RUNNING HEAD: A NATURALIST PHYSICALIST DEFENSE 1

A Naturalist Physicalist Defense Against Schneider’s Problem of the Base

Author Name Redacted

Author Institutional Affiliation Redacted

A NATURALIST PHYSICALIST DEFENSE 2

Abstract

This paper examines a pair of papers from Susan Schneider (2015; forthcoming) which

argue physicalism is a failed metaphysical stance for philosophers of mind. She argues

physicalism cannot suitably account for the ontological status of the objects in a

microphysical base because those objects are individuated mathematically (by

abstracta) and a physicalist can appeal to neither nominalism nor Platonism for

physicalistically kosher truthmakers. I sketch a plausible naturalistic physicalism for the

philosopher of mind which can adequately respond to Schneider’s demands by (1)

defending nominalism via Melia’s (2000) weaseling argument and (2) dispensing with

the notion of individuation posed by Schneider in the first place.

A NATURALIST PHYSICALIST DEFENSE 3

A Naturalist Physicalist Defense Against Schneider’s Problem of the Base

Schneider (2015; forthcoming) argues against physicalism as the leading metaphysical thesis in philosophy of mind debates.1 She claims physicalists who employ Platonic realism about mathematical objects run aground of a basic definition of physicalism since, though they vary, most contemporary philosophers understand it to mean ‘everything supervenes on the physical’. An obvious problem arises:

The physicalist cannot accept nonphysical mathematical objects into her completely physical ontology.

Schneider writes, “Mathematical entities do not come for free” (forthcoming, p. 1). The problem concerns the base (viz. the most fundamental entities) of a completed physics – hence her argument is called The Problem of the Physical Base (hereafter, the problem of the base). Schneider observes fundamental physical theories (e.g. quantum gravity – quantum loop gravity or string theory) are highly mathematical in nature. For the physicalist, if the most fundamental entities are individuated by mathematics, then one’s metaphysics of mathematical objects must cohere with one’s metaphysics in general.

Schneider poses a dilemma which proves unsatisfying on both accounts. If the physicalist accepts Platonic realism about mathematical objects, then she has snuck in an ontological dualism

(abstract otherworldly mathematical objects plus concrete thiswordly objects). If she accepts nominalist anti-realism about mathematical objects, she holds mind-dependent objects individuate purportedly mind-independent microphysical objects.2 Neither Platonic realism nor nominalist anti-realism meets two desiderata which should lead one to accept a monistic physicalism in the first place: 1) ontological economy and 2) explanatory robustness. Schneider concludes that an updated version of metaphysical idealism (she variously refers to it as panprotopsychism and micromonism – hereafter micromonism) is the preferable route over physicalism for philosophers of mind.

1 In particular, she refers to debates over the nature of consciousness. 2 According to Schneider this commits one to the idea that mental properties are fundamental – an unsavory view for the physicalist. A NATURALIST PHYSICALIST DEFENSE 4

The aim of this essay is to defend physicalism against Schneider’s alternative. Section 1 is a sketch of my brand of physicalism and I’m inclined to think most contemporary physicalist philosophers of mind would assent to it. Section 2 is a summation of Schneider’s problem of the base. I decompose her argument into two distinct problems: an ontological problem and an individuation problem. Section

3 is a sketch of the ontological problem. Section 4 is a review of indispensability arguments as responses to the ontological problem and an argument in favor of nominalism. In section 5 I review the individuation problem and in section 6 I dispense with a lynchpin premise in Schneider’s argument in virtue of considering her problem on naturalist grounds.

Section 1: Whose Physicalism is it Anyway?

Schneider’s target physicalist in her essays is mostly undefined, but her argument is purportedly general enough to cover all cases. Physicalism is not a unified metaphysical stance though and nuance can make a difference. The kind of physicalism I have in mind to overcome Schneider’s problem of the base should appeal to physicalist philosophers of mind (Schneider’s intended target).3 I’m defining my physicalism as the sum total of the naturalistic project. The naturalistic project is broadly defined as the project of the sciences.4 The naturalist physicalist holds philosophy as continuous with the sciences and so the task of philosophy is to gain clarity about what there is, the limits of inquiry, and so on using the natural method.5 Put another way, philosophy should stand side-by-side with the sciences and take seriously actual scientific practice. The strongest argument for this brand of physicalism is an argument from methodological naturalism:

The first premise…is that it is rational to be guided in one's metaphysical commitments by the methods of natural science…The second premise…is that, as a matter of fact, the metaphysical picture of the world that one is led to by the methods of natural science is physicalism. The conclusion is that it is rational to believe physicalism, or, more briefly that physicalism is true (Stoljar, 2015).

3 This would purport to include both reductive and non-reductive flavors of physicalism. 4 It might appear Quinean, but I disagree with Quine on abstract admitting objects into the physicalist ontology This is a controversial break, but not uncommon. See Azzouni (2004) and Raley (2007) as examples. 5 I borrow the term ‘natural method’ and a sketch of the idea from Flanagan (1995). A NATURALIST PHYSICALIST DEFENSE 5

I have already noted such a physicalism places philosophy as continuous with the sciences and this may engender worries, but I would think most are amenable to the idea – especially physicalist philosophers of mind. As for the content of the argument, one could reject premise one, but this seems counterintuitive unless one rejects scientific knowledge – not a popular position. One could reject premise two and the motivation for doing so could be: 1) a belief that current scientific practice does not support the physicalist worldview; 2) a rejection of reductionism of the sciences; or 3) a belief that a non-physicalist worldview is preferable. I think the first objection is interesting, albeit unfounded, and I will not address it fully here.6 The second objection doesn’t hold either. Physicalism does not entail a denial of the explanatory autonomy of the special sciences.7 On the third objection, yes, sure. There might be other views, but physicalism is the best option. To that end, I should like to next take up

Schneider’s challenge to physicalism.

Section 2: The Problem of the Base

Drawing on literature in quantum gravity, Schneider observes fundamental physics is deeply mathematical. Our macrophysical world of pens, mugs, and books supervenes on a world of “ripples or thickenings in the quantum field, which is explained mathematically” (2015, p. 2). Enter the problem for the physicalist who also happens to be a mathematical Platonist: physics gives us a world of concreta, but fundamental physical objects are ‘individuated’ by abstracta (acausal, non-spatial, immutable, and non-mental objects). Schneider gives the argument thusly:

Premise 1. Abstracta individuate at least some of the entities in the physical base.

6 That naturalism is wedded to physicalism here should be uncontroversial. I take the physicalism of the empirical sciences as not simply a background assumption or metaphysical stricture, but; rather, the outcome of the pursuit of knowledge of the world. See Polger (2004) in his discussion of the natural method and the “No Ghosts Rule”. 7 Cf. Stoljar (2015) for more. Also, I want to be careful about my use of ‘autonomy’ here. I don’t mean something like Fodorian autonomy of the special sciences. Instead, I mean something more like Polger and Shapiro’s (2016) ‘Actual Autonomy’. Both psychology and cognitive neuroscience, for instance, can have interesting things to say without the need to be collapsed into one another. A NATURALIST PHYSICALIST DEFENSE 6

Premise 2. If abstracta individuate at least some entities in the physical base, then those entities have (at least partly) abstract natures. C1: Thus, some entities in the physical base have (at least partly) abstract natures. Premise 3. Abstract entities are non-physical. C2: Therefore, some entities in the physical base have (at least partly) non-physical natures. Premise 4: If some entities in the physical base have (at least partly) non-physical natures, then physicalism is false. C3: Therefore, physicalism is false (Schneider, 2015, p.4).

Schneider’s argument has two strands. Strand 1 draws upon an extant problem in the philosophy of science and the philosophy of mathematics: the ontological status of mathematics in the physical sciences. Let’s call this the ‘ontological problem’.8 Strand 2 is what I will call the ‘individuation problem’.

The ontological problem, according to Pincock (2007), is the problem of two competing principles. The principles are: Mathematics is both (1) theoretically indispensable (there are no acceptable non- mathematical versions of physical theories) and (2) metaphysically dispensable (they lack any causal role in the physical world).

Section 3: The Ontological Problem

Schneider’s ontological problem for the physicalist seeks to undermine both nominalism and physicalism as acceptable views of mathematical objects. Physicalists tend toward nominalism as their preferred view of abstracta. In particular, Schneider identifies fictionalism as a main target.9 Fictionalism is the view that mathematical discourse (the total of mathematical objects – sets, numbers, and so on) is fictional; i.e. math is a fictional language and the mathematician is merely following the ‘rules’ of the story when she proves theorems, performs calculations, and so on. Thus, mathematical objects such as

8, π, or ∅ have the same ontological status as Hester Prynne or Frankenstein’s monster. But is such a nominalism ontologically viable? Schneider thinks not. Though the nominalist may object that scientific

8 More generally, this is a meta-ontological problem and is called the problem of ontological commitment. 9 This is largely because most philosophers of math who espouse nominalism adhere to fictionalism. A NATURALIST PHYSICALIST DEFENSE 7

theories can be ‘nominalized’ and stripped of their mathematical content, for instance, Field’s (1980) formalization of Newtonian gravitational theory where the quantifiers range over space-time points relying on non-mathematical relational predicates and Balaguer’s (1996) quantum mechanical nominalization procedure,10 Schneider argues that quantum gravitational theories theorize space-time as emergent and so quantifying over space-time points to explain more fundamental entities in the base would raise direction of explanation worries. Too, both Field’s and Balaguer’s nominalizations remain controversial in the philosophy of mathematics and the consensus is that they are unsuccessful.11 My physicalist objects to Field and Balaguer’s project because of its discontinuity with actual scientific practice.12 The ontological problem for the physicalist could lead her to adopt Platonism.

Mathematical Platonism is glaringly problematic for the physicalist. Schneider raises three worries about Platonistic physicalism, but I shall only consider the one I find most challenging – lost ontological economy.13 Platonism about mathematical objects sneaks in a dualism of concrete thisworldly objects plus abstract otherworldly objects. Schneider’s motivation for this argument is to defend mental properties as fundamental, so, on my view, the physicalist should equally recoil at

10 Balaguer’s work was in reply to Malament’s (1982) criticism of Field – Malament argued quantum mechanical theories could not be nominalized. 11 See Macbride (1999) and even Field’s (1998) own skepticism about the project. 12 Melia (2000) makes this point, “After all, if and when a philosopher manages to find a reformulation of General Relativity which does not entail the existence of abstracta, the practice of physicists is unlikely to change” (p. 457). 13 In fact, I find it immediately discrediting to an acceptable physicalism. The other challenges Schneider raises are: 1) three naturalization challenges and 2) the problem of object natures. The three naturalization challenges are: The three naturalization challenges are: a) if the base is abstract, naturalist theories of meaning, intentionality, and reference will be unavailable to the Platonistic physicalist; b) mental and physical causation become mysterious for the Platonist physicalist since the base would be constituted by otherworldly abstracta; and c) an issue of how claims about the macroscopic concrete world can be true arises for the Platonist physicalist since the base is abstract. The problem of object natures is The problem of object natures raises worries for the Platonist physicalist since she cannot appeal to the two leading theories of substance in analytic metaphysics – the bundle theory and the substratum theory (both constituency theories) – since this would claim that an immanent universal (some abstract mathematical object) is constituent of a microphysical entity. A NATURALIST PHYSICALIST DEFENSE 8

micromonism and an ontology including numbers and other mathematical objects as ‘nomological danglers’14 outside of space-time. Any dualism is not a viable option for my physicalist.

The engine of the physical sciences and many of the special sciences15 is mathematics. Robust

Platonism about mathematical objects in the physical sciences gives them such explanatory power that much twentieth century philosophy of science and mathematics was guided by a firm commitment to

Platonism about mathematical objects. Recent work in philosophy of science has centered on the extent to which mathematical models have any explanatory power in a relevant sense – i.e. is mathematics indispensable? (Melia, 2000; Colyvan, 2002; and Baker, 2005). The ontological problem is an ongoing controversy in the philosophy of science and the strongest arguments from mathematical Platonists claim that realism about mathematical objects is necessary for empirical science. In short, they are indispensable for actual scientific practice. The argument for the acceptance of mathematical Platonism in a scientific ontology is the Quine-Putnam indispensability thesis.

Section 4: Weaseling an Acceptable Nominalism

How shall my physicalist proceed considering the ontological problem Schneider raises? In the philosophy of science and the philosophy of mathematics, the ontological problem has been framed by indispensability arguments. Here are two varieties of the argument:16

(1) We ought to believe the claims our best scientific theories make about the world – after all, they are our best scientific theories. But a casual glance through any book of theoretical physics reveals that our best scientific theories entail the existence of numbers, sets and functions…since such claims entail the existence of abstracta, we cannot consistently assert or believe in our scientific theories whilst denying the existence of abstracta (Melia, 2000, p. 455).

14 Much ado to Smart (1959) for this clever phrasing. 15 E.g. economics, psychology, biology, and so on. 16 Colyvan (2015) offers the following generalized formal version: (P1) We ought to have ontological commitment to all and only the entities that are indispensable to our best scientific theories; (P2) Mathematical entities are indispensable to our best scientific theories :: (C) We ought to have ontological commitment to mathematical entities. A NATURALIST PHYSICALIST DEFENSE 9

This line of thinking is vigorously defended in Putnam’s Philosophy of Logic (1971). The second version is:

“(2) We ought to believe in abstracta for the very same theoretical reason we believe in the concrete, unobservable entities postulated by scientific theory. We postulate such things as quarks and space-time points not because we directly observe these entities, but for pragmatic or aesthetic reasons: because doing so either increases the explanatory power of our theory, or increases the theory’s simplicity, or increases the theory’s strength – or a combination of all three” (Melia, 2000, p. 456).

This line of thinking is Quinean (Quine, 1948; 1951; and 1960). Both (1) and (2) express indispensability and putatively entail a mathematical Platonism, but for different reasons. The Putnam horn (1) relies on a commitment to a logical holism; that one cannot consistently accept the truth of the theory (in the scientific realist sense) and deny a fundamental component (Platonic realism about abstracta). The

Quinean (2) horn is less committed to logical consistency, but focused on negotiating ontology – specifically equating abstracta with unobservable concrete objects viz. quarks and space-time points – based on scientific values (e.g. accuracy, consistency, simplicity, fruitfulness, etc.)

Melia (2000) addresses both the Putnam and Quinean horns. On the Putnam horn, he argues nominalization procedures of theories (i.e. replacing mathematical content with nominalistically kosher predicates) do not have the same consequences as Platonist theories. The sentences entailed by

Platonist theory T and nominalist theory T* are different and the sentences entailed by T do have meaningful consequences. He writes, “the Platonist language enabled us to say something about the way the sums were that was not expressible in the nominalist language” (p. 466). Specifically, Melia adds Number Theory (Peano Arithmetic) to the nominalist theory T*. He concludes, “By adding new predicates to our theory and new entities to our ontology, we were able to guarantee the existence of a certain kind of concrete entity whose existence we were unable to guarantee in the nominalist system”

(p. 466). Thus, nominalizing procedures fail against their competition. How should the nominalist A NATURALIST PHYSICALIST DEFENSE 10

proceed? Contra Putnam, Melia argues it is possible to consistently use mathematics in physical theories and deny abstracta in one’s ontology. He calls this weaseling.17

It is reasonable to make assertoric claims only to edit/revise them at a later time. But an obvious question arises: “How can anyone coherently assert P, know that P entails Q, yet deny that Q is the case? How could it ever be rational to assert that P whilst denying a logical consequence of P?” (p. 466).

The argument relies on the pragmatic nature of everyday discourse and how this filters into actual scientific practice. A common example is making an exception even after a categorical claim has been asserted. For instance, the following example is not uncommon:

Jones: Did everyone turn in their work I asked for?

Smith: Yes, except for Brown.

Jones’s question was framed categorically – Did All X’s Y? Smith’s initial response assigns an affirmative truth-value to the claim, but is immediately revised to include some X who did not-Y. Melia extends this common example to scientific practice. He writes,

“We sometimes talk about a two-dimensional world by first talking about a three- dimensional world and then picking out a surface in this world. For example, we pick out a possible two-dimensional world in the following way by considering the surface of a sphere. Now, a sphere is a three-dimensional object – the collection of all points which are n metres or less away from point p0. But of course, in a two-dimensional world which is the surface of a sphere, there is no point p0 which is n metres away from every point!” (p. 468)

Most working scientists will use mathematics in practice, but go on to deny the existence of mathematical objects in any Platonic sense. Melia writes, “It is surely more charitable to take scientists to be weasels rather than inconsistent hypocrites” (p. 469). I turn to Melia’s other consideration – the

Quinean horn of indispensability.

17 Azzouni (1997 & 2004) explores a similar strategy. A NATURALIST PHYSICALIST DEFENSE 11

The Quinean horn ontologically equates unobservable objects with mathematical objects. The postulation of these entities in scientific practice are for aesthetic reasons: “simplicity, economy, and elegance” (Melia, 2000, p. 472).18 In particular, simplicity is of great interest here. Consider two mereological theories: T1 and T2. T1 has infinitely many place relations as primitive and T2 includes only a single three place predicate and it ranges over real numbers. T1 and T2, are, ceteris paribus, explanatorily identical. The difference is ontological commitments – T1 has a simple ontology but has an infinite number of primitives whereas T2 has fewer primitives. Simplicity, commonly understood, cannot arbitrate here since each has pros and cons, but this isn’t how we ought to think about simplicity and I agree. Melia writes, “I accept that considerations of simplicity play an important role in theory choice.

But I prefer the hypothesis that makes the world a simpler place” (p. 473). Postulating concrete unobservables in physics actually makes the world a simpler place. Postulating quarks assists in a completed worldview where higher-level objects exist out of lower-level objects, viz. quarks. Postulating mathematical objects may simplify theories, but postulating them as actually existing in the world does not simplify our picture of the world.

To bolster the rationality of weaseling out of ontological commitment to abstracta, consider scientific idealizations. Consider Planck’s radiation law in quantum mechanics as an example. The physicist in explaining energy radiation postulates a “black body”. A black body is an idealized entity which emits thermal radiation and absorbs incoming light without reflecting any. A black body does not exist in the physical world yet its postulation adds to the stock of knowledge about the world. The sciences are rife with idealizations: “fluids are incompressible (in fluid mechanics), growth rates are constant (in population ecology), and the gravitational influence of distant bodies can be ignored (in celestial mechanics)” (Colyvan, 2013, p. 1337). The successes of idealizations in science do not commit

18 Credit to Dr. Cate Sherron for pointing out ‘simplicity’ is not merely aesthetic, but has another sense in which it can mean ‘ease of calculation’. Thus, simplicity directly impacts a theory’s fruitfulness. A NATURALIST PHYSICALIST DEFENSE 12

us to their ontological existence though and do not undermine a moderate scientific realism.19 One can reasonably accept idealizations to scientific practice and deny them as part of their ontological landscape.

Section 5: The Individuation Problem

Individuation is crucial to Schneider’s argument. She writes, “mathematical entities seem to make the objects and properties figuring in the physical base the types of objects and properties they are. If something individuates something else it is generally considered to be a part, or even all, of the entity’s nature, unless an argument is provided to the contrary” (2015, p. 3). Schneider considers an example from traditional metaphysics: the nature of persons. The entities under consideration for individuation are persons; i.e. ‘how do we individuate one person from another?’ One theory to address this problem is the psychological continuity theory. The theory gives the identity conditions for individuating persons as an unbroken memory/phenomenal psychological experience since no two people share such experience.20 Thus, we have done two things in the process of individuation: (1) we individuated the entities desired (viz. persons) and (2) established something about the nature of those entities (viz. they have ‘psychological continuity’).

Looking back to the problem of the base, it’s clear why one might worry about microphysical entities having mathematical natures if mathematical objects are abstract and if mathematical entities being figured in the identity conditions mean they establish the nature of the microphysical objects.

These are big ifs. Schneider’s example of personal identity makes sense for conceptually clarifying the individuation problem in traditional metaphysics, but I wish to try and understand the problem by

19 There’s much vigorous debate about the status of idealization and whether idealizations make scientific theories literally false (cf. Cartwright, 1983). Quine’s view was to wait until a theory was properly regimented before accepting objects into one’s ontology. Recently, philosophers have become interested in scientific models and the fictions sometimes represented in them and what this means for questions of a naturalized ontology. 20 There are obvious problems with this, but this isn’t the place to consider thought experiments and objections to psychological continuity theories of personal identity. A NATURALIST PHYSICALIST DEFENSE 13

considering something from physics itself since it is the discipline under consideration. I will consider an example already previously mentioned: Planck’s radiation law in quantum mechanics. Planck’s radiation law is formalized thusly:

The entity being individuated is energy radiated per unit volume (Eλ) and among the properties figuring in its identity conditions is h. This is Planck’s constant; found to be 6.62606957 × 10−34 joule∙second.

Here, a mathematical object is doing the ‘heavy lifting’ in describing the energy radiated by a black body.

Planck’s constant (h) is not merely instrumental in individuating the energy radiated from a black body; rather, it’s a part of its nature since it figures into its identity conditions on Schneider’s view. To wit, I have dispensed with mathematical Platonism as a viable option for my physicalist, so abstracta individuating is of no concern, but can the physicalist appeal to nominalism to individuate the entities in the base? Schneider thinks not.

Schneider holds that the physicalist cannot allow nominalism to individuate the entities in the base. She writes, “[nominalism] explains mathematical discourse in terms of mental phenomena such as pragmatic and aesthetic interests” (2015, p.9). The objects of mathematics, the rules, and so on are a mental endeavor. To that end, the physicalist would have mind-dependent objects individuating putatively mind-independent objects in the base. Further, Schneider claims there is another glaring problem for the fictionalist (and mathematical object anti-realist, in general), “insofar as a law or prediction in fundamental physics is couched in a mathematical vocabulary, it will turn out to be untrue, that is, either false or vacuous” (p. 9). Put another way, how can an untruth in a physical theory produce a truth about the world?

Section 6: Quining the Individuation Problem A NATURALIST PHYSICALIST DEFENSE 14

My physicalist has denied premise 1 of the argument and salvaged a workable nominalism and must now face up to the individuation problem. The physicalist should deny premise 2 of Schneider’s argument (concomitantly denying premise 1). She calls denial of premise 2 and also denial of premise 1

The Alternate Individuator Approach since something else is doing the individuating. The alternate individuator approach, on Schneider’s view, is quizzical since it’s unclear what would be both physicalistically kosher and able to do the individuating. My physicalist has no qualms with the nominalism defended in section 4 and, without belaboring the point, would certainly assent to its utility to physical science. The crucial point for my physicalist is to what extent my nominalism is physicalistically kosher for Schneider’s problem. My physicalist must deny there is an “individuation problem” in the first place. But how could she reasonably do so? Her solution will be methodological, ontological, and tied directly to her naturalist commitments. She will have to Quine21 the problem itself.

This requires a metametaphysical discussion to clarify a way forward.

For Quine, the task of metaphysics is to “say what exists” (Schaffer, 2009, p. 348) and the method is “to extract existence commitments from our best theory” (p. 348). The Quinean turn in contemporary metaphysics is dominant and few other positions are on the map. I take Schneider’s view to be one of the other positions. For her, the task of metaphysics is not “what exists?” but “to say what grounds what?” (p. 351). The method is “to deploy diagnostics for what is fundamental, together with diagnostics for grounding” (p. 351). I see Schneider’s individuation problem as such a diagnostic tool. For her and others occupying the ‘what grounds what’ space on the map, metaphysics probes the fundamental nature of reality and the nature of substance. On my view, it does so in a way discontinuous with the sciences. For my physicalist, Schneider’s view of individuation doesn’t make

21 I use the term “Quine” here in the online “Philosopher’s Lexicon” sense. From the 2008 edition: quine, v. (1) To deny resolutely the existence or importance of something real or significant. "Some philosophers have quined classes, and some have even quined physical objects." Occasionally used intr., e.g., "You think I quine, sir. I assure you I do not!" (2) n. The total aggregate sensory surface of the world; hence quinitis, irritation of the quine. http://www.philosophicallexicon.com/ A NATURALIST PHYSICALIST DEFENSE 15

sense then and is not methodologically sound.22 The demand to define the entities in the physical base for the naturalist physicalist can still be answered, but the rules are changed.23

Without Schneider’s individuation problem facing the physicalist, there remains a question of how to define postulates in the base. Recall Schneider’s motivating question: What resources does the physicalist possess to define the physical base? The physicalist, following work in physics, most likely holds contemporary theories of quantum gravity (viz. quantum loop gravity) will rely heavily on existing theory of gravitation – general relativity (Oriti, 2003). According to Oriti (2003), some conceptual demands on a theory of quantum gravity are background independence,24 relationality,25 discreteness of space-time,26 covariant formulation,27 operational significance of the objects included,28 the principle of symmetry, and a notion of causality built in. Each of these six desiderata force demands on the practice of physicists and philosophers of science and they guide a physicalist ontology. The resources demanded by Schneider are the tools and principles of the natural method – they should see the project forward.

Section 7: Concluding Remarks

Against Schneider’s challenge to the physicalist philosopher of mind, I have argued for a nominalist strategy to explain mathematical objects and taken a metametaphysical stance which dispenses with the individuation problem. I admit regarding both the ontological problem and the individuation problem, my resolutions could be read as, at best, deflationary, and, at worst, cheap. I prefer to think they are classed as the former. The naturalistic physicalism I sketched in section 1 can be

22 Recall that the kind of physicalism I sketched in section 1 has its metaphysical commitments tied to the methods of natural science. 23 She is constrained by the natural method and ‘stands on the shoulders of giants’. 24 viz. no pre-existing absolute geometric plane to map space-time points. 25 viz. physical objects are relative to some dynamical object. 26 viz. unit measures are applied to the manifold of space-time. 27 viz. space and time are relational. 28 viz. observable entities and states are concrete and few idealizations are invoked. A NATURALIST PHYSICALIST DEFENSE 16

read as deflationary, but charges of deflation – if used in the pejorative sense – ostensibly have an alternative in mind. The alternative, as Schneider would have it, is not preferable for two reasons.

The naturalistic physicalism I sketched is (1) ontologically conservative and (2) externally consistent and so should be more appealing to philosophers of mind. It is uncontroversial to view metaphysics as an exercise in theory choice between competitors based reasonable desiderata: parsimony, simplicity, accuracy, consistency, and so on.29 Recall in section 4 my criterion of simplicity is outward looking when making theory-choice considerations: Does the theory make the world a simpler place? If the choice is between maintaining a concrete physical base defined by the method of the physical sciences (as my physicalist would have it) or injecting experience into the physical base and cluttering one’s ontology with new conceptual states like ‘protoexperience’ and ‘micro-subjects’

(Schneider, forthcoming), then I must claim victory for the naturalist physicalist. Adding mentalistic truthmakers to the furniture of the world is unwarranted and undesirable. On external consistency,

Schneider’s view does not cohere with current scientific practice in the physical sciences and certainly not in the cognitive sciences and so lacks on this theoretical virtue as well. For the naturalist, ontological compatibility with the sciences is important. Again, the naturalist physicalist seems at a comparative advantage, all things considered. While the view I give is possibly deflationary, the alternative in question is unappealing to the physicalist philosopher of mind.

29 Schneider agrees since she claims to prove physicalism is less economical over her micromonism. A NATURALIST PHYSICALIST DEFENSE 17

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