de la première Critique, Kant attribue une signification transcendantale aux catégories et aux principes purs de l’entendement. Kant distingue entre les principes mathématiques, lesquels autorisent d’appliquer les mathématiques aux phénomènes, et les principes dynamiques ou analogies de l’expérience. Les premiers sont constitutifs, donnant les conditions a priori de l’intuition et étant absolument nécessaires ; un principe est constitutif quand il fonde, conditionne et détermine les objets scientifiques. Les seconds sont régulateurs, et, vu que l’existence des objets d’une intuition n’est que contingente, ils ont un caractère de nécessité a priori d une manière médiate et indirecte [Kant 1783, § 13], fin de la Remarque III, [Kant 1781-1787, A180].
18 Dans l’appendice à la Dialectique transcendantale, Kant considère l’usage régulateur des idées de la raison pure, revenant à l’intérêt des principes de convenance pour la systématisation de la connaissance obtenue par l’entendement [Kant 1770, § 30, II, 418]. Celui-ci, utilisant les catégories, constitue l’objet (donnant forme à l’intuition sensible), mais ne fournit pas le lien systématique permettant d’organiser la diversité des objets dans une science. Pour les grouper de façon systématique il faut une idée qui nous guide pour constituer une totalité. Les idées doivent être prises de façon analogique et non comme des objets, car elles ne s’appliquent pas à une intuition (sensible) mais à l’entendement, en structurant le système de la connaissance. Ces idées heuristiques constituent un ensemble ouvert, évoluant historiquement. En guidant l’élaboration théorique, elles se clarifient, changent et sont révisées. Leur usage régulateur correspond à l’usage hypothétique de la raison, présent dans l’induction ; cet usage demande que les hypothèses soient unies systématiquement avec leurs conséquences et qu’elles soient systématiquement unies avec d’autres hypothèses et sous des hypothèses de niveau supérieur14.
19 Bien que Kant ait distingué les deux fonctions, constitutive et régulatrice, des principes, il reconnaît qu’un même principe peut être utilisé des deux façons. Aussi, la notion de constitutif peut être séparée de celle de nécessaire au sens d’unique ; c est-à-dire un cadre de principes est constitutif dans un certain contexte théorique. Un même
Philosophia Scientiæ, 16-2 | 2012 177
principe peut être jugé régulateur du point de vue de la logique de la découverte, de l’ars inveniendi, et peut être jugé constitutif du point de vue de la « légitimation de la science [...] déjà constituée et établie », de l’analyse structurelle des théories [Ribeiro dos Santos 2008, 8].
20 De son côté, Poincaré s’est efforcé de mettre en évidence les présupposés du travail créateur de l’esprit du scientifique (concernant l’usage de l’entendement, de l’imagination, de la raison), ce qu’on peut nommer heuristique transcendantale [Ribeiro dos Santos 2008, 8]. Une idée centrale de cette heuristique transcendantale poincaréenne est la quête d’analogies permettant l’extension et la comparaison des théories. Cela est lié à l’engagement pluraliste, d’inspiration maxwellienne, qui favorise la prolifération de « langages », et le conséquent conflit et besoin d’explicitation d’hypothèses, en nous forçant « à envisager les choses sous différents aspects » [Poincaré 1900a, 1164]. Par là même on arrive à découvrir l’harmonie cachée : Il en est des symboles mathématiques comme des réalités physiques ; c est en comparant les aspects différents des choses que nous pourrons en comprendre l’harmonie intime, qui seule est belle et par conséquent digne de nos efforts. [Poincaré 1897b, 859]15
21 Dans la terminologie kantienne, on peut dire que Poincaré attribue un rôle régulateur « aux principes généraux tels que le principe de moindre action ou celui de la conservation de l’énergie ». Il note que ce dernier principe est lié à l’idée d’invariant et à l’incapacité de donner une définition générale de l’énergie : Quelles que soient les notions nouvelles que les expériences futures nous donneront sur le monde, nous sommes sûrs d’avance qu’il y aura quelque chose qui demeurera constant et que nous pourrons appeler énergie.
22 Les principes, bien qu’issus de l’expérience (et donc représentant dans des cas concrets des rapports réels), ont une puissance d’extension qui semble indéfinie ; l’expérience ne peut pas les contredire directement. Leur genèse montre leur appartenance à un méta- niveau parmi les lois physiques : Ces principes ont une très haute valeur ; on les a obtenus en cherchant ce qu’il y avait de commun dans l’énoncé de nombreuses lois physiques ; ils représentent donc comme la quintessence d’innombrables observations. [Poincaré 1900a, 1170]
23 Le méta-statut des deux principes résulte de leur souplesse, du fait qu’ils sont des « formes presque vide de matière », puisque U = T + V et L = T - V, sont des fonctions à concrétiser pour chaque domaine de phénomènes. La fécondité des principes peut néanmoins s’éteindre au moment où ils ne nous permettent plus de « nous faire prévoir sans nous tromper des phénomènes nouveaux » [Poincaré 1900a, 1170].
24 Les principes régulateurs sont pris comme des règles heuristiques de guidage vers une systématisation optimale, un contrôle, une extension et une unification de l’ensemble des lois empiriques. Par là ils finissent par devenir, de façon assez indirecte, une condition de possibilité de l’expérience. Les grands principes de la physique de la fin du XIXE siècle n’ont pas le même « rang hiérarchique », dans une perspective transcendantale, que le besoin d’unité, de simplicité, d’ordre et d’harmonie. Ces derniers sont des formes plus vastes, vagues et durables. Les principes de la physique ont une fonction épistémique semblable aux postulats/axiomes des géométries mais ont une base empirique mouvante qui peut les rendre inutiles/révisables. Aussi, la subsomption de lois physiques à un système de principes est historiquement changeante comme l’est aussi la hiérarchie interne de ce supposé système. Les
Philosophia Scientiæ, 16-2 | 2012 178
différents principes peuvent ne pas avoir le même degré de généralité. En 1904, parlant de la menace qui pèse sur la validité des principes, Poincaré note que : Le principe de moindre action est intact jusqu’ici, et Larmor paraît croire qu’il survivra longtemps aux autres ; il est en effet plus vague et plus général encore. [Poincaré 1904, 318]
25 Le mélange des deux fonctions, constitutive et régulatrice, se trouve dans le concept poincaréen d’hypothèses naturelles (1900). Celles-ci, « auxquelles on ne peut guère se soustraire », sont constitutives et en même temps guident la recherche en physique mathématique : Il est difficile de ne pas supposer que l’influence des corps très éloignés est tout à fait négligeable, que les petits mouvements obéissent à une loi linéaire, que l’effet est une fonction continue de sa cause. J’en dirai autant des conditions de symétrie. Toutes ces hypothèses forment […] le fond commun de toutes les théories de la Physique mathématique. Ce sont les dernières qu’on doit abandonner. [Poincaré 1900a, 1166]
26 Dans la section « Origines de la Physique mathématique », Poincaré identifie « les conditions qui ont permis le développement de la physique mathématique » basée sur les équations différentielles. Ces conditions se divisent en deux niveaux, le premier systématise les façons de décomposer un phénomène complexe en un nombre très grand de phénomènes élémentaires, le second concerne le fondement de cette décomposition. Les méthodes de décomposition sont décrites comme des hypothèses, qui, ne résistant pas à l’épreuve, doivent donner lieu à d’autres hypothèses. Sur la physique des milieux continus, Poincaré élabore des considérations proches de celles de Joseph Boussinesq : la simplicité des lois est liée au fait « que nous observons des effets moyens où les discordances individuelles disparaissent et se neutralisent en vertu de la loi des grand nombres » [Boussinesq 1879, 28 et 33]. Un autre exemple est le principe de superposition, dans lequel l’interaction simultanée de corps se décompose parce que leurs actions (représentées, par exemple, par des vecteurs) sont indépendantes, le fait élémentaire étant l’action d’un seul corps. Considérant la décomposition par rapport au temps, la loi de Newton s’obtient en postulant que l’état actuel ne dépend que du passé plus proche : « Au lieu d’étudier directement toute la succession des phénomènes, on peut se borner à en écrire l’équation différentielle, aux lois de Képler, on substitue celle de Newton » [Poincaré 1900a, 1167]16.
27 La connaissance du fait élémentaire permet d’écrire l’équation et le complexe se déduit par combinaison. Sur les conditions transcendantales, constitutives, permettant que la généralisation prenne la forme mathématique, Poincaré note que l’homogénéité, l’indépendance relative des parties éloignées, la simplicité du fait élémentaire, permettent la décomposition du complexe (seul observable) en phénomènes élémentaires dans l’espace et dans le temps. Poincaré note que le principe de superposition est applicable là où « le phénomène observable est dû à la superposition d’un grand nombre de phénomènes élémentaires tous semblables entre eux » et conclut : « Ainsi s’introduisent tout naturellement les équations différentielles » [Poincaré 1900a, 1168]. Les faits élémentaires sont simples et obéissent tous à la même loi. Leur combinaison implique une répétition d’opérations que seule l’induction mathématique rend possible.
28 En résumé, les réflexions méthodologiques de Poincaré sont susceptibles d’une lecture kantienne qui en fait une analyse de la fonction régulatrice des principes de convenance et de la fonction constitutive des mathématiques. La modélisation
Philosophia Scientiæ, 16-2 | 2012 179
mécanique des phénomènes, la hiérarchisation des lois et l’évolution de leur statut sont des thèmes poincaréens apparentés.
2.3 Objectivité, composition et évolution des théories
Le thème de la faillite de la science était à la mode dans la France de la fin du XIXE siècle. Le prétendu anti-intellectualisme bergsonien a favorisé le nominalisme radical d’Edouard Le Roy, auquel Poincaré s’est crû obligé de répondre. Pour Poincaré, l’histoire de la physique n’est pas une accumulation de ruines sur des ruines, parce que quelques éléments, ancrés dans le sol de l’expérience, survivent au changement. Ces résidus sont fondamentaux car ils expriment des rapports vrais : Ce qui succombe ainsi, ce sont les théories proprement dites, celles qui prétendent nous apprendre ce que sont les choses [...] Si l’une d’elles a fait connaître un rapport vrai, ce rapport est définitivement acquis et on le retrouvera sous un déguisement nouveau dans les autres théories qui viendront successivement régner à sa place. [Poincaré 1902a, 292]17.
29 Les réflexions de Poincaré suggèrent une stabilisation structurelle de la toile de fond puisque les théories physiques présupposent le continu, le cadre spatiotemporel, une géométrie commode, et utilisent, depuis Newton, l’Analyse. Cela va déjà contre le nominalisme de LeRoy. De surcroît, Poincaré admet certainement une notion de progrès. En 1897, considérant le système des deux principes de l’énergie et de la moindre action (système énergétique), Poincaré note qu’il représente un progrès par rapport au système classique, celui des lois de Newton (basé sur les notions de masse, force et accélération, lequel comporte des définitions déguisées). Dans son allocution de 1900, il conclut son jugement sur l’état actuel de la physique en affirmant : « Tout compte fait, on s’est rapproché de l’unité [...] en définitive on a gagné beaucoup de terrain » [Poincaré 1900a, 1175]. En 1902, il note que « le progrès est lent, mais continu » et que « les synthèses scientifiques [...] tendent à absorber en elles les synthèses partielles » [Poincaré 1902a, 293]18.
30 Cette idée de progrès s’accorde avec l’esquisse, faite en 1904 devant le Congrès à Saint- Louis, des grandes lignes de l’évolution des théories physiques jusqu’à la physique des principes : Une loi, pour nous […] c est une relation constante entre le phénomène d’aujourd’hui et celui de demain ; en un mot, c’est une équation différentielle. Voilà la forme idéale de la loi physique […] c est la loi de Newton qui l’a revêtue la première […] Néanmoins il est arrivé un jour où la conception des forces centrales n’a plus paru suffisante [...] Que fit-on alors ? On renonça à pénétrer dans le détail de la structure de l’Univers […] et l’on se contenta de prendre pour guides certains principes généraux qui ont précisément pour objet de nous dispenser de cette étude minutieuse. [Poincaré 1904, 304-305] Cette évolution est un grand pas en avant dans la direction de l’unité car : Ces principes sont des résultats d’expériences fortement généralisés ; mais ils semblent emprunter à leur généralité même un degré éminent de certitude. Plus ils sont généraux [... ] plus on a fréquemment l’ occasion de les contrôler et les vérifications, en se multipliant, en prenant les formes plus variées et les plus inattendues, finissent par ne pas laisser de place au doute. [Poincaré 1904, 306]
31 La vérification des principes est complexe et le plus souvent indirecte. Par exemple, les principes de la mécanique « sont des vérités [...] vérifiées d’une façon très approchée » pour des systèmes isolés qui deviennent des conventions commodes, des « postulats applicables à l’ensemble de l’univers » [Poincaré 1902b, 151]. Dans sa critique à Le Roy,
Philosophia Scientiæ, 16-2 | 2012 180
Poincaré décrit un processus assez idéalisé, correspondant à une attitude nominaliste, par lequel une loi peut être convertie dans un principe : Par un nominalisme inconscient, les savants ont élevé au-dessus des lois ce qu’ils appellent des principes. Quand une loi a reçu une confirmation suffisante de l’expérience, nous pouvons adopter deux attitudes ; ou bien laisser cette loi dans la mêlée ; elle restera soumise alors à une incessante révision [...] Ou bien on peut l’ériger en principe, en adoptant des conventions telles que la proposition soit certainement vraie [...] La loi primitive énonçait une relation entre deux faits bruts A et B ; on introduit [...] un intermédiaire abstrait C, plus ou moins fictif [... ] Et alors nous avons une relation entre A et C que nous pouvons supposer rigoureuse et qui est le principe ; et une autre entre C et B qui reste une loi révisable. Le principe, désormais cristallisé pour ainsi dire, n’est plus soumis au contrôle de l’expérience. Il n’est pas vrai ou faux, il est commode. [Poincaré 1902a, 276]
32 Cette description semble très simplifiée quand on la compare à la discussion de la conservation de l’énergie dans la Thermodynamique ou à celle des principes de la mécanique dans l’article sur la Mécanique de Hertz [Poincaré 1892a, VII-XIII], [Poincaré 1897a]. Elle sert surtout à montrer l’élément de décision dans le choix de l’attitude nominaliste (par laquelle on souligne la fonction régulatrice des principes) et le fait que la physique des principes reste une science expérimentale : Toute loi peut se décomposer en un principe et une loi, mais il est bien clair par là que, si loin que l’on pousse cette décomposition, il restera toujours des lois. [Poincaré 1902a, 276] Venons-en aux rapports vrais. Un rapport vrai commence par être une hypothèse : Les hypothèses de la troisième catégorie sont les véritables généralisations. Ce sont elles que l’expérience doit confirmer ou infirmer. Vérifiées ou condamnées, elles seront toujours fécondes. [Poincaré 1900a, 1167]
33 Celles-ci différent des hypothèses naturelles (voir ci-dessus) et des hypothèses indifférentes (voir plus bas). Poincaré ne définit pas ce qu’est un rapport vrai mais il en donne plusieurs exemples ; il souligne qu’il est une relation entre des choses, et cela en inscrivant son analyse dans le cadre du criticisme qui refuse l’accès à la chose en soi. Ce sont les rapports qui, s’organisant en système, rendent compte de l’objectivité : « La science [. . . ] est un système de relations » [Poincaré 1902a, 290]. Un exemple de rapport vrai est celui des lois qui permettent de prévoir les phénomènes d’un certain domaine ; c est le cas de quelques équations différentielles de la théorie optique de Fresnel qui restent valables dans le cadre de la théorie de Maxwell ; l’œuvre de Fresnel n’a pas été vaine : Car le but de Fresnel n’était pas de savoir s’il y a réellement un éther, s’il est ou non formé d’atomes [...] c’était de prévoir les phénomènes optiques [...] Les équations différentielles sont toujours vraies […] Ces équations expriment des rapports et, si les équations restent vraies, c’est que ces rapports conservent leur réalité [...] Mais ces appellations n’étaient que des images substituées aux objets réels que la nature nous cachera éternellement. [Poincaré 1900a, 1168-1169]
34 Un autre exemple, plus complexe, est celui de l’analogie mathématique entre différents phénomènes, par exemple quand il s’agit de divers phénomènes périodiques. Cette analogie relève d’une unité supérieure en ce qu’il est une conséquence des principes : Qu’il y ait entre l’oscillation électrique, le mouvement du pendule et tous les phénomènes périodiques une parenté intime qui correspond à une réalité profonde ; que cette parenté, cette similitude, ou plutôt ce parallélisme se poursuive dans le détail ; qu’ elle soit une conséquence de principes plus généraux, celui de l’énergie et celui de la moindre action ; voilà ce que nous pouvons affirmer :
Philosophia Scientiæ, 16-2 | 2012 181
voilà la vérité qui restera toujours la même sous tous les costumes dont nous pouvons juger utile de l’affubler. [Poincaré 1900a, 1169]
35 L’évolution historique des théories physiques ne nous fournit pas seulement une accumulation de lois mais des niveaux de généralité nouveaux. Cet exemple suggère qu’un principe général peut être un exemple de rapport vrai. Un autre exemple confirme cette hypothèse : Carnot a établi [son principe] en partant d’hypothèses fausses ; quand on s’aperçut que la chaleur n’est pas indestructible […] on abandonna complètement ses idées ; puis Clausius y revint et les fit définitivement triompher. La théorie de Carnot, sous sa forme primitive, exprimait, à côté de rapports véritables, d’autres rapports inexacts, débris de vieilles idées [...] Clausius n’a eu qu’à les écarter comme on émonde des branches mortes. Le résultat a été la seconde loi fondamentale de la Thermodynamique. [Poincaré 1900a, 1170]
36 Pour qu’un rapport puisse être saisi comme vrai il faut d’abord qu’il soit saisi comme simple, et il n’est simple, c est-à-dire intelligible, que d’après un cadre expérimental et théorique qui rend intéressant ce rapport ; si l’on n’a pas un bon cadre théorique « les progrès des observations ne serviront qu’à faire croire au chaos » [Poincaré 1897b, 858]. Un rapport vrai ne peut pas être une relation mathématique à validité absolue, car les lois ne sont qu’approchées, dépendant de la précision des moyens d’observation, les vérifications se limitant à augmenter la vraisemblance (probabilité subjective) d’une loi ; sa validité découle aussi d’ un système d’idées scientifiques dont l’ organicité est changeante. Sa discussion sur les relations entre le simple et le complexe suggère qu’un « rapport simple » s’appuie sur une base empirique qui étant élargie (pour des raisons théoriques) précisera les limitations d’une loi, inconnues au départ. Il suffit de penser à la loi de Boyle-Mariotte et aux corrections successives, mélange complexe de considérations théoriques et d’améliorations expérimentales, de l’équation qui veut représenter un gaz réel. La simplicité d’une loi peut être réelle et profonde, « cas où elle résisterait à la précision croissante de nos moyens de mesure » [Poincaré 1900a, 1166]19.
37 Pour le principe de conservation de l’énergie, Poincaré note que : « Les différentes choses auxquelles nous donnons le nom d’énergie sont liées par une parenté véritable ; le principe affirme un rapport réel [...] il est assuré d’avance d’être vérifié dans l’acception stricte du mot » [Poincaré 1900a, 1170]. La contradiction apparente avec son affirmation nominaliste de l’invérifiabilité du principe de l’énergie résulte en partie du fait que ce principe a une puissance d’extension de ses applications qui semble indéfinie. Celle-ci est fonction de la créativité qui crée des conventions adaptant les principes aux lois expérimentales de niveau inférieur. Un principe physique est une convention d’un type spécial car l’expérience peut le condamner « sans le contredire directement » ; c est le cas où on n’arrive qu’à l’utiliser de façon ad hoc [Poincaré 1905, 146]. Dans sa Thermodynamique, il valorise la souplesse du principe de conservation de l’énergie : « La loi de Meyer est une forme assez souple pour qu’on y puisse faire rentrer presque tout ce que l’on veut. » Sa souplesse « est une raison de croire à sa longue durée » [Poincaré 1892a, XIII]. La souplesse et la fécondité des principes sont liées à leur usage quasi nominaliste en tant que principes régulateurs, favorisant l’inclination phénoménologique. L’attitude opposée, qui affirme une ontologie particulière (par exemple : tout réduire à des interactions entre atomes centres de force) est bien plus rigide. La physique des principes reflète le pluralisme épistémologique de Poincaré, qui reconnaît le rôle de la multiplicité des représentations et leur intertraductibilité. Et elle reste compatible avec l’idée d’une vérification expérimentale (indirecte) des principes.
Philosophia Scientiæ, 16-2 | 2012 182
Il suffit de considérer l’attention que prête Poincaré à la complexité de la détermination de l’équivalent mécanique de la chaleur ou aux expériences concernant le vent d’éther20.
38 Dans la réplique à Le Roy de 1902, Poincaré essaie d’harmoniser sa notion de rapports vrais avec le fait que les théories scientifiques ont une structure complexe, liant des éléments disparates, des sensations, des perceptions et des expériences par un mélange de langage naturel et de langage mathématique. Ses discussions antérieures montraient l’importance des conventions, particulièrement en ce qui concerne le choix de la géométrie en fonction de laquelle les lois de la physique s’expriment. L’univocité des rapports vrais enchassés dans les théories est garantie par l’intertraductabilité, basée sur l’ intersubjectivité ; même si deux groupes de chercheurs « ayant des sens analogues aux nôtres et sensibles aux mêmes impressions, et d’autre part admettant les principes de notre logique » mais appartenant à des mondes différents (mais pas incommunicables), bâtissent leurs conceptions physiques de manière assez diverse, en commençant par des choix différents du cadre géométrique, le fait qu’une partie de leurs langages soit traduisible permettra de tout traduire.
39 Dans sa critique de la notion de fait, Poincaré montre que bien qu’il soit caractérisé essentiellement par son rapport aux sens, qui décident de sa vérité ou fausseté, le fait scientifique présuppose des synthèses et un système de conventions (langage). Les faits scientifiques, à partir desquels on extrait les lois, sont obtenus par des synthèses successives à partir de faits plus bruts, par exemple des données élémentaires des sens. Cette synthèse est opérante, de manière paradigmatique, dans la construction des objets de la perception : Les objets extérieurs […] ce ne sont pas seulement des groupes de sensations, mais des groupes cimentés par un lien constant. C est ce lien, et ce lien seul qui est objet en eux, et ce lien c est un rapport. [Poincaré 1902a, 290-291]
40 Parmi les « composantes » du système de conventions on trouve une langue naturelle (le français, l’allemand, etc.) et les mathématiques. La première est constituée d’un nombre fini de termes qui servent à classer en catégories les faits plus bruts ; ce premier langage est confronté au besoin « d exprimer les nuances en nombre infini que mes impressions pourraient revêtir » ; cette possibilité n’étant actualisée que par l’interposition des mathématiques. La conclusion de la discussion ressemble plus à un postulat, à une croyance bien fondée, qu’à une proposition apodictique : « Les lois invariantes ce sont les relations entre les faits bruts, tandis que les relations entre les "faits scientifiques" restaient toujours dépendantes de certaines conventions » [Poincaré 1902a, 208]21.
41 Dans l’introduction à La Valeur de la science de 1905, Poincaré considèrera que l’objectivité est une propriété essentiellement architectonique et intersubjective, basée sur la construction d’un système de lois mathématiques portant sur les phénomènes : « La réalité objective [...] ce ne peut être que l’harmonie exprimée par des lois mathématiques. C est donc cette harmonie qui est la seule réalité objective » [Poincaré 1905, 23]. Cela traduit le caractère complexe des systèmes théoriques et aussi le but de systématisation qui se manifeste dans le progrès scientifique.
42 Poincaré note que les théories ne sont pas, habituellement, des touts complets et logiquement cohérents, obéissant strictement au principe d’économie qui empêche la multiplication des hypothèses. Elles peuvent contenir des branches qui vont se révéler
Philosophia Scientiæ, 16-2 | 2012 183
mortes et qu’il faudra émonder ; les rapports vrais y surgissent souvent déguisés. Un même rapport vrai peut apparaître dans deux théories qui semblent contradictoires : Quand un physicien constate une contradiction entre deux théories [...] il dit quelquefois : Ne nous inquiétons pas de cela mais tenons fermement les deux bouts de la chaîne bien que les anneaux intermédiaires nous soient cachés [...] Il peut se faire qu’elles expriment l’une et l’autre des rapports vrais et qu’il n’y ait de contradiction que dans les images dont nous avons habillé la réalité. [Poincaré 1900a, 1169]
43 Dire que les théories sont des images veut d’abord signaler que les théories sont des analogies partielles pour le champ phénoménal : Les rapports véritables entre ces objets réels sont la seule réalité que nous puissions atteindre, et la seule condition, c est qu’il y ait les mêmes rapports entre ces objets qu’entre les images que nous sommes forcés de mettre à leur place. [Poincaré 1900a, 1169]
44 La distinction entre rapports vrais et images veut signaler que les théories déguisent les rapports vrais, en les présentant vêtus de « costumes ». Ceux-ci peuvent correspondre soit à des modèles au sens des Britanniques, soit à des théories qui postulent l’existence d’identités physiques non-observables, maintes fois à portée ontologique. Ces costumes deviennent superflus du point de vue de la critique, œuvre de la physique mathématique.
45 Parmi les « costumes », Poincaré décrit ce qu’il nomme les hypothèses indifférentes. Bien que superflues, du point de vue de l’économie finale, elles ont néanmoins un rôle : Elles peuvent être utiles, soit comme artifices de calcul, soit pour soutenir notre entendement par des images concrètes [...] Il n’y a donc pas lieu de les proscrire [...] Les hypothèses de ce genre n’ont qu’un sens métaphorique. [Poincaré 1900a, 1166-1167, 1169-1170]
46 Les hypothèses indifférentes sont invérifiables car elles postulent des identités ou des rapports non-observables. Elles ont des concurrentes et illustrent le théorème de Maxwell sur la pluralité des représentations. Un exemple typique est la physique moléculaire laplacienne où les forces intermoléculaires deviennent insensibles à des distances sensibles. La connaissance de la loi d’interaction élémentaire, inaccessible à l’observation, est inutile à cause de l’effet des moyennes et l’hypothèse de la matière continue permet d’obtenir les mêmes résultats. Tout cela dépend intimement des mathématiques qui montrent comment on bâtit l’état moyen et qui permettent de comparer les différentes théories et de montrer l’équivalence de différentes représentations. Poincaré note que « ces hypothèses indifférentes ne sont jamais dangereuses, pourvu qu’on n’en méconnaisse pas le caractère » [Poincaré 1900a, 1166]. L’ontologie de la tradition de la physique laplacienne (réductionnisme par forces centrales) constitue un obstacle épistémologique car elle empêche de bien saisir le rôle de ces hypothèses de base (surtout heuristique) et annihile l’intérêt pour des alternatives plus souples. Si on revient à la classification des stades des théories physiques, on peut dire que les hypothèses indifférentes sont typiques de la physique des forces centrales. Puisque la physique des principes écarte la connaissance des mécanismes inobservables, elle semble dépourvue de ce genre d’hypothèses, ce qui représente un progrès dans le sens de l’économie et de l’unité22.
Philosophia Scientiæ, 16-2 | 2012 184
Conclusions
47 Les réflexions philosophiques de Poincaré sont suscitées par des problèmes scientifiques et la subtilité de ses arguments découle de sa connaissance profonde des sciences mathématiques. Les inspirations directement détectables sont celles de savants philosophes comme Helmholtz ou Maxwell. Ses textes étaient destinés à des audiences disparates, ce qui rend difficile l’harmonisation de la totalité de ses considérations épistémologiques.
48 On note habituellement que la pensée épistémologique de Poincaré commence avec son conventionnalisme géométrique (1887). Dans son analyse du statut des postulats géométriques, il montre que les prétentions ontologiques de quelques empiristes et le cadre kantien de l’esthétique transcendantale ne sont pas acceptables. Le choix d’un groupe spécifique de transformations géométriques est conventionnel, en raison de l’intertraductibilité des géométries et de l’intrication entre géométrie et physique. Par ailleurs, il signale les liens profonds entre arithmétique, analyse et géométrie et affirme le caractère synthétique a priori, constitutif et nécessaire, du principe de récurrence et de la notion de groupe. Poincaré partage avec Helmholtz un intérêt pour une relecture de Kant dans laquelle la machinerie transcendantale est assouplie. Helmholtz admet qu’on peut considérer « transcendantal le concept de construction géométrique rigide de l’espace », mais note que les formes de l’intuition apriori kantiennes doivent être « si vides et libres qu’elles puissent recevoir tout contenu qui apparaît dans la forme correspondante de perception » [Helmholtz 1878]. De même pour Poincaré, il y a, en dessous des conventions, des principes constitutifs et nécessaires qui définissent un ensemble de constructions possibles dont certaines s’actualisent à l’occasion de l’expérience23.
49 Les réflexions initiales de Poincaré sur la physique sont contemporaines de celles sur la géométrie. Il s’est vivement intéressé aux théories électromagnétiques de Maxwell et à leur signification générale. Les réflexions du savant écossais anticipent une idée centrale de la pensée de Poincaré, celle d’une pluralité de langages et de leur intertraductibilité. Les deux savants valorisent les analogies, sont favorables à une méthodologie pluraliste et soulignent le rôle fécond des différences psychologiques et de style scientifique des savants. Tous deux dénoncent les dangers de l’adhésion prématurée à des cadres ontologiques qui postulent l’existence d’identités inobservables et restreignent les méthodes admissibles. Pour tous deux, les analogies permettent à l’esprit de saisir des rapports d’une façon convenable, commode et concrète. L’évaluation d’une analogie se fait par voie mathématique, si bien que pour le Maxwell du Treatise et pour Poincaré les analogies formelles peuvent prendre le pas sur les imageries géométriques, les analogies mécaniques et les modèles. Les deux savants signalent le rôle heuristique et didactique de ces dernières analogies et ne nient pas leur valeur cognitive. La formulation lagrangienne de l’électromagnétisme par Maxwell, avec le théorème qui en découle de l’existence d’un nombre infini de modèles mécaniques compatibles, est mise en valeur par Poincaré qui y voit un argument de sous-détermination des théories par l’expérience, et un remède contre la réification d’hypothèses indifférentes. Il faut toutefois noter que la lecture poincaréenne de l’électromagnétisme maxwellien est peu fidèle à d’autres égards.
50 L’établissement d’analogies formelles entre théories suggère que Maxwell et Poincaré ne songent pas à la possibilité de théories absolument incommensurables : « It is the
Philosophia Scientiæ, 16-2 | 2012 185
glory of a true science that all legitimate methods must lead to the same final results » [Maxwell 1890, II, 301]. Ils reconnaissent le progrès de la connaissance scientifique, le caractère en général révisable des théories, et le caractère contingent de leur développement historique. Contrairement aux philosophes des sciences du milieu du XXE siècle, très influencés par le positivisme viennois, ils ne distinguent pas entre contexte de la découverte (alogique) et contexte de la justification (logique). Ils valorisent l’idée d’une psychologie de l’invention où principes de convenance et stratégies dépendent de la nature des sujets cognitifs.
51 Un éclairage kantien des considérations de Poincaré sur la méthode les rattache aux fonctions constitutives et/ou régulatrices de principes ayant des degrés de généralité divers. Les plus généraux sont les grands principes de convenance et les vrais principes synthétiques apriori, nécessaires et uniques, qui sont à la base des mathématiques utilisées par les physiciens. Parmi les grands principes de convenance, on trouve la quête de simplicité qui mène le savant à faire des choix commodes. Ces considérations de commodité sont le plus souvent si puissantes qu’il ne reste pratiquement que peu de chose de la liberté dans le choix des conventions. Souligner le libre choix des conventions sans noter ces restrictions rend inexplicable la hiérarchie des domaines des sciences mathématiques, reconnue au XIXE siècle, et le fait que le pluralisme théorique est limité (on démontre qu’il n’y a que trois géométries à courbure constante mais on préfère celle d’Euclide ; il y a plusieurs théories mécaniques de l’éther, en attendant une théorie mûre, etc.). Cette hiérarchie définit la structure de La Science et l’Hypothèse (1902).
52 Poincaré dégage une partie de ces principes de l’examen des théories physiques disponibles jusqu’à la fin du XIXe siècle, pour la plupart utilisant des équations différentielles. Ces principes ont des fonctions régulatrices du point de vue de l’ars inveniendi mais peuvent être vus comme constitutifs du point de vue de l’analyse des théories déjà élaborées. Par ailleurs, Poincaré s’intéresse aux grands principes de la physique de la fin du XIXe que sont le principe de l’énergie et le principe de moindre action. L’aspect nominaliste de la pensée de Poincaré permet de mieux comprendre son intérêt pour la physique des principes, dont les principaux avocats sont Helmholtz et Maxwell. L’analyse que donne Poincaré de cette physique souligne son pouvoir d’éviter la réification des hypothèses indifférentes, et montre la structure complexe du système de lois et de principes, impliquant le choix d’une géométrie et l’usage de mathématiques. Elle met aussi en valeur le rôle médiateur des conventions qui lient les principes de la physique au sol de l’expérience.
53 Poincaré croit au progrès scientifique par accumulation de faits et de lois, bien qu’il soit conscient des problèmes de l’induction. Il voit les sciences comme des systèmes de relations, le progrès correspondant à une extension de l’ensemble des rapports vrais et à sa systématisation conduisant à des degrés supérieurs d’unité. L’objectivité de la physique est donc une propriété architectonique et intersubjective, intimement liée à l’existence d’harmonies mathématiques qui découlent d’un processus historique où le changement n’est jamais totalement discontinu. La notion de rapport vrai est complexe et Poincaré n’en donne aucune définition ; une loi particulière ou un principe peuvent être conçus comme des rapports vrais, bien que leur degré de généralité et leur rapport avec l’expérience puissent être divers. Ces rapports sont pensés dans un cadre criticiste où l’accès à la chose en soi est nié. Les faits scientifiques présupposent des synthèses (perceptions) et des langages (naturels et mathématiques) ; ils s’obtiennent par
Philosophia Scientiæ, 16-2 | 2012 186
synthèse de faits plus bruts, bien que Poincaré ne semble pas croire à la possibilité de connaître des faits absolument bruts. On accède aux rapports entre les choses par l’intermédiaire de rapports entre images qu’on est forcé de mettre à leur place ; ces images ce sont des analogies partielles. Les théories, avec leurs images, peuvent recéler les rapports vrais. Son criticisme le porte à dénoncer les adhésions à des ontologies prématurées (hypothèses indifférentes) et lui fait voir que les théories physiques ne sont presque jamais des touts complets et logiquement cohérents. L’engagement pluraliste émerge comme une maxime régulatrice qui est condition d’un progrès historiquement contingent.
BIBLIOGRAPHIE
ACHARD, FRANCK 1998 La publication du Treatise on Electricity and Magnetism de James Clerk Maxwell, La Revue de Synthèse, 119, 511-544. 2005 James Clerk Maxwell, A Treatise on Electricity and Magnetism, dans Landmark Writings in Western Mathematics 1640-1940,édité par GRATTAN-GUINNESS, I., Amsterdam: Elsevier, 564-587.
BOUSSINESQ, JOSEPH 1879 Étude sur divers points de la philosophie des sciences, Paris : Gauthier-Villars.
BOUTROUX, PIERRE, HADAMARD, JACQUES, LANGEVIN, PAUL & VOLTERRA, VITO (ÉD) 1914 Henri Poincaré, L’œuvre scientifique, l’œuvre philosophique ,Félix Alcan, Je cite de l’édition en ligne de 2003 des éditions Vigdor.
CAMPBELL, LEWIS & GARNETT, WILLIAM 1882 The life of James Clerk Maxwell, London: MacMillan.
CAT, JORDI 2001 On understanding Maxwell on the methods of illustration and scientific metaphor, Studies in history and philosophy of modern science, 32(3), 395-441.
DARRIGOL, OLIVIER 1993 The electrodynamic revolution in Germany as documented by early German expositions of ’Maxwell’s theory’, Archive for the history of exact sciences, 45, 189-280. 1995 Henri Poincaré’s criticism of fin de siècle electrodynamics, Studies in history and philosophy of modern physics, 26(1), 1-44. 2000 Electrodynamics from Ampère to Einstein, Oxford: Oxford University Press. 2002 Between hydrodynamics and elasticity theory: The first five births of the Navier-Stokes equation, Archive for History of Exact Sciences, 56, 95-150.
DUHEM, PIERRE 1892 Quelques réflexions au sujet des théories physiques, Revue des questions scientifiques, 31, 139-176. 1896 L’évolution des théories physiques, Revue des questions scientifiques, 40, 463-498.
Philosophia Scientiæ, 16-2 | 2012 187
FRIEDMAN, MICHAEL 1999 Reconsidering Logical Positivism, Cambridge : Cambridge University Press.
GIEDYMIN, JERZY 1977 On the origin and significance of Poincaré’s conventionalism, Studies in history and philosophy of science, 8(4), 271-300.
HARMAN, PETER M. 1998 The Natural Philosophy of James Clerk Maxwell, Cambridge: Cambridge University Press.
HELMHOLTZ, HERMANN VON 1878 Ùber den Ursprung und Sinn der geometrischen Sàtze: Antwort gegen Herrn Professor Land, Mind, 3, 212-225, version allemande de l’article "The Origin and meaning of geometrical axioms", cf. [Helmholtz 1968, 1-31]. 1968 Uber Geometrie, Darmstadt: Wissenschaftliche Buchgesellschaft.
HESSE, MARY 1974 The Structure of Scientific Inference, London: MacMillan Press.
KANT, IMMANUEL 1770 De mundi sensibilis atque intelligibilis Forma et Principiis (Dissertation de 1770), traduction portugaise préface et notes par Leonel Ribeiro dos Santos : Kant, E. (1985) Dissertaçâo de 1770,Estudos Gerais,Lisbonne : Imprimerie nationale (INCM) . 1781- Critique de la raison pure, Flammarion, traduction française par 1787 Jules Barni revue par P. Archambault, 1976. 1783 Prolégomènes à toute métaphysique future, Paris : Vrin, traduction française par J. Gibelin. 1974.
KRAUSSER, PETER 1988 On the antinomies and the appendix to the dialectic in Kant’s critique and philosophy of sciences, Synthèse, 77(3), 375-401.
LY, IGOR 2008 Mathématique et physique dans l’œuvre philosophique de Poincaré,Thèse de doctorat, Université Nancy 2.
MAXWELL, JAMES CLERCK 1873 A Treatise on Electricity and Magnetism, Oxford: Clarendon Press, 2 vol. 1890 The Scientific Papers of James Clerk Maxwell, Cambridge: Cambridge University Press, réédité par Dover editions en 1952.
MOYER, DONALD FRANKLIN 1977 Energy, dynamics, hidden machinery: Rankine, Thomson and Tait, Maxwell, Studies in Historyand Philosophy of Science, 8(3), 251-268.
PATY, MICHEL 2008 Les analogies mathématiques au sens de Poincaré et leur fonction en physique, dans Le statut de l’analogie dans la démarche scientifique. Perspective historique, Paris : L’Harmattan, 171-193.
PHILONENKO, ALEXIS 1993 L’Œuvre de Kant, t. 1, Paris : Vrin.
POINCARÉ, HENRI 1887 Sur les hypothèses fondamentales de la géométrie, Bulletin de la Société Mathématique de France, 15, 203-216. 1889 Leçons sur la théorie mathématique de la lumière I, Nouvelles études sur la difraction. — Théorie de la dispersion de Helmholtz, leçons professées pendant le premier semestre 1887-1888,
Philosophia Scientiæ, 16-2 | 2012 188
Cours de la Faculté des Sciences de Paris publiés par l’association amicale des élèves et anciens élèves de la faculté des sciences. 1890 Electricité et optique I - Les théories de Maxwell. Leçons professées pendant le second semestre 1888-89, Paris : Georges Carré. 1891a Les géométries non-euclidiennes, Revue générale des sciences pures et appliquées, 2, 769-774. 1891b Sur l’expérience de M. Wiener, Comptes-Rendus hebdomadaires des séances de l’Académie des Sciences, 112, 325-329. 1892a Thermodynamique, leçons professées pendant le premier semestre de 1888-1889, Paris : Georges Carré, 2e édition 1908. 1892b La théorie mathématique de la lumière II, Nouvelles études sur la difraction. — Théorie de la dispersion de Helmholtz, leçons professées pendant le premier semestre 1891-1892, Paris : Gauthier- Villars. 1897a Les idées de Hertz sur la mécanique, Revue générale des sciences pures et appliquées, 8, 734-743. 1897b Les rapports de l’analyse et de la physique mathématique, Revue générale des sciences pures et appliquées, 8, 857-861, publié également dans SH, chapitre XI. 1899a La théorie de Maxwell et les oscillations hertziennes, Paris : Carré et Naud. 1900a Relations entre la physique expérimentale et de la physique mathématique, Rapports présentés au Congrès international de physique réuni à Paris en 1900, 1, 1-29, publié également dans SH, chapitres IX et X. 1900b Du rôle de l’intuition et de la logique en mathématiques, dans Compte-rendu du deuxième Congrès international de mathématiciens tenu à Paris du 6 au 12 août 1900, Paris : Gauthier-Villars, 115-130, publié également dans VS, chapitre I. 1902a Sur la valeur objective de la science, Revue de métaphysique et de morale, 10, 263-293. 1902b La Science et l’Hypothèse [SH], Flammarion, Je cite d’après l’édition de 1968, avec une préface de Jules Vuillemin. 1904 L’état actuel et l’avenir de la physique mathématique. Conférence lue le 24 septembre 1904 au Congrès d’Art et de Science de Saint-Louis, Bulletin des sciences mathématiques, 23, 302-324, publié également dans VS, chapitre IX. 1905 La Valeur de la science [VS], Flammarion, Je cite d’après l’édition de 1970, avec une préface de Jules Vuillemin. 1913 Foundations of Science (Science and Hypothesis, The value of science, science and method), New York: The Science Press, traduction anglaise par G. B. Halsted avec une préface par Henri Poincaré.
PRINCIPE, JOÂO 2008 La réception française de la mécanique statistique, Épistémologie et histoire des sciences et des techniques, Université Paris 7, thèse présentée pour l’obtention du Doctorat d’Épistémologie et Histoire des Sciences et des Techniques. 2010 L’analogie et le pluralisme méthodologique chez James Clerk Maxwell, Kairos Journal of philosophy and science, 1, 55-74.
RIBEIRO DOS SANTOS, LEONEL 2008 L’apport de Kant au programme de l’ars inveniendi des modernes, conférence dans Kant and the philosophical tradition — Kant Today, Brasilian-Italian-Portuguese Kant Conference 22-23 January 2008 Università degliSudi diVerona. ftp://www.cle.unicamp.br/pub/kant-e-prints/ Vol-3-2-2008/ Santos-2-3-2-2008.pdf.
ROLLET, LAURENT 1999 Henri Poincaré - Des mathématiques à la philosophie, Thèse de doctorat, Université Nancy 2.
SCHAFFNER, KENNETH F. 1972 Nineteenth-Century Aether Theories, oxford: Pergamon Press.
Philosophia Scientiæ, 16-2 | 2012 189
SIMPSON, THOMAS K. 1970 Some observations on Maxwell’s Treatise on electricityand magnetism, Studies in History and Philosophy of Science, 1(3), 249-263.
TORRETI, ROBERTO 1978 Philosophy of Geometry from Riemann to Poincaré, Dordrecht: Reidel.
NOTES
1. L’idée de coordination réapparaît dans [Poincaré 1897b, 734]. Voir sur les théories de l’éther [Schaffner 1972], surtout chapitre IV ; Pierre Duhem, s’opposant à la physique des modèles, critique Poincaré, voir [Duhem 1892, § 8] et [Duhem 1896]. 2. Sur Maxwell, voir [Achard 1998], [Achard 2005], [Cat 2001], [Campbell & Garnett 1882], [Darrigol 2000], [Harman 1998], [Hesse 1974], [Moyer 1977], [Principe 2010], [Simpson 1970]. 3. Voir [Darrigol 1993, 221] ou [Darrigol 2000, 154-166]. Sur le Treatise, voir [Moyer 1977, 259-267], [Achard 1998] et [Achard 2005]. Sur le « true method of physical reasoning » voir [Maxwell 1890, II, 308-309], [Hesse 1974, 259-281], [Cat 2001, 219], [Principe 2010, 62-65]. 4. Sur les spécificités de la lecture poincaréenne des théories de Maxwell, voir [Darrigol 1993, 216-218, 220, 223]. 5. Souligné par moi. Voir [Poincaré 1890, Introduction], [Darrigol 1993, 221-222], [Principe 2008, § 12.1], Langevin dans [Boutroux, Hadamard, Langevin et al. 1914, 73]. 6. Des descriptions semblables de la physique des modèles anglaise se trouvent dans [Poincaré 1897a, 742] et dans la préface de [Poincaré 1913, 6]. Sur les analogies mécaniques dans [Poincaré 1890], voir [Darrigol 1995, 8]. 7. Une première référence au besoin de simplicité, ordre et harmonie se trouve dans [Poincaré 1892a, VI-VII]. Sur analogie et intuition, voir [Paty 2008, 185]. 8. Voir [Poincaré 1892a, VI], [Poincaré 1897b, 858], [Poincaré 1900a, 1163, 1167, 1169]. 9. Dans les travaux qui débutent en 1887 avec la méthode du balayage, « on est toujours ramené à l’intégration d une même équation aux dérivées partielles du second ordre avec des conditions aux limites qui seules varient suivant les problèmes », Langevin in [Boutroux, Hadamard, Langevin et al. 1914, 65-67]. 10. Voir [Principe 2010, 60-62]. 11. Sur ses premiers articles concernant le statut des géométries voir [Giedymin 1977, 271-272, 287]. Sur la perspective de Helmholtz et son inspiration sur Poincaré voir [Torreti 1978, 163, 166-168] et [Rollet 1999, 31, 35, 50]. 12. La règle de ne pas multiplier les principes sans nécessité se trouve dans [Kant 17811787, A652]. 13. Cité d après [Ribeiro dos Santos 2008, 11]. Leibniz a fréquemment utilisé le nom « principes de convenance » pour « se référer aux principes métaphysiques qui, ne correspondant pas à une ’nécessité du type géométrique découlant de la nature de la chose ou de son concept, résultaient d un besoin de la nature architectonique et esthétique de la raison », Ribeiro dos Santos dans la traduction portugaise de [Kant 1770, note 126]. 14. Kant considère les principes régulateurs comme des maximes : [Kant 1781-1787, A666-667]. Voir [Philonenko 1993, §25], [Krausser 1988, §4-6]. 15. Les analogies de l’expérience sont des principes régulateurs de l’intuition mais sont constitutifs par rapport à l’entendement, [Kant 1781-1787, A664]. Sur l’apriori relativisé voir [Friedman 1999]. Sur le pluralisme maxwellien voir [Principe 2010, 65-69]. 16. Voir [Darrigol 2002, 131] et [Principe 2008, 139]. 17. Une pensée similaire se trouve dans [Poincaré 1900a, 1168-1169].
Philosophia Scientiæ, 16-2 | 2012 190
18. Le système de Newton nécessite l’hypothèse des forces centrales et de celle des atomes et il est compatible avec des mouvements que la Nature ne réalise jamais, voir [Poincaré 1897a, 738]. 19. Voir aussi [Poincaré 1889, I], [Poincaré 1900a, 1164], [Poincaré 1902a, 268, 273, 289]. 20. Voir [Darrigol 2000, 357]. 21. Igor Ly discute amplement, dans sa thèse, les rôles de ces deux systèmes linguistiques. Il arrive à la conclusion que se sont les mathématiques qui permettent de bien saisir l’infinité des nuances données aux sens : « C’est la notion mathématique de grandeur continue qui permet d exprimer les rapports entretenus par les nuances que prennent les impressions sensibles », [Ly 2008, 217, § 4.2 : « La catégorie "espace sensible" et le continu physique »]. 22. Sans les nommer explicitement, Poincaré en avait déjà parlé dans [Poincaré 1889, III]. 23. Cité d’après [Torreti 1978, 166]. Voir [Torreti 1978, 163, 166-168].
RÉSUMÉS
Cette étude montre que les réflexions épistémologiques de Poincaré émergèrent dans le cadre de ses recherches scientifiques et qu’elles furent en partie inspirées par sa lecture de savants philosophes comme Helmholtz et surtout Maxwell. Elle donne une analyse systématique des textes philosophiques publiés par Poincaré vers 1900, au moment où il juge que la physique des principes constitue le sommet de l’évolution des théories. Enfin, elle met en rapport certaines de ses thèses sur la physique avec l’Analytique et la Dialectique transcendantales kantiennes.
This study shows that the epistemological reflections of Poincaré emerged as part of his scientific researches and they were partly inspired by his reading of Helmholtz and especially Maxwell. It provides a systematic analysis of philosophical texts published by Poincaré about 1900, where he finds that the physics of principles is the culmination of the evolution of theories. Finally, it brings together some of his theses on physics with Kant’s Transcendental Analytic and Dialectic.
AUTEUR
JOÂO PRINCIPE Universidade de Évora - CEHFCi (Portugal)
Philosophia Scientiæ, 16-2 | 2012