GROUNDING TRUTHMAKING
A Dissertation
Submitted to the Graduate School of the University of Notre Dame in Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy
by
Bradley Rettler
Michael Rea, Director
Graduate Program in Philosophy
Notre Dame, Indiana
February © Copyright by
Bradley Rettler
Some Rights Reserved This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike . Unported License http://creativecommons.org/licenses/by-nc-sa/./ GROUNDING TRUTHMAKING
Abstract
by
Bradley Rettler
This is a dissertation in meta-ontology. In it, I attempt to develop some alternative rules to the standard Quinean meta-ontology. The alternative is intended to allow for a minimal ontology, while still maintaining fit with folk discourse. I hope that this dissertation will help to make such alternative rules precise, and understandable to Quineans, most of whom consider such talk to be “murky metaphysical waters”.
The new rules revolve around the relation of ground. In Chapter , I discuss my understanding of grounding. The majority of attempts at articulating a theory of grounding have treated ‘grounds’ as univocal. There has been a recent attempt to argue that ‘grounds’ does not refer. I argue against both of these options, and defend a third: ‘grounds’ is univocal, and grounding is a genus.
In Chapter , I turn my attention to one species of grounding—truthmaking. I argue that the measure of ontological commitment is not what a theory says exists, but what a theory requires as truthmakers. A person is ontologically committed to the existence, in the fundamental sense of ‘existence’, of there being truthmakers for the sentences of her theory. In Chapter , I turn my attention to the question of what sort of things these truthmakers are. Generally, truthmaker theorists have accepted truthmaker neces- sitarianism, which has led them to reify states of affairs, facts, or tropes. But these things are dubious posits. I want to retain truthmaking, but I give four arguments Bradley Rettler against truthmaker necessitarianism. This allows us to admit only substances into our ontology.
In Chapter , I discuss the language of the ontology room. The received view was that the language of the ontology room is English: words mean the same thing when doing ontology as they do at the fireworks show. I argue for an alternative: when we’re doing ontology, we’re not using ‘exists’ the same way others do, or the same way we do when we’re not doing ontology. I also say what ‘exists’ means inside the ontology room: it’s a restriction of the quantifier at the fireworks show. For my parents, Steve and Sherry Rettler, without whom I would not have even one degree in philosophy.
ii CONTENTS
ACKNOWLEDGMENTS ...... v
INTRODUCTION ......
CHAPTER : HOW TO THINK ABOUT GROUNDING ...... . Grounding as Univocal ...... .. Defending the Principles ...... .. Counterexamples ...... ... Brain States and Mental States ...... ... Shapes ...... ... Everything Exists ...... ... There Are Facts ...... ... General Facts ...... .. Points of Disagreement ...... .. The Options ...... . No Work for a Theory of Grounding? ...... . Grounding as Genus ...... .. Ontological Dependence ...... .. Truthmaking ...... .. Reductive Analysis ...... .. Metaphysical Explanation ...... . Is Grounding a Genus? ...... . Conclusion ......
CHAPTER : TRUTHMAKERS AND ONTOLOGICAL COMMITMENT . . . The Ontological Question ...... . Ontological Commitment ...... . Two Ways of Understanding Truthmaker Views ...... .. Denying () ...... .. Denying () ...... . The Meinongian Contrast ...... . The Quinean Contrast ...... . Advantages of Truthmaker Views ...... . Other Truthmaker Views ...... .. The Specific Truthmaker View ......
iii .. John Heil’s View ...... .. David Armstrong’s View ...... .. Ross Cameron’s View ...... . Conclusion ......
CHAPTER : TRUTHMAKERS AND SUBSTANCES ...... . Introduction ...... . The Argument ...... . Truthmaking ...... . Truthmaking and Grounding ...... . Truthmaking and Substances ...... .. The Criteria of Substancehood ...... .. Substances as Truthmakers ...... . Ultimate Truthmakers and Intermediate Truthmakers ...... . Objections and Replies ...... .. Objection : Truthmaker Necessitarianism ...... .. Objection : Explanation ...... .. Full Truthmaking and Partial Truthmaking ...... . Conclusion ......
CHAPTER : THE FUNDAMENTAL QUANTIFIER ...... . What is the Fundamental Quantifier? ...... . The Semantics of Quantifier Restriction ...... .. A Brief Overview of Quantifier Restriction ...... .. A Brief Overview of the Semantics of Quantifier Restriction . .. Syntactic Explanation ...... .. Semantic Explanation ...... .. Pragmatic Explanation ...... .. The Semantics of Quantifier Restriction and the Fundamental Quantifier ...... . Ways of Restricting Quantifiers ...... .. Inferential Restriction ...... .. Restriction to a Predicate ...... .. Domain Restriction ...... . The Fundamental Quantifier is a Restricted Quantifier ...... .. Inferential Restriction ...... .. Restriction to a Predicate ...... .. Domain Restriction ...... .. The Fundamental Quantifier is a Restricted Quantifier . . . . . Toward a Stronger Conclusion ...... . The Quinean Contrast ...... . Conclusion ......
BIBLIOGRAPHY ......
iv ACKNOWLEDGMENTS
This dissertation started (in one of the broader senses of ‘started’) in , when professors Wilbert Ratledge, Arnold Hustad, and Lem Usita told me that I ought to go to graduate school. Though neither my grades nor my effort had been great, they thought I could change. Because of their prompting, I decided to apply; my heartfelt thanks to them for starting me on this path. Despite not having taken a philosophy class as an undergraduate, I chose to do an M.A. in the subject—but I had to wait a year. During that year I worked as a landscaper, and Brian Kurbis was my roommate and first philosophical conversation partner. He taught me how incredibly important it was to think carefully about the things most important to us, and how much fun it could be to discuss them. We spent hours at Old Chicago© arguing over beers, which prepared me well for life as a philosopher. When I got to my M.A. program, I was fortunate to be surrounded by students with passion and enthusiasm for philosophy, and dedication to helping each other learn how to do philosophy and to figure out the truth. In particular, I spent many hours on the porch with my roommates John Craw, David Gilbert, Jon LaSalle, and
Craig Mather, talking over the ideas in class and exploring new ones. My writing sample for Ph.D. programs came from conversation with Jon, and he read several drafts; I doubt I’d be in any Ph.D. program without him. I also cannot overstate the impact that Tom Crisp had on my personal and philosophical development during the generous amount of time he spent with me, modeling how to be an excellent philosopher without sacrificing the other important things in life.
When I got to Notre Dame, I was fortunate to be surrounded once again by peo-
v ple who were interested in developing as philosophers and helping me do the same. As a first-year Ph.D. student who lacked confidence, I spent countless hours talking philosophy with Scott Hagaman, trying out my ideas and practicing being a philoso- pher. Scott was a tireless interlocutor and always excited to point out my mistakes, but just as willing to help fix the problems in my arguments. The members of my cohort, most of whom worked in areas wildly different from my own, broadened my knowledge and interests, and made me a more well-rounded philosopher; they also were crucial to my passing the history comprehensive exams. The two metaphysi- cians in my cohort—Aaron Segal and Jeff Snapper—are a delight to talk metaphysics with, and our discussions and their comments on my seminar papers taught me cre- ativity and how to anticipate objections.
When I started this dissertation, Josh Rasmussen was a source of encouragement and ideas; his emails were clear and precise articulations of the Quinean position against which I’m arguing, and I benefitted greatly from reading and re-reading them. During the first two years of my writing, I met weekly with Alex Skiles to talk about our own work and to discuss what we were reading. Alex is one of the most careful philosophers I’ve ever talked with, and is a model of how to read and interact with metaphysics. He was selfless with his time, always eager to talk about my work, and every chapter of this dissertation has improved for his involvement. When Alex finished the program, the void he left was filled by Tim Pawl and Noël Saenz; we met weekly to read each others’ work, and they helped me tighten my arguments and pointed me to tons of relevant literature. Alex Arnold, Bryan Pilkington, and Jeff
Tolly are excellent philosophers with whom I share many other interests. Spending time with them watching football, playing tennis, and interspersing philosophical conversation provided needed (and enjoyable) breaks from writing.
There are a number of people who read (and often reread) chapters of this dis- sertation and discussed them with me; their comments and suggestions helped me
vi correct errors and anticipate many objections. Thanks to Kenny Boyce, Scott Brown, Ben Caplan, Jonathan Jacobs, Dan Korman, Kathrin Koslicki, Andrew Melnyk, Tim
Pawl, Kate Ritchie, Noël Saenz, Ted Sider, Jeff Snapper, Jeff Speaks, Jason Turner, and Jessica Wilson. I hope that they can see their involvement in this dissertation, because I certainly can. Portions of this dissertation were given at the Baylor Philosophy of Religion
Conference, Central States Philosophical Association, University of Texas at Austin Graduate Student Conference, Biola University Graduate Student
Conference, Pacific APA, Pacific APA, and University of Geneva
Workshop in Metaphysics and Mathematics. Thanks to those in the audience for their careful comments and incisive questions, and to the philosophy department and Graduate School at the University of Notre Dame, the APA, the Institute for
Scholarship in the Liberal Arts, Jon Kvanvig, and Michael Rea for financial support.
The members of my committee have been instrumental in different ways. Each of them has offered comments on multiple chapters and has been more than willing to meet with me. But their influence extends beyond the classroom. Sam Newlands has taught me the importance and effectiveness of budgeting my time, and the satisfaction of working on a project until I was so proud of it that I wouldn’t change a word. Peter van Inwagen is a clear and methodical thinker, and his writing style is a model I hope to follow. Meghan Sullivan is incredibly precise and demands precision, and also brings energy and enthusiasm to philosophy. Dean Zimmerman generously gave up his time in for a directed readings with me, the result of which was my writing sample for Ph.D. programs; he has supported and prodded me ever since.
My experience with my director, Mike Rea, has been better than I could have imagined. Despite denying (at least early on) every conclusion for which I wanted to argue, he was committed to helping me make the arguments for them as strong as I could. He read multiple drafts of everything I wrote in metaphysics since the start
vii of the Ph.D. program, and usually had comments back to me by the time I woke up the next morning. His comments were always insightful and difficult to respond to, and my work was always better after having done so.
I owe a huge portion of my success to my family. My sister, Erin, encouraged me in my academic endeavors, and was always a model of intelligence and effort; she’s one of the smartest people I know, and she’s never given less than her best. I wish I’d followed her example in that regard earlier. My parents, Steve and Sherry, believed I could succeed long before they had sufficient evidence—and if they hadn’t supported me, I wouldn’t have. In addition to all they did to make me a good person, they also modeled for me qualities that have contributed to my being a philosopher: to question, to think critically, to consider all sides of an argument, and to see the weaknesses in my own positions.
My greatest philosophical debt is to Andrew Bailey, my roommate of four years, my best man, and my best friend. As a philosopher, Andrew taught me to come up with valid arguments with plausible premises, to be clear, concise, and precise, and to write up (at least briefly) every idea I have and see what comes of it. I’ve written
papers since I started at Notre Dame, and Andrew has read and discussed of them with me. He’s sacrificed countless hours of his time to help me, and I can only hope he considers it having been worthwhile. Finally, the most important person in my life, my wife Lindsay, to whom my debts are both personal and philosophical. Lindsay has provided more support and encouragement than I could have imagined, and far more than I deserve. She has picked me up when I’m down, and brought me down to earth when my head is in the clouds. She has been a model of many important traits in a philosopher: careful attention to detail, guiding a reader through a paper, and charitably reading others.
She’s encouraged me to work when I had to and has helped me with that work, and encouraged me to take a break when she could tell I needed it. I might have been able
viii to do write this dissertation without her, but both it and I would have been the worse for it. She has been a perfect spouse of a dissertation-writer, and I look forward to trying to follow her example.
ix INTRODUCTION
Ontology has been going on for a long time. Meta-ontology has been going on for just as long, but the amount of attention given to it has ebbed and flowed during that time. Whereas ontology has enjoyed constant discussion, “ontology” has not; and the discussion of “ontology” is meta-ontology, which has often been relegated to presuppositions and assumptions. Meta-ontological views have been taken for granted, in large part because they’ve been widely agreed upon.
The standard Quinean picture teaches that in order to figure out one’s ontology, one must translate her theory into first order logic, and then look to the valuables of the bound variables; the referents of those variable are the things in one’s ontology.
Quine proposed the picture in , and it has been widely taken for granted since then. This is not to say that it was universally accepted, but rather that those who accepted it did not feel it was in need of argument or defense. For example, van
Inwagen:
All ontological disputes in which the disputants do not accept Quine’s strategy of ontological clarification are suspect. If Quine’s “rules” for conducting an ontological dispute are not followed, then…it is almost certain that many untoward consequences of the disputed positions will be obscured by imprecision and wishful thinking. (van Inwagen )
Thankfully, not everyone believes this; but most do. So, non-Quineans have been interested to articulate alternative “rules”, so that the consequences of first-order ontological positions are not obscured by imprecision or wishful thinking. These al- ternative sets of rules have made use of a number of notions that aren’t acknowledged in the Quinean strategy: grounding, truthmaking, metaphysical structure, ontologi-
cal dependence, “in virtue of”, and so on. In this dissertation, I attempt to develop some alternative rules. My main purpose is to make such rules precise. I hope that their precision helps them be understand- able to the Quinean, who considers such talk to be “murky metaphysical waters”.
Another purpose is to allow for a minimal ontology while still maintaining fit with folk discourse. A tertiary purpose is to satisfy the requirements for a Ph.D.
On the Quinean strategy, one’s ontology is comprised of all and only the things one thinks exist. For every person S and every x such that one is willing to say,
“⌜x⌝ exists”, accept it as strictly and literally true, and not supply a paraphrase the logical translation of which doesn’t quantify over x, S must accept ∃y(y = x); and because of that, x is in S’s ontology. And for every person S and kind F , if S is willing to say “There are F s”, accept it as strictly and literally true, and not supply a paraphrase the logical translation of which doesn’t quantify over F s, then S must accept “∃xF x”, and F s are in S’s ontology. But while most people want to say that my shadow exists and that there are holes, very few people want to admit shadows and holes into their ontologies. This is a problem for the Quinean. Most Quineans have accepted shadows and holes into their ontologies and attempted to make that a legitimate move. Some have not, and have thus denied that shadows and holes exist.
I want to be able to accept that shadows and holes exist, but not admit them into my ontology. Similar with properties, ordinary non-fundamental objects like tables and chairs, past and future objects, and other such things. In order to do that, I need to play by different rules.
So, I will engage in some “wishful thinking”; I think that I can argue for and de- fend a small ontology without accepting Quine’s strategy for determining ontological commitments. This dissertation is an attempt to make such wishful thinking more precise.
The new rules revolve around the relation of grounding. So in Chapter , I discuss
what I take grounding to be. Grounding is the relation that holds between a set and its members, an object and its shadow, a whole and each of its parts, and so on. The majority of attempts at articulating a theory of grounding have treated ‘grounds’ as univocal. They go on to state a number of axioms, develop a number of principles, and see what follows from the axioms and principles. There is substantial overlap on many of the principles: transitivity, irreflexivity, and some others. But a number of philosophers have offered counterexamples to these axioms and principles. There is widespread disagreement over the truth of these principles—and not by Quineans, most of whom claim not to understand grounding, but by proponents of grounding.
This widespread disagreement gives us reason to look in another direction. If we’re not to treat ‘grounds’ as univocal, then we must either treat it as equivocal or deny that it has a referent. There have been two recent arguments for the latter: one by Thomas Hofweber, and one by Jessica Wilson. Michael Raven () has responded persuasively to Hofweber’s argument, but Wilson’s has not yet been re- sponded to. (This can be forgiven, I think, because it has not yet been published.)
I think Wilson’s argument is not sufficient to show that grounding is not necessary, and I respond to her arguments for that conclusion.
That leaves open the option that we should think of ‘grounds’ as equivocal. I conclude Chapter by developing a theory of how we should do that. We should treat grounding as a genus, and think that people use ‘grounds’ to refer to various species of grounding—ontological dependence, truthmaking, reductive analysis, and metaphysical explanation. (And perhaps others.)
In Chapter , I turn my attention to one species of grounding—truthmaking. I argue that the measure of ontological commitment is not what a theory says exists, but what a theory requires as truthmakers. Specifically, a person is ontologically committed to the existence, in the fundamental sense of ‘existence’, of there being truthmakers for the sentences of her theory. The truthmakers for an existential sen-
tence may very well not be the things quantified over in a translation of the sentence into first order logic.
This view has three main advantages. First, it allows us to say that there are some things that aren’t in our ontology, and accept “F s exist” and not allow F s into our ontology. Most meta-ontologies that allow for this don’t give principled rules for determining when something is in your ontology; my view does. The second advantage is that questions of ontology are settled by doing metaphysics (figuring out the truthmakers of sentences) rather than looking at how we use language (figuring out the extension of the existential quantifier). The third advantage is that it doesn’t demand that we provide a paraphrase for a sentence that seems to ontologically commit us to something if we want to avoid ontological commitment to something.
After all, many people are not clever enough to think of paraphrases for sentences involving average families or shadows, but they very well know there aren’t any such things. This view of ontological commitment is much more amenable to a combination of a minimal ontology and a fit with folk discourse. We can say that properties exist, that there are . children in the average family, that shadows are dark, and that tables hold up my cup: but it’s not obvious that properties, average families, shadows and tables make those sentences true, and thus we need not admit them into our ontologies.
In Chapter , I turn my attention to the question of what sort of things these truth- makers are. Generally, truthmaker theorists have accepted truthmaker necessitarianism— the thesis that truthmakers necessitate the things they make true. This has led them to reify states of affairs, facts, or tropes, so that those things can play the role of truthmakers. But these things, to my mind, are dubious posits. (Tropes are the least dubious, but the least obvious satisfiers of truthmaker necessitarianism; after all, what trope(s) necessitate(s) the truth of, “When my sister worked at the Kohler
Company, she was a product manager for stainless steel kitchen sinks, and even got to name many of them”?)
I want to retain truthmaking, but deny truthmaker necessitarianism. I give four reasons for denying it. First, truthmaker necessitarianism requires more ontology and more ideology than its denial. It requires facts, or states of affairs, or tropes, or something for every possibly true proposition such that, if it exists, that proposition is true. This is a mysterious kind of thing, and there have to be a great deal of them. Second, truthmaker necessitarianism is an instance of the following schema: x makes y F only if there is some G such that necessarily, if Gx then F y. But most instances of this schema are false. In order to motivate truthmaker necessitarianism, one should say what’s special about truth that makes that one instance of the schema true. Third, truthmaker necessitarianism is unmotivated because truthmaker theory can require truth to depend on the world, or truths to be “tied down by being”, or whatever the motivation for truthmaker theory is, without the world necessitating the truths. Finally, truthmaker necessitarianism is unmotivated because the way the world is can necessitate truths without there being some thing in the world that itself necessitates the truths.
Denying truthmaker necessitarianism not only allows us to eliminate the kinds of things previously mentioned, but other things besides. Indeed, I argue that once we deny truthmaker necessitarianism, it is open to us to say that all truthmakers are substances. Since our ontology is comprised of all and only the things required for the sentences of our theory to be true, and since all and only the substances are required for the sentences of our theory to be true, our ontology is comprised of all and only the things we take to be substances. This is a the minimal ontology I wanted.
In Chapter , I discuss a topic that’s been receiving a lot of attention lately, due in large part to the work of Eli Hirsch—the language of the ontology room. The
received view, at least among metaphysicians, was that the language of the ontology room is English; that is, words mean the same thing when doing metaphysics and ontology as they do when talking with your parents at the fireworks show. But several metaphysicians have challenged this view. Some think it’s a bad thing; because we’re doing metaphysics and saying things that would be false in ordinary contexts, we’ve lost touch and are saying “esoteric” things. But some think it’s a good thing; because we’re doing metaphysics and our interest is in figuring out the structure of the world, the meanings of our words are “better” than their meanings at the fireworks show.
This might be because they’re more natural, or because they’re more joint-carving, or because they’re reference magnets, or some other reason. I cast my lot with this last option; when we’re doing ontology, we’re not using
‘exists’ the same way others do, or the same way we do when we’re not doing on- tology. This is why most ontologists give surprising answers to the question, “What is there?” But then the charge by people like Hirsch and Hofweber is that, while ev- eryone understands what ‘exists’ means outside the ontology room, nobody knows what ‘exists’ means inside the ontology room. In this chapter, I answer that charge.
I say that the meaning of ‘exists’ inside the ontology room is a quantifier, and the meaning of ‘exists’ at the fireworks show is a quantifier, and the quantifier that’s the meaning of ‘exists’ in the ontology room (which I call ‘the fundamental quantifier’) is a restriction of the quantifier at the fireworks show (which I call ‘the ordinary
English quantifier’). After discussing restricted quantification and the semantics of quantifier restriction, I argue that the fundamental quantifier is a restriction of the ordinary English quantifier. I explicate three senses of quantifier restriction, and argue that on every sense, the fundamental quantifier counts as a restriction of the English quantifier.
The main service of this chapter is to provide an analysis of why some ontological disputes seem to have obvious answers, and why some ontological debates seem
to be intractable. They seem to have obvious answers because they do—at least when the quantifier in question is the ordinary English quantifier. But the ontologists who are giving different answers are not using the English quantifier—they’re using the fundamental quantifier. And I explain what the fundamental quantifier is—a restriction of the ordinary English quantifier to the fundamental things. The things that one takes to be in the domain of the fundamental quantifier—the things that exist in the fundamental sense of ‘exist’—are the things that are in one’s ontology. So if when S is doing ontology she denies the existence of F s, then even if she accepts the existence of F s at the fireworks show, that doesn’t entail that F s are in her ontology. This allows for a minimal ontology. In sum, this dissertation is my attempt to articulate some plausible meta-ontological principles that allow for me to have a minimal ontology, while not denying the exis- tence of things that even my grandma knows exist.
CHAPTER
HOW TO THINK ABOUT GROUNDING
The notion of grounding has played an increasing role in metaphysics over the last few years. Metaphysicians have put grounding to use in debates about material objects, presentism and eternalism, physicalism and dualism, and many others. The usual way of introducing the notion of grounding is by example: () truth is grounded in being, () the existence of singleton sets are grounded in the existence of their members, () existential generalizations are grounded in their instances, () wholes are grounded in their parts (or vice versa), () holes in a piece of cheese are grounded in the piece of cheese, () mental facts are grounded in physical facts, and the like.
Since many debates in metaphysics revolve around grounding, it’s useful for meta- physicians to investigate the notion.
Most people think that few or none of these grounding claims tell the whole story about the grounded things; that is, in most of these examples there are further grounds than just what is stated. It seems that these examples are examples of partial grounding. For the purposes of this paper, partial grounding is compatible with whole grounding; it might be that x partly grounds y and x wholly grounds y. But it needn’t be. And I will sometimes speak as though facts are the relata of the relation of grounding; though many people accept this, I do so for ease of example, and one can freely substitute other kinds of things.
The earliest well-known appeal to the relation of grounding is in Plato’s Euthy- phro, where Socrates wonders “…whether the pious or holy is beloved by the gods
because it is holy, or holy because it is beloved of the gods” (a). One way of construing the question is as a question of grounding. For any act A such that A is holy and beloved by the gods, there are two facts: ) [A is beloved by the gods], and
) [A is holy]. Socrates is asking Euthyphro whether the fact that () grounds the fact that (), or vice versa. So, it seems that we have an intuitive notion corresponding to ‘grounds’, that talk of grounding is meaningful, and that such talk can be used to formulate theses in metaphysics, ethics, and perhaps other areas of philosophy. However, there are a number of people that have challenged the legitimacy of appealing to grounding in philosophy. Before we can rest content with attempting to figure out various grounding relationships, we must first defend the legitimacy of the enterprise. In this paper, I will do that.
When it comes to grounding, we have three options. First, we can treat ‘grounds’ as univocal, denoting a single relation on all occasions of use. Second we can treat ‘grounds’ as multivocal, denoting different relations on different occasions of use.
Third, we treat ‘grounds’ as meaningless, denoting nothing on any occasion of use.
Correspondingly, we can also be grounding monists or pluralists. Grounding monists think that there is a single grounding relation, or many grounding relations all of which can be analyzed in terms of a single relation. Grounding pluralists think that there is no single relation of grounding, and that the many relations denoted by
‘grounds’ cannot be analyzed in terms of a single relation. Obviously those who
One might naturally think of the pre-Socratics as thinking about grounding; Thales didn’t think everything literally was water, but rather than everything is grounded in water. And so on.
I follow the convention of using brackets around a declarative sentences as a name for the fact expressed by that sentence. So ‘[x]’ is a name for the fact that x.
Most notably Hofweber (), Oliver (), Daly (), Wilson (MS), Koslicki (Manuscript), and the referent of the third stanza of the st Century Monads’ “I think I might be grounded in you”.
Thanks to Alex Skiles for suggesting this two-fold classification.
think ‘grounds’ is meaningless are neither grounding monists nor grounding plural- ists. And perhaps it is most natural for grounding pluralists to think that ‘grounds’ is multivocal, and for grounding monists to think that ‘grounds’ is univocal. But as one is a semantic thesis and one a metaphysical thesis, they do not hang together.
In this paper, I argue for the conjunction of grounding monism and the multi- vocity of ‘grounds’. To do this, I will first argue against two prominent approaches to grounding: the monist univocity approach of Kit Fine, and the meaninglessness approach of Jessica Wilson. If we have reason to reject these two approaches to grounding, we have reason to accept the one I will propose.
. Grounding as Univocal
The most well-developed attempt to work out a univocal notion of grounding has been that of Kit Fine, in his Fine (a), Fine (b), and Fine (). In this section, I lay out some of the principles that Fine takes to govern the logic of grounding, and offer counterexamples. I then discuss how we should respond to the counterexamples.
In this series of papers, Fine is concerned with developing the pure logic of grounding— axioms which use grounding relations, and no other connectives or predicates or rela- tions. For example, one can formulate T (if A grounds B and B grounds
C, then A grounds C), but not H (it’s not the case that if (A grounds B and necessarily B if and only if C), then A grounds C) or C
(if A grounds C and B grounds C, then A & B ground C). Fine accepts fewer grounding principles than most other proponents of ground- ing. For example, most accept I (∀x¬(xGx)) and A (∀x∀y¬(xGy∧ yGx)), but Fine does not. He thinks that there is a notion of grounding that is re-
flexive, which he calls “weak ground”, and a notion of grounding that is irreflexive,
which he calls “strict ground”. And he allows that there is a notion of grounding that “moves us sideways in the explanatory hierarchy” (Fine, b, ), which may allow for a denial of A. At least, it removes one motivation for accepting
A, which is that grounding ought to take us from the more fundamental to the less fundamental. Here are some axioms and theorems of Fine’s system:
T: ∀x∀y∀z((xGy ∧ yGz) ⊃ xGz)
F: ∀x∀y(xGy ⊃ (x is true ∧ y is true)).
N-: ¬∀x∀y(xGy ⊃ (∀z((x ∧ z)Gy))).
∃-G: ∀x(F x ⊃ ([F x]G[∃y(F y)])).
It is worth noting that not everyone who accepts talk of grounding accepts all of these principles. Nearly everyone accepts I, A, and T-
. Most people accept F and N-, though they aren’t explicitly mentioned as often as the first three. ∃-G is mentioned even less often, but is accepted by some and not rejected by any. There are reasons to accept each of the principles that Fine accepts. But in the sec- tion following, I offer several counterexamples to various conjunctions of the princi- ples. The counterexamples are cases that we intuitively take to be cases of grounding, but which entail the falsity of at least one of the above principles.
Fine likely thinks that ‘grounds’ is thus often ambiguous between weak ground and strict ground (and in fact also what he calls “partial ground” and “full ground”), but this is not to say that ‘grounds’ is not itself univocal. For in the phrases ‘weak ground’, ‘strict ground’, ‘partial ground’, and ‘full ground’, ‘ground’ means the same thing.
See Audi (Forthcoming), p; Bohn (), ch; Cameron (d), p; Correia (), pff; Rosen (Forthcoming), p-; Schaffer (), p; Schaffer (a), p and p; Schaffer (MS), p; and Whitcomb (). Kit Fine states in his (), p, that partial grounding is at least transitive and irreflexive. Karen Bennett states in her (), p, that grounding is at least irreflexive and asymmetric.
See Fine (a) and Whitcomb ().
.. Defending the Principles
I says that nothing grounds itself. Most of the support for this comes from reflecting on the nature of grounding. But here’s a further argument.
Grounding is closely linked with fundamentality. The more fundamental things ground the less fundamental. Whatever things are the ultimate grounds are the fun- damental things. But then nothing can ground itself, since nothing can be more fundamental than itself.
A says that no two things ground each other. One could give a fundamentality- inspired argument similar to the one above for this; nothing can ground something that grounds it, since nothing can be more fundamental than a thing more funda- mental than it. Another reason to accept A is that violations of asymmetry would lead to a vicious grounding circle. However, this seems question-begging; the only reason to think the circle is vicious is that one already thinks that grounding is asymmetric.
T says that for any a, b, and c, if a grounds b and b grounds c, then a grounds c. Support for this is primarily from reflection on cases and on the nature of the relation of grounding.
F says that the relata of the relation of grounding must both be true. Or, if one thinks that the relata of grounding aren’t truth-apt, then the relata must be factual, or obtain, or what have you. One reason to accept this is that grounding is an explanation relation, and there are no false explanations.
N- says that not every collection involving some thing a grounds anything that a grounds. Support for this is from reflection on obvious counterexam- ples to monotonicity. For example: if [snow is white] grounds [something is white], it does not follow that [snow is white] and [grass is green] together ground [something is white].
∃-G says that general existential facts are grounded in each of their
instances. Here are three reasons to accept ∃-G. () Reflection on cases of general existential facts and intuitions about what ground them. The fact that there are philosophers is partly grounded by the fact that I am a philosopher, and partly grounded by the fact that you are a philosopher. The fact that there are philoso- phers may also be partly grounded in fundamental physical facts and some social facts about professions and groups, but it is partly grounded by facts about specific philosophers. () If instances of general existential facts don’t ground general exis- tential facts, nothing does; there are no other candidates in the offing. But general existential facts seem to be exactly the sort of facts that seem to stand in need of grounding. () One can look at an instance of a general existential fact and, purely on the basis of it, come to know the general existential fact itself. For example, even if one doesn’t know anything else, from “Karen is a philosopher” one can deduce,
“There are philosophers.” One might then wonder what grounds the truth of the latter. Since she knows the latter purely on the basis of the former, and the former entails the latter, there is a (defeasible) reason for thinking the former grounds the latter.
.. Counterexamples
In this section, I give several counterexamples to the above principles and to con- junctions of the above principles. I do not endorse all of these counterexamples, and no doubt the reader will find herself in a similar position. But that’s not so important.
What is important is that each of the counterexamples is to some principle that at least one grounding theorist (and frequently many more) thinks is obvious, and the counterexample is taken to be an obvious counterexample by at least one grounding theorist (and often many more). Furthermore, there is no principle, axiom, or the- orem that is totally uncontroversial. Each principle is taken to be obviously true by some and obviously subject to counterexample by others.
... Brain States and Mental States
This is an example offered by Carrie Jenkins (). Jenkins argues that it is perfectly coherent to think that a certain feeling of pain P is grounded in a certain physical state S. It is also perfectly coherent to think that P just is S—that is, P is identical to S. But not only is it coherent to believe either one of those things; it is coherent to believe them both—it is perfectly coherent to believe both that P is grounded in S and that P just is S. But if S partly grounds P and S is identical to
P , then S partly grounds S, and P partly grounds P . Thus, either I or
T is false.
Note, however, that this requires that anything that grounds x also grounds any- thing identical to x; that is, it requires that grounding be extensional. One is free to deny this, of course. However, if grounding is extensional, and Jenkins’ counterex- ample is true, then either I or T is false.
... Shapes
This case is courtesy of Jonathan Schaffer. Suppose you have a ball that is roughly spherical except for a small dent. The following seem true: () [The ball has shape S] partly grounds [the ball is roughly spherical]; this follows from D-
, since having shape S is a precise way of being roughly spherical. () [The ball has a dent] partly grounds [the ball has shape S], since having a dent is one com- ponent into which being shape S is analyzed. If T is true, then it follows that: () [The ball has a dent] partly grounds [the ball is roughly spherical]. But that doesn’t seem right; having a dent detracts from rough sphericity. So T is
To preserve facts as the relata of the relation of grounding, this could be translated “the fact that a subject has P is grounded in the fact that the subject is in physical state S”.
See Schaffer (). Schaffer offers two additional counterexamples; I have chosen what I take to be the most compelling.
false.
... Everything Exists
Kit Fine (, p) offers the following case, though he says, “It is hard to see how the general principles of ground [Transitivity, Irreflexivity, or Factivity] might reasonably be rejected…”(p). Nevertheless: Let F be the following fact: [every- thing exists]. Since [F exists] is an instance of [everything exists], [F exists] partly grounds [everything exists], by ∃-G. But [everything exists] partly grounds
[F exists], since [everything exists] is a constituent of [F exists]. So [everything ex- ists] partly grounds [F exists] and [F exists] partly grounds [everything exists]. And by T, [F exists] partly grounds [F exists], and [everything exists] partly grounds [everything exists]. So, either I, T, A, or ∃-G is false.
... There Are Facts
Consider the fact that there are facts; call this fact ‘y’. Now, each fact is an instance of the fact that there are facts. Since y is a fact, it is an instance of the fact that there are facts. So, y is an instance of itself. By ∃-G, y grounds itself.
So, either ∃-G or I is false.
One might deny that there are general facts, like the fact that there are facts, or the fact that there are philosophers, or the fact that Terrence knows something or other. But first, if it is true that there are facts, then it is a fact that there are facts. For all true propositions, there is a fact that obtains if and only if that proposition is
He advocates denying one of the extra-logical principles on which he claims his counterexample depends.
Where ‘everything’ is a referring term, not a quantifier.
The explanations are my own, as Fine doesn’t give reasons to think that [everything exists] partly grounds [F exists], or that [F exists] partly grounds [everything exists].
true. Second, if there are philosophers, then it is a fact that there are philosophers. It certainly isn’t a fact that there aren’t philosophers. At any rate, if there are facts, it’s not clear why [there are philosophers] or [there are facts] isn’t one of them. The believer in facts owes an explanation of why there are no general facts.
... General Facts
Consider three facts: the fact that I have arms, the fact that someone in this room has arms, and the fact that there are facts about this room. [I have arms] partly grounds [someone in the room has arms], and [someone in the room has arms] partly grounds [there are facts about this room]. But [I have arms] does not partly ground [there are facts about this room]. If this is right, then T is false.
I can think of three ways to deny that the case is a counterexample to T-
. The first is to maintain, as above, that there are no facts like [there are facts about this room]. My reply is along the same lines as above; [this room is spacious] certainly seems to be a fact about this room. The second is to object that [I have arms] does ground [there are facts about this room]; it just doesn’t seem to until we realize that since I am in the room, facts about me are facts about the room. But following this line with respect to all cases of this type this leads to an explosion of partial grounding, and one might be surprised at just how much partial grounding one has to admit in order to endorse this response.
The proposed response has the following consequences: ) Every fact partly grounds the fact that there are facts about the world. (Since the fact that x partly grounds the fact that something in the world is such that x, and the fact that something in the world is such that x partly grounds the fact that there are facts about the world.) ) [I have arms] partly grounds (i) [someone in the room can use a pen], (since [I have arms] partly grounds [I can use a pen] and [I can use a pen] partly grounds [someone
This was floated by Brad Monton in an all-too-brief conversation.
can use a pen]), (ii) [there are facts about hotels] (since [I have arms] partly grounds [someone in the hotel has arms], and [someone in the hotel has arms] partly grounds
[there are facts about hotels]), and thousands of others. And ) Every fact about me partly grounds [there are facts about this room], (since because I am in the room, every fact about me is a fact about the room), and every fact about me partly grounds [there are facts about cities] (since because I am in a city, every fact about me is a fact about a city), and so on. Of course, one is free to accept these consequences and hold on to the transitivity of partial grounding.
The final way is to deny that [I have arms] partly grounds [someone in the room has arms]; rather, [I have arms] and [I am in the room] partly grounds [someone in the room has arms]. However, an attractive thought is that conjunctive facts are partly grounded by each of their conjuncts. So, [I have arms and am in this room] is partly grounded by [I have arms], and it is partly grounded by [I am in this room].
But then the failure of the transitivity of partial grounding remains: [I have arms] partly grounds [I am in the room and have arms], which partly grounds [someone in the room has arms], which partly grounds [there are facts about this room]; but intuitively [I have arms] does not partly ground [there are facts about this room].
.. Points of Disagreement
So, we have a very well-worked out theory of grounding, but we also have several counterexamples to the axioms that the theory takes to be partly constitutive of the pure logic of grounding. This is supposed to be the most minimal sort of theory, stating only the completely uncontroversial assumptions; but already there are half a dozen putative counterexamples that a number of people find obvious and a number
This objection was offered by Alex Skiles.
So, [you are a philosopher and I am a philosopher] is partly grounded by [I am a philosopher] and partly grounded by [you are a philosopher]. And [dolphins are mammals and +=] is partly grounded by [dolphins are mammals] and partly grounded by [+=].
find obviously wrong. And all these are people who accept that talk of grounding is meaningful! There is widespread disagreement over whether certain axioms are true of grounding—axioms that grounding’s foremost proponents take to be partly con- stitutive of the concept of grounding. This serves as evidence that grounding is not univocal. But there’s more. Not only are there a number of putative counterexam- ples to the axioms of the most well worked out theory of grounding, but there is also major disagreement among grounding theorists who take ‘grounds’ to be univocal over extra-logical features of grounding.
First, there is disagreement about whether grounding is a relation. Jonathan
Schaffer (a) and Kathrin Koslicki (Forthcoming) think that it is, while Kit Fine (a) and Fabrice Correia () think that it’s a logical operator or connective.
Second, there is disagreement about what the relata of the grounding relation are, or what flank the sides of the logical connective. Jonathan Schaffer (a) and Ross Cameron (d) think they can be entities of any category at all, Gideon Rosen (Forthcoming) and Paul Audi () think they are facts, and Kit Fine (a) thinks they are propositions.
Third, there is disagreement about whether grounding holds necessarily or con- tingently; or put differently, whether the grounding facts are necessary or contin- gent. grounding necessitarians include Kelly Trogdon (Forthcominga), Louis deRos- set (), Elijah Chudnoff (MS), and Fabrice Correia (). Contingentists in- clude Joanthan Schaffer (b), Benjamin Schnieder (), and Alexander Skiles
(MSa).
Fourth, there is disagreement about whether grounding is explanatory. Fine
(a) thinks that grounding is “a distinctive kind of metaphysical explanation” (p), and deRosset () and Gonzalo Rodriguez-Pereyra () agree. Audi
() and Schaffer () disagree; at least, they think that a grounding relation is not sufficient for an explanatory relation.
In light of all this disagreement, we might well wonder what they all agree about. The answer is that they agree about some of the cases, and that’s it. They agree that x partly grounds {x}, and that x partly grounds x’s shadow, and a few others. Though even here, they will disagree about the relata; some will say that “x partly grounds
{x}” really means that the fact that x exists partly grounds the fact that {x} exists, and similarly for objects and shadows.
.. The Options
There is not a single principle about grounding that is universally accepted, and there are a host of other disagreements beside. The number and variety of coun- terexamples to the grounding axioms, in addition to the widespread disagreement about the nature and relata of grounding, should leave the reader somewhat unset- tled as to the prospects of affirming a univocal notion of ‘grounds’. So, we have a choice to make.
In this case, it’s not clear what would legitimate denying the counterexamples and being confident in one’s denial. One is supposed to have latched on to grounding through the very sorts of examples that end up undermining one’s belief that it has the formal features it does. Why throw out these putative counterexamples as cases of grounding instead of those at the beginning of the paper by which I introduced the notion of grounding? And given the variety of the counterexamples and the different principles to which they are counterexamples, one can hardly be confident that one’s intuitions are correct. We may be able to deny some of the counterexamples, but not all.
The second option is to deny some of the principles, and retain others. But it is not clear which principles to deny, and which to retain. We arrived at the principles
Compare supervenience, which everyone agrees is reflexive, transitive, and non-symmetric. Or ontological dependence, which everyone agrees is irreflexive and asymmetric and transitive.
through reflection on obvious cases and on the nature of grounding. Once we dis- cover that at least one of the principles is false, we have equal reason to doubt each of them. And it’s not clear, once we learn that our intuitions regarding grounding have led us astray, what legitimates retaining any of the principles ahead of the others.
Another option is to admit that ‘grounds’ is multivocal, and to offer a number of relations it denotes. I will conclude the paper by investigating this option. But a final option is to admit that nothing answers to ‘grounds’; this is the topic of the next section.
. No Work for a Theory of Grounding?
Jessica Wilson (manuscript) has recently argued that there is no such thing as grounding, so a theory of grounding is unnecessary. In light of the argument of the previous section, this may seem like the right conclusion to draw. So, in order to show that treating ‘grounds’ as multivocal is the best option, I shall first argue that there is such a thing as grounding, and that there is work for a theory of grounding.
Wilson’s paper contains two main sections. In the first section, she argues against the sufficiency of grounding—that grounding is not the primitive relation of meta- physical dependence. In the second section, she argues against the necessity of grounding— that grounding is not the unifier of the various “grounding relations”. I agree with
Wilson that grounding is not sufficient for discussing metaphysical dependence, be- cause I think there are a variety of grounding relations, which are species of the genus grounding. So, though I think grounding is insufficient, I think that it’s necessary— that it is the unifier of its species. In this section, I respond to Wilson’s arguments to the contrary.
Hofweber () has also put forth a challenge, but it is amidst other challenges to metaphysics and not nearly as pointed as Wilson’s; also, it has been thoroughly answered by Raven (). So, I shall restrict myself to responding to Wilson.
Wilson claims that we do not need to posit a relation of Grounding (with a capital “G”) because we already have grounding relations (lowercase “g”). Her examples of grounding relations are parthood, identity, and realization (and there are some other candidates). We can do everything with the grounding relations that is supposed to be done by Grounding, and more besides. So, she argues, positing Grounding in an addition to grounding relations is unmotivated.
She goes on to consider four responses to this, responses which attempt to mo- tivate the posit of Grounding in addition to grounding relations. My response is to admit that Grounding doesn’t tell us the whole story of metaphysical structure; we must appeal to other relations. But, those other relations don’t tell the whole story of metaphysical structure, either; we must appeal to Grounding to give a metaphysics.
In addition to identity, realization, and the like, we also need Grounding, to specify the priority relation that accompanies the other relations.
Wilson agrees that what she calls “grounding relations” aren’t always grounding relations. That is, sometimes x and y stand in a “grounding relation”, but x doesn’t ground y and y doesn’t ground x. For example, she thinks parthood is a grounding relation; but when we encounter a situation in which x is a part of y, we are not yet given whether x grounds y or y grounds x or neither. But, Wilson says, we still need not appeal to Grounding. This is because in such a case, either (i) x is fundamental, (ii) y is fundamental, or (iii) neither x nor y is fundamental. If (i) or
(ii) (but presumably not both), then whichever one is fundamental grounds the other.
That is, we don’t learn anything new by saying that x grounds y if we’re given that
Wilson calls this the “crucial appeals” response.
To follow Wilson, I’ll use ‘Grounding’ instead of ‘grounding’, though I’m not sure what the distinction is supposed to be.
For example, Schaffer (c) would think y grounds x, but Skiles (MSb) would think x grounds y.
x is a part of y and x is fundamental. If neither x nor y is fundamental, then their relationship vis a vis Grounding somehow derives from one’s account of what’s fundamental.
It’s not at all clear how this is to go. Suppose I think atoms are fundamental, and
I wonder whether my hand grounds my body or my body grounds my hand. Wil- son says that in such a case I couldn’t think that my hand grounds my body because my hand is not fundamental and thus I can’t treat my hand as a “one” of which the body is the “many”. But this doesn’t follow. Suppose one has a view like Peter van Inwagen (), but instead of thinking that the only things that exist are sim- ples and organisms, she thought that the only fundamental things were simples and organisms. Then she might well think that the simples that compose her body are fundamental, and she is fundamental, and neither her body nor her hand is funda- mental; but her body is more fundamental than her hand because it constitutes her.
This seems like a reasonable view, but if Wilson is right, it’s not. The biggest problem with Wilson’s response is that it assumes that (i) everyone who thinks Grounding is worthwhile has an account of what’s fundamental, and
(ii) Grounding is only worthwhile if there’s a fundamental level. But with respect to (i), someone might well be interested in whether the hand grounds the body or the body grounds the hand without having any commitments with respect to what’s fundamental or in virtue of what something is fundamental. Someone might won- der about the Grounding relations between things without having an account of the fundamental. And theories of Grounding provide a vocabulary (and a relation) for doing so. With respect to (ii), there might be no fundamental level at all.
Lest the reader think that ‘fundamental’ is to be analyzed as ‘ungrounded’, Wilson argues that this is a “negative” conception of fundamentality, and the right conception of fundamentality is most certainly a “positive” one.
See Schaffer (). More generally, if there are gunky worlds and the parts of things are more fundamental than the wholes of which they’re parts, then there’s no fundamental level; if there are junky worlds and wholes are more fundamental than their parts, then there’s no fundamental level.
It’s also important to note that Wilson makes much use of the phrase “grounding relation” when arguing that we don’t need to talk of Grounding. But if “grounding relation” just means ‘a relation that is not Grounding but holds between all and only pairs between which Grounding also holds’, then no progress has been made at all; Wilson can’t merely be replacing ‘Grounding’ with ‘a grounding relation’, or else we’ve made no progress at all. If Wilson’s arguments succeed, then we need to be able to give the structure of reality without using ‘Grounding’ or ‘grounding’ or
‘grounding relation’. We should just be able to make do with ‘part’, ‘identity’, and the like. But it is not at all clear that we can, since even Wilson can’t help but use
‘grounding relation’. A natural thought is that ‘Grounding’ refers to a group of relations, unified in virtue of standing in a certain relation to Grounding; this is what I’ll argue for in the next section. But Wilson rejects this, specifically considering proposals like mine that attempt to unify a number of relations by calling them “grounding relations”. She doesn’t give arguments against such proposals; rather, she attempts to remove the motivation for positing such a unifying relation. She says, “...even granting that the specific relations are unified in any or all of these ways, nothing directly follows about whether or not a distinctive relation should be posited as the metaphysical locus of the commonalities at issue” (p). I agree that nothing follows; but I will give reasons for thinking that grounding is a genus with several species. Even though it doesn’t follow from the fact that those relations are unified that grounding should be posited as the unifier, there are good reasons to think it should be. She also wonders,
“Why suppose that such commonalities support a distinctive, much less primitive, metaphysical posit—Grounding?” But I will give reasons for thinking there is such a posit. She also claims, “Nor do the formal features associated with the specific relations, even in cases where they serve as grounding relations, serve as evidence of real unity.” The unity is not to be found in the formal features, but in the fact that
all of them are Grounding relations. The difference in the formal features is reason to think there is not one single relation, but many; it is not reason to think the many relations are not unified.
So much for my responses to Wilson’s objections. I now turn to three (related) objections to her proposal. First, Wilson does not have the resources to make sense of a debate that seems substantive. Consider the debate between priority monists like Jonathan Schaffer
(c) who think that the Cosmos grounds the existence of everything, and mere- ological universalist priority atomists, who think that the smallest things ground the existence of everything. Both camps agree that atoms, medium-sized objects, and the Cosmos exist. Both camps agree that the atoms are proper parts of the medium- sized objects, and that the atoms and medium-sized objects are proper parts of the
Cosmos. But they differ as to which direction the relation of grounding holds; one side says parts ground wholes, and other that wholes ground parts. If there is no such thing as grounding, only grounding relations, then there is no debate here. But it seems clear to many that there is.
Second, recall that there are some of Wilson’s grounding relations that are some- times Grounding relations but at other times aren’t. That is, sometimes the relations that Wilson calls grounding relations hold between pairs between which Grounding also holds, and sometimes they don’t. More precisely: For most relations R (that
Wilson considers grounding relations), there is some x and y that stand in R such that x grounds y, and there is some a and b that stand in R such that a does not ground b. We must be able to say something further about x and y that we can’t say about a and b; it’s not that they stand in R, since so do a and b. What we want to say is that there is a further relation that holds between x and y that doesn’t hold between a and b—Grounding. For example, sometimes there’s an x and y such that x is a part of y and y grounds x, but sometimes there’s an x and y such that x is a part
of y and y doesn’t ground x. Even if that’s not the case, it’s at least an intelligible position in metaphysics; but if Wilson is right, we cannot even state the view!
Third, there are views that we should be able to state that we cannot state if we are only allowed specific grounding relations and not Grounding. For example, suppose you are a physicalist in the following sense: you think mental properties are grounded in physical properties. You know which options are available to you: type- identity, token-identity, epiphenomenalism. You are considering only these options precisely because you accept the thesis that everything is grounded in the physical.
But you have no idea in which particular grounding relation the physical stands to the mental. Without ‘Grounding’ or ‘a grounding relation’, how can this view be expressed? It’s not that physical properties are fundamental and mental properties are not; you might think there is no fundamental level, or you might think that something else is fundamental and the physical is grounded in it.
So, I think there is work for grounding to do in giving a theory of the way the world is. And if that right, then there’s work to do in giving a theory of what ground- ing is.
. Grounding as Genus
We can say a lot of interesting things and improve the status of a lot of debates in metaphysics by characterizing them in terms of grounding, so we shouldn’t eliminate it from metaphysics. But we clearly don’t understand grounding very well. Ground- ing takes a variety of relata, and there are reasons to think that the relation lacks the formal features presented in the first section. One way to make sense of this is to think of grounding as a genus, which admits of several species.
Wilson thinks that identity is a grounding relation, and the above example would be even more persuasive using identity. But I imagine a lot of people would not think identity is a grounding relation, and simply denying that a relevant relation is a grounding relation is not an adequate response to the objection I’m trying to push.
A rough characterization: F is a species of G just in the case that everything that is a member of F is a member of G and not everything that is a member of G is a member of F . Of course, this will have to be tweaked—it might be that everything that is red is square, but there are also blue squares; in such a case, the definition would have it that red is a species of square, which we don’t want to say. And this definition also has it that being red and square is a species of being red and being a donkey. One might construe the conditional as entailment—F is a species of G just in the case that necessarily, everything that has F has G and not everything that has G has F —but this won’t do either. On this construal, bachelorhood turns out to be a species of rationality; nobody wants that. We can add some non-logical vocabulary to the entailment to state the conditions on the genus-species relationshipThe two important ones are that genera are not maximally specific, whereas species are, and that having a species entails having a genus under which that species falls. A species is a specific way of having a genus. In order to understand what it would mean to think of grounding as a genus, it’s useful to look at a classic example of a genus: animal. Humanity is a species of animal; so being human is a specific way of being an animal, and anything that is human is an animal. Womanhood is a species of humanity and a species of animal; so being a woman is a specific way of being human and also a specific way of being an animal. (So, something can be a species of two different genera.)
The usual way of explaining species is that they are genera plus differentia. To characterize a species, one gives the genus that it falls under and a characteristic that distinguishes it from the other species that fall under that genus. To give the essence of a living thing, you state its genus and differentia. One can do that here as well. The essence of truthmaking is that it’s the grounding of a thing’s truth in an object.
The essence of metaphysical explanation is that it’s the grounding of a thing’s truth
Thanks to Mike Rea for this point.
in other, usually more fundamental, truths. The essence of ontological dependence is that it’s the grounding of a thing’s existence in another thing’s existence. The essence of reductive analysis is that it’s the grounding of some facts about a thing or kind of thing in some facts about some other (standardly thought to be more fundamental) thing or kind of thing. I think grounding is a genus. I suggest that the following are species of the relation of grounding.
.. Ontological Dependence
This is a notion that Kathrin Koslicki (MS) and (Forthcoming), EJ Lowe (), Kit Fine (), and Fabrice Correia () are talking about. It holds between two objects, like a singleton and its member (the set ontologically depends on the mem- ber), a hole and its host (the hole ontologically depends on the host), a whole and its parts (there is dispute over which direction the ontological dependence goes in this case). It also holds between a fist and a hand, a smile and a mouth, and other such pairs. It is when something depends for its very existence on something else, or when something depends for its very essence on something else. It is nonreflex- ive, nonsymmetric, and transitive. And it seems that N is false of ontological dependence. Some of the standard paradigm cases of grounding are cases of ontological de- pendence: a set is grounded in its members, a hole is grounded in its host, a whole is grounded in its parts, and the like. Ontological dependence relates things to more fundamental things, just like grounding. If there are any species of grounding, on- tological dependence is one of them. And it cannot be that grounding is a species of ontological dependence, because grounding can hold between things that don’t ontologically depend on each other (e.g., the fact that I am a philosopher and the
See the cited papers for explications of these phrases.
fact that there are philosophers).
.. Truthmaking
Truthmaking holds between a truth-bearer (sentence, proposition, etc.) and a thing (the kind of thing is up for debate). It holds when the truth-bearer is true in virtue of the thing, or when the truth-bearer is true because the thing exists and is the way it is.
Truthmaking is nonreflexive, nonsymmetric, and nontransitive. Why is it not ir- reflexive? Well, there might be propositions like [this proposition is about itself], in which the proposition is the truthmaker for itself. It is nonsymmetric rather than asymmetric because there might be pairs of propositions like [The proposition ex- pressed by the sentence appearing after this sentence is about this sentence] and [The proposition expressed by the sentence appearing before this sentence is about this sentence]. It is at least non-transitive, because in most cases the thing doing the truthmaking is not a proposition; for example, Barney the blue fish might make true the proposition [some fish are blue], and [some fish are blue] might make true [There are propositions about fish], but Barney the blue fish doesn’t make true [There are propositions about fish]. However, it seems truthmaking is not intransitive, because in cases in which the thing doing the truthmaking is a proposition, I see no reason why it can’t be the case that a makes b true, b makes c true, and a makes c true. As in [Barney is a blue fish] makes true [There are propositions about blue fish], which in turn makes true [there are propositions]; and [Barney is a blue fish] makes true [There are propositions]. (After all, things can have multiple truthmakers.) So, truthmaking is not intransitive, but neither is it transitive. One might think that the first couple of cases are impossible, in which case one could (but wouldn’t have to) think that truthmaking is irreflexive, asymmetric, and non-transitive. Additionally, it seems that N- is false when the
relation of grounding in question is truthmaking. It used to be thought that truthmaking ought to be understood using a superve- nience principle: x makes p true just in the case that necessarily, if x exists, then p is true. That is inadequate, because on it everything makes necessarily true propo- sitions true, and impossible things make everything true. Lately some philosophers have proposed understanding truthmaking in terms of grounding. This is some reason to think truthmaking is a species of grounding. Another is that grounding or dependence language is often used in giving informal statements of the intuition behind truthmaking: “truth depends on the world”, “truth is grounded in being”,
“what there is grounds what’s true”, and the like.
.. Reductive Analysis
A standard attempt at a reductive analysis is reductive physicalism, which is often put thus: mental events just are physical events. It is standard to interpret just are as an identity claim: ‘x just is y’ =df. x = y. But that analysis doesn’t seem to capture the asymmetry and dependence that reductive physicalists really want. It’s not merely that every mental event is identical to a physical event. Without notions of grounding or dependence, we can’t put the thesis any stronger than something extensional. But reductive physicalists want an asymmetry; physical events are more fundamental than mental events. Reductive analysis, then, is asymmetric, as well as irreflexive. But it is not transitive. And F is false of reductive analysis.
We can give some more examples of reductive analysis: what it is to be a bachelor is to be an unmarried male, what it is to be grue is to be green and examined before time t or blue and not examined before t, what it is for my fist to exist is for my fingers to be curled into my palm, mental properties just are physical properties,
See Cameron () and Schaffer (). If grounding is the relation that answers to the “in virtue of” locution, then this is also the view in Cameron (Forthcoming).
squares just are equilateral rectangles, water just is H2O, the property being morally wrong just is the property being generally disapproved of, and so on. There is debate over what reductive analyses are, and I shan’t enter too far into it. Suffice it to say that these are not merely claims about language use or conceptual analysis; they are metaphysically interesting claims about properties and objects and natural kinds. There are two reasons to think that reductive analysis is a species of grounding.
The first is reflection on cases. Many of the standard cases of reductive analysis are taken to be cases of grounding. For example, “mental events just are physical events” and “mental events are grounded in physical events”; “modal facts are reducible to actual facts” and “modal facts are grounded in actual facts”; “tensed truths are reducible to tenseless truths” and “tensed facts are grounded in tenseless facts”. And so on.
The second is by reflection on what one is doing when one gives a reductive analy- sis. One is saying that some particular thing or kind of thing A is to be understood in terms of some other thing or kind of thing B. It would be odd, in such a case, if one thought that B is less fundamental than A, even though A ought to be reduced to B.
Why would we reduce something that’s more fundamental to something that’s less fundamental? However, one might think that A is reducible to B even though A and
B are equally fundamental. Of course, one might think the same thing in the case of grounding; it might be that A grounds B, and A and B are equally fundamental. As long as one thinks that reductive analysis and grounding both have the same profile with respect to the relative fundamentality of the relata, it seems natural to think of reductive analysis as a species of grounding.
.. Metaphysical Explanation
Metaphysical explanation holds between two propositions, or two facts, or a proposition and a fact. The intuitive thought behind metaphysical explanation is
that x metaphysically explains y only if y is not reducible to x, but y because (in the non-causal sense of ‘because’) x. That is, either y is true because x is true, or y obtains because x obtains, or y is true because x obtains, or y obtains because x is true. So, a candidate metaphysical explanation for [This ball is red] is [This ball stands in the instantiation relation to the Platonic universal redness]. A candidate metaphysical explanation for [Jeremy played soccer as a child] is [Jeremy has past temporal parts some of which are playing soccer]. [This ball stands in the instantiation relation to the Platonic universal redness] and [Jeremy has past temporal parts some of which are playing soccer] likely admit of further metaphysical explanation. Metaphysical explanation is different than reductive analysis in that when one reductively analyzes x as y, one purports to say everything captured in x by saying y, but by using more fundamental terms.
So, we can say that x metaphysically explains y just in the case that (i) x does not cause y, (ii) y is not reducible to x, and (iii) y because x. What of the formal features of metaphysical explanation? If nothing can non-causally explain itself, then metaphysical explanation is irreflexive. But it is not obvious that that is the case. The big bang might non-causally explain itself; it certainly seems like nothing else can explain it, since nothing else was around to. However, perhaps it’s unexplained. If one thinks that everything has a metaphysical explanation explained, then one either ought to think explanations go on infinitely, or that some things explain themselves.
If some things explain themselves, metaphysical explanation is not irreflexive. As to transitivity, it again seems that the counterexamples above tell against metaphysical explanation being transitive. Anyone who has an inkling that the counterexamples might be true ought to postpone judgment on whether metaphysical explanation is transitive.
Metaphysical explanation is likely the relation of grounding one has in mind
I take it that this is the kind of grounding Dasgupta (MS) has in mind.
when one thinks of ∃-G, and when one claims that knowledge is partly grounded in truth. It is not clear whether N is true of metaphys- ical explanation; it depends on whether one thinks explanations must be entailing.
One can see why it’s important to distinguish between metaphysical explanation and reductive analysis: they hold between the same sorts of entities, and they both have a claim to be what we mean when we say ‘x because y’, or ‘x grounds y’. But they have different features, formal and otherwise. The failure to distinguish between the two may very well be the cause of warring intuitions about certain putative cases of grounding.
One reason to think that metaphysical explanation is a species of grounding is that it links less fundamental truths with more fundamental truths, just as grounding links the less fundamental with the more fundamental. Another reason to think that metaphysical explanation is a species of grounding is that ∃-G is most plausible when thinking of grounding as metaphysical explanation.
. Is Grounding a Genus?
Grounding might have more species than mentioned above. For example, some want to say that the fact that I have two legs partly grounds the fact that I can walk, but it’s not clear that this kind of grounding is one of the four listed above. There is room to further explore the potential species of grounding, and what principles might be true of them. We’ll have found them when everything that’s grounded stands in one of them, the way to ground or be grounded is to stand in one of them, and they bear a great deal of similarity to each other. They might also have their own species.
The first reason to think that grounding is a genus is that it explains the widespread
On the latter, see Whitcomb ().
Perhaps metaphysical explanation?
disagreement about the axioms, principles, and counterexamples concerning ground- ing; that is, it explains why principles that some grounding theorists think are partly constitutive of grounding are denied by other grounding theorists. If there are multi- ple distinct relations on to which we are latching when we hear ‘grounds’, this is not surprising. Someone is thinking about one of them, while others are thinking about different ones. The relations are importantly unified, but lack a single set of formal features.
Second, thinking of grounding as a genus allows us to explain the tight concep- tual connection between ontological dependence, truthmaking, metaphysical expla- nation, and reductive analysis. We want to say that they are related, since they are all “in virtue of” locutions, or they are all non-causal explanations, or the like. Various people have argued that we should understand ‘grounds’ in terms of each of these notions. And people freely substitute ‘grounds’ or ‘is grounded by’ for ‘makes true’,
‘ontologically depends on’, ‘metaphysically explains’, and ‘is a reductive analysis of’. Thinking of grounding as a genus makes sense of this tendency. We can say that the properties in question fall under the same genus, and that explains why we think that they have something in common and substitute ‘grounds’ for each of them. And since we don’t freely substitute ‘ontologically depends on’ for ‘is made true by’, or ‘makes true’ for ‘is a reductive analysis of’, or in fact any species of grounding for any other, ‘grounds’ is the best candidate for a genus. Ontologically depending on something, being reductively analyzed as something, being made true, and being metaphysically explained by something are all ways of being grounded.
Third, we speak of grounding as though it can take as relata a wide variety of things. It can hold between two objects, an object and a trope, an object and an absence, a proposition and an object, a proposition and an object in a different way, two propositions, two facts, a fact and an object, a fact and a proposition. However, there is substantial disagreement over the truth of the claims in the last two sentences;
some people think that grounding holds only between facts, some thinks it holds only between propositions, and some think it holds only between objects. The proponent of grounding as genus can explain this: they have latched on to one of the genera of grounding and are calling it ‘grounding’.
Fourth, thinking of grounding as a genus is the best way to respond to the pur- ported counterexamples. The other responses are costly, and this response allows us to respect the counterexamples and the intuitions about the principles.
Finally, it might be that some of these relations are genera which admit of fur- ther determination. Perhaps ontological dependence is a genus of which existential dependence and essential dependence are species. Perhaps reductive analysis or metaphysical explanation are genera. Perhaps there are different ways of truthmak- ing that are species of truthmaking. Thinking of grounding as a genus opens the door to thinking of these other relations as genera as well.
Recognizing grounding as a genus does not mean we should eliminate grounding, any more than we should eliminate being an animal. Often we can recognize that a relation of grounding holds before we can properly categorize which type of ground- ing it is; so there is still work for grounding, and work for ‘grounds’. Furthermore, we can make interesting claims about grounding. For example, “everything either grounds something or is grounded”. I think we can make sense of this, and more than that—it will probably strike many people as plausible, much like, “anything that’s extended is colored.” There is still a use for grounding; but once we recognize a case of grounding, the work is not over. We must figure out which species of grounding holds in the particular case.
Koslicki () argues for this. And there may be more species of ontological dependence, and existential and essential dependence might themselves admit of species.
On ways of truthmaking, see Barnes (Forthcoming).
This, at least, Wilson will be happy to hear from a proponent of grounding.
. Conclusion
‘Grounds’ is either univocal, multivocal, or doesn’t refer to anything. Grounding is either one relation, many relations, or there is no such relation. A univocalist about
‘grounds’ thinks that the word has one sense in metaphysics, and means the same thing across contexts (not including the sense of the stuff under our feet). A multi- vocalist about ‘grounds’ thinks that there are many senses of the term ‘grounds’, and that at various times it’s used in different ways. A pluralist about grounding thinks there a multitude of different relations that answer to the concept. A monist about grounding thinks that there’s a distinguished relation that answers to the concept of grounding. There are two ways to be a monist. Some monists think that there is only one relation answering to the concept of grounding, while others think there are many relations, all explicable in terms of—or reducible to—one central notion.
The best attempt to figure out a univocal notion of grounding is Kit Fine’s; but it fails, because there are devastating counter-examples to multiple axioms. This might lead us to think that there’s no such thing as grounding. The best attempt to argue for such a conclusion is Jessica Wilson’s. But her arguments fail. In this paper, I’ve offered a middle way—being a monist about grounding while treating
‘grounds’ as multivocal. I suggested that we should think of grounding as a genus which admits of several species (which might themselves be genera that admit of species). In addition to being the best response to the counter-examples, thinking of grounding as a genus has other positive features as well. Grounding is an important concept for giving a theory of the metaphysical structure of the world, theories of grounding are worthwhile, and the theory of grounding given here is the one best supported by our reflections on cases of grounding.
CHAPTER
TRUTHMAKERS AND ONTOLOGICAL COMMITMENT
Truthmaker views, let us say, are views that posit a close relationship between truthmakers and ontological commitment. I hold a truthmaker view; on the truth- maker view I favor, when one affirms a sentence, one is ontologically committed to there being something (or some things) that makes (or make) true the sentence; I call this the ‘general truthmaker view’. The truthmaker view I don’t like is the view that when one affirms a sentence, one is ontologically committed to whatever hap- pens to make true the sentence; I call this the ‘specific truthmaker view’. I begin the paper by giving a characterization of ontological commitment. I then develop the general truthmaker view of ontological commitment and argue that it has significant advantages over its Quinean rival. I conclude by arguing that it also has significant advantages over other truthmaker views. On the general truthmaker view, our ontological commitments are not particu- lar, nor are they perspicuously determined. Rather, by affirming sentences, we just
Though I’ll speak in terms of sentences being the bearers of truth and falsity, one can freely substitute whatever she takes to be the bearers of truth and falsity.
I think that all true sentences have truthmakers, which earns me the label ‘truthmaker maxi- malist’. But there are those who think that some true sentences have truthmakers, and other true sentences do not—negative existentials, perhaps. There is a danger for such people in accepting the general truthmaker theory. They would want to modify it in some way like the following: “If one affirms a sentence, then if the sentence has a truthmaker, one is ontologically committed to there being something or some things that makes or make it true”. This is problematic, not in the least because one doesn’t occur any ontological commitments by uttering false sentences. I cannot think of an obviously unobjectionable modification.
Much more on other truthmaker views in §.
ontologically commit to there being some things or other that make them true. One thought behind this is that there are entities in the world such that their existence and the way they are makes true all (or most) true sentences; these things we call ‘truth- makers’. Those who think that there are truthmakers have sought to formulate a precise statement of the necessary and sufficient conditions for being one of them; this has proved to be difficult. Three main candidates have emerged. The first says that a is the truthmaker for p if and only if any world in which a exists is a world in which p is true. The second says that a is a truthmaker for p if and only if for any two worlds, if those worlds differ with respect to the truth-value of p, then they differ with respect to what a is or how a is. The third says that a is a truthmaker for p if and only if p’s truth is grounded in what a is and how a is.
There are problems for each of these formulations. In this paper, I won’t endorse or assume a specific version of the truthmaker principle. I shall limit my discussion to the general truthmaker view. It might seem illegitimate to discuss a thesis all of whose terms I can’t define. But while I won’t formulate the truthmaker principle precisely, I do have an intuitive understanding of it, as do many others. This suffices
I speak of people incurring ontological commitments (rather than theories or propositions or sentences or what have you), and I shall speak of them doing so by affirming sentences (rather than believing propositions or assenting to sentences or what have you). I do not mean this to be taken too literally. The reader can feel free to substitute other things that incur ontological commitments, and other ways of incurring them.
I add the “or most” qualifier because many people who hold to a truthmaker principle are not truthmaker maximalists.
See Bigelow (), Armstrong (). Armstrong (, p) adds ‘and p is true in virtue of a’. Because they accept this formulation, they are forced to say that the truthmaker(s) for p exist in all and only the worlds in which p is true—this is known as “truthmaker necessitarianism”. Truthmaker necessitarians usually posit facts or concrete states of affairs as truthmakers.
See Lewis () and Bricker ().
See Schaffer (b) and Schaffer ().
For an overview of truthmaker principles, see Beebee and Dodd (). For formulations of truth- maker principles, see Armstrong (), Schaffer (), Cameron (a), and Cameron (Forth- comingb). For arguments against, see Merricks (), Cox (), and Simons ().
in other areas of philosophy: people endorse the knowledge norm of assertion with- out being able to define ‘knowledge’, they endorse the total evidence requirement without knowing exactly what evidence is, and they endorse endurantism without knowing exactly what whole presence is. My discussion of the truthmaker views is similar; I believe there’s something that we’re latching onto when we think about truthmaking, despite not being able to say precisely what it is. And I suggest that we think of truthmaking as closely related to ontological commitment.
. The Ontological Question
Ontology is often characterized as an attempt to answer a question—“the onto- logical question”. Because there is no agreed-upon ontological question, and each ontologist is attempting to answer that which she considers the ontological question, ontologists are not all doing the same thing. Some are in the business of saying what there is, or what kinds of things there are. Some are trying to give an account of the structure of reality. Some are trying to tell the deep story of the world. What an ontologist thinks the ontological question ought to be will determine what she’s up to when she does ontology.
Quine () thought the ontological question was, “What is there?” So Quine was in the business of saying what things there are. He didn’t do so by listing them all, but by figuring out the predicates of our best theories. The extensions of those predicates are sets, and the members of those sets are the things there are. Recently,
Schaffer (a) has argued that the ontological question is “What grounds what?” So Schaffer is trying to say what things are the grounds, and what things those things
See Quine () and its many ancestors.
See Sider ().
See Heil ().
ground. Fine () argues that the ontological question is “What is real?” So he is trying to list the things that are real; there are, according to him, fewer real things than things there are. (Sider, , p viii) thinks “the goal of metaphysics is to give a fundamental description of the world”; this suggests that for him the ontological question is, “What things show up in the fundamental description of the world?” I disagree with Quine’s characterization of the ontological question. It is far too easy to come up with examples of things that there are, but which many ontologists deny populate their ontologies (or, to which to which they deny being ontologically committed): unicorns, fictional detectives, ways to skin a cat, paths to victory, and the like. It is only because they have thought “What is there?” is the ontological question that some philosophers have denied such obvious claims as “I have a com- puter” (since it is equivalent to “there is an x such that x is a computer and I have x”) and “This desk on which I am now writing is made of wood” (since it equivalent to “there is an x such that x is a desk and I am now writing on x and x is made of wood”), and “unicorns are fictional characters with horns” (since it is equivalent to “there is an x such that x is a unicorn and x is a fictional character and x has a horn”). They don’t want to populate their ontologies with such things, and they think that by saying there are such things they thereby populate their ontologies with them, so they deny there are such things. I also disagree with Schaffer’s characterization of the ontological question, be- cause I don’t think it is interesting to figure out what things are grounded. It is a far more interesting question to figure out what the grounds are. Everything else is grounded. I suggest the interesting ontological question in the vicinity is “What are the grounds for everything else?” Because the grounds are the fundamental things, the most natural way of asking this is, “What is fundamental?” This is what I take to be the ontological question. And I shall argue that the fundamental things are the truthmakers for our ordinary assertions. One way of figuring out the answer to
the ontological question is figuring out what things are fundamental. These things will be the truthmakers for all our ordinary sentences. So the easiest way of figur- ing out which things those are is figuring out what the truthmakers for our ordinary sentences are. This is what ontologists should be up to.
I also disagree with Fine’s characterization of the ontological question, though I think there are similarities between his question and mine. He thinks that someone can sensibly think that (i) there are tables, (ii) tables exist, and (iii) tables aren’t real.
This sounds odd, but I accept something similar. I think one can accept that (i) there are tables, (ii) tables exist, and (iii) tables aren’t fundamental. If Fine means by ‘real’ what I mean by ‘fundamental’, then Fine and I agree, and our dispute is merely ter- minological. But we don’t, and it isn’t. Fine also speaks in terms of fundamentality, and he denies that something is fundamental just in the case that it’s real.
However, Fine and I both think one doesn’t do ontology by figuring out what’s in the domain of the English existential quantifier. Fine thinks we should figure out to what things the predicate ‘is real’ applies; those are the things to which we are ontologically committed. I also think we should figure out to what things a certain predicate applies; in my case, it’s ‘is fundamental’. And the role that being real plays in the rest of Fine’s metaphysics is very different from the role that being fundamental plays in mine. I further supplement my view by saying that the fundamental things are the truthmakers for all truths, and the grounds for the existence of everything else, and they are the substances (which are simple), and they are the things in the domain of the fundamental quantifier. Fine says that the real things are such that
He says, “Just as we cannot read off what is real from what is basic, so we cannot read off what is nonreal from what is nonbasic. Indeed, it is possible to imagine metaphysical scenarios in which the nonbasic, or grounded, is plausibly taken to be real” (Fine, , p). And he thinks the ungrounded things are fundamental.
Fine also agrees that a quantifier can be defined in terms of the predicate. But he thinks of that as merely a logical nicety and “irrelevant to the understanding of ontology” (Fine, , p), whereas on my proposal it turns out to be important, especially in Chapter .
it is constitutive of reality that they are the way that they are, I do not think this is helpful, and it leaves too much of a picture yet to be painted. So while I agree with the spirit of Fine’s proposal, I think there is much more that can be said.
I agree with Sider’s characterization of the ontological question to the extent that
I think the answers to our ontological questions are the same. I think that the things that show up in the fundamental description of the world are the fundamental things, and these things are the truthmakers for our ordinary assertions. But Sider under- stands (what I’ve called) his formulation of the ontological question to be reducible to questions about metaphysical structure, and I do not. If anything, “What things show up in the fundamental description of the world?” is reducible to “What things are fundamental?” And, as I said, this is what I take to be the ontological question.
For the rest of this paper, I shall take it for granted that it is at least an open question whether “What is there?” is the ontological question, or whether some other question deserves (or should deserve) that distinction. This implies that “the ontological question” doesn’t mean “the question of what there is”. On my view, the ontological question is, or at least ought to be, “what is fundamental?”
. Ontological Commitment
It’s standardly thought that one’s ontology is one’s answer to the ontological question—whatever one takes that question to be. So, since Quine thought the on- tological question is, “What is there?”, Quine’s ontology is the things he thought there are. Since Schaffer thinks the ontological question is, “What grounds what?”, Schaffer’s ontology is what he thinks the grounds are and what he thinks is grounded.
Since Fine thinks the ontological question is, “What is real?”, Fine’s ontology is what he takes to be real. And so on. So, where one takes the ontological question to be a
Which I take to will have the same answer as “What are the ultimate grounds?”, “What are the truthmakers?”, and “What exists, in the fundamental sense of ‘exists’?”
substitution instance of “What satisfies O?”, one’s ontology is the thing(s) one takes to satisfy what she substitutes for O.
One’s ontological commitments are generally thought to be broader than just one’s ontology. One’s ontological commitments are one’s ontology (which we might call “explicit ontological commitments”), plus some more things—what we might call one’s “implicit ontological commitments”. But to which things are our implicit ontological commitments? One thought is that S’s implicit ontological commitments are the things that S’s answer to the ontological question entails satisfy what one sub- stitutes for O. That is, where S substitutes “P ” for O and thus takes the ontological question to be, “What satisfies P ?” and S answers the ontological question with “F s and Gs satisfy P ”, then S is explicitly ontologically committed to F s and Gs, and S is implicitly ontologically committed to any Hs such that it is impossible that
F s and Gs satisfy P and Hs not satisfy P .
But this characterization of implicit ontological commitment will not do. If the classical theist is right, then God is a necessary being and the ultimate ground of everything and has more reality than anything else. So if the classical theist is right, it is necessary that God satisfies what Quine and Schaffer and Fine substitute for O.
But if ontological commitments are what the above paragraph says and the classical theist is right, then Quine and Schaffer and Fine are ontologically committed to God. But Quine and Schaffer and Fine are not ontologically committed to God. So explicit ontological commitment must be something else.
A better answer, I think, is that one’s implicit ontological commitments are to the things that her answer to the ontological question obviously entails satisfy what she substitutes for O. Quine, Schaffer, and Fine would disagree that their answers to
Generally this would be thought of as a predicate; but many people think the ontological question is, “What exists?”, and many think that ‘exists’ isn’t a predicate.
Obviously it’s tricky to spell out what it means for an entailment to be “obvious”, but I trust the notion is familiar enough and close enough to accurate to be helpful.
their ontological questions entail that God satisfies what they substitute for O. And it is not obvious that they are wrong. So, they are not ontologically committed to God.
But we do want to say that they are committed to any things (‘the F s’) such that it is obvious that it is impossible that the things they take to satisfy their substitutions of
O do satisfy O and yet the F s don’t satisfy O. This is the understanding of ontological commitment with which I’ll operate in this paper.
So, then, as far as ontological commitment goes, I agree with both Schaffer and
Quine that the existential quantifiers express existence, and that what one thinks ex- ists can therefore be read off of one’s literal, serious quantificational claims. I agree with Schaffer and Fine that figuring out what one quantifies over isn’t an interest- ing question for an ontologist to answer. This is because existents, qua existents, don’t do any interesting work in ontology. What does the interesting work is the fundamentalia; they ground the existence of all the other existents (which Fine and
Schaffer would also say) and they make true whatever sentences are true (which nei- ther Fine nor Schaffer would say). Ontological commitments are to the things with which you answer the ontological question, whatever you take it to be. Since I take the ontological question to be “What are the truthmakers for our sentences?”, I hold a truthmaker view of ontological commitment. On my view, ontological commit- ment does not have to do with what there is, or what we quantify over. Rather, it has to do with what is fundamental. And the way to figure out what is fundamental is to figure out the truthmakers for our assertions.
Quine’s characterization of the ontological question and ontological commitment is metaphysical orthodoxy. The general truthmaker view is a foe of the Quinean view, which tells us that our ontological commitments are to the things that the ordinary English sentences we accept (in our most reflective and philosophical moods as being strictly and literally true) say exist. And the things that our sentences
I speak throughout the paper of English sentences and quantifiers and the like. The point gener-
say exist are the values of the variables in the scope of the existential quantifiers occurring in the translations of our sentences into first-order logic. The proponent of a truthmaker view (hereafter ‘a truthmaker theorist’) responds that some ordinary
English sentences that we accept in our most reflective and philosophical moods as being strictly and literally true might say “F s exist”, and yet we are not ontologically committed to F s. That is, we might think F s exist, and quantify over F s, yet not be ontologically committed to F s.
One might respond, “But to ‘ontologically commit’ to something just means to say that it exists.” The truthmaker theorist responds in the voice of Cameron:
It’s true that ‘ontological commitment’ is a technical term, and there are a bunch of claims we associate with it: the ontological commitments of a theory are what must exist if it is true; the ontological commitments of a theory are what counts against it when judging it for ontological par- simony; the ontological commitments of a theory are those things whose existence its truth entails that have real being. For the Quinean, of course, these don’t come apart; but if we think they do come apart, we must make a decision about how to use the term ‘ontological commitment’. I think they come apart: what has real being - what there really is - is what makes the true theory of the world true. (, p)
Quine thought it was “obvious and trivial” that we are ontologically commit- ted to the values of the bound variables of the translations of our theories into
first-order logic. But ontological commitment does have the other associations Cameron claims, and thus an argument is required to show that quantification— being the value of a variable—has all of them as well. Given the above discussion of ‘ontological commitment’, it is at least not an analytic truth that a person’s onto- logical commitments are the things over which she quantifies when her sentences are translated into first-order logic. After all, it’s become a matter of debate of late as to what the ontological question is; it’s not an analytic truth that Quine is right and alizes, of course, to French and German and all other non-fundamental languages.
See Quine (, p-).
Schaffer and Fine and Sider are wrong. Introducing some new terminology will help make this idea clearer. Let us say that S is existentially committed to F s just in the case that an F is the value of a bound variable of the most logically perspicuous statement of one of S’s beliefs. Let us say that S is metaphysically committed to F s just in the case an F makes true the most logically perspicuous statement of at least one of S’s beliefs. I take it the following is an open question: are S’s ontological commitments co-extenseive with her existential commitments, her metaphysical commitments, or neither?
If an opponent thinks that this is not an open question, I am happy to give up the term ‘ontological commitment’ and conduct the rest of the paper in terms of ‘meta- physical commitment’. But in that case, I’ll think that metaphysical commitments are more important than ontological commitments—a person’s metaphysical com- mitments are the things that must exist if her sentences are to be true, a person’s meta- physical commitments are the things that make true her sentences, a person’s meta- physical commitments are to the fundamental things in virtue of which the things she says exist exist, a theory’s metaphysical commitments are what must be taken into account when deciding whether to accept or reject the theory, and a theory’s meta- physical commitments are what count against it when thinking about parsimony. On this construal, ontological commitments are just what things one quantifies over; but given that such things don’t play any other role in a metaphysical theory (at least, not simply in virtue of being quantified over), ontological commitment is not important.
Surely there must be some room here for disagreement. I originally sought to sever the link between ontological commitment and quantification; if one insists that that link is analytic, then I shall sever the one between ontological commitment and theory judgment. In other words, I assume that not all of the following can be analytic truths:
. If S quantifies over F s, then S thinks F s exists.
. If S thinks F s exists, then S is ontologically committed to F s.
. If S is ontologically committed to F s, then (i) F s must exist for S’s sentences to be true, (ii) S’s theory must be judged for parsimony on the basis of F s, and (iii) F s must make true the sentences of S’s theory.
. Therefore: if S quantifies over F s, then (i) F s must exist for S’s sentences to be true, (ii) S’s theory must be judged for parsimony on the basis of F s, and (iii) F s must make true the sentences of S’s theory. (,,, modus ponens)
The truthmaker theorist denies (), so she must deny either (), (), or (). I sought to deny (), but if one were to maintain that () is an analytic truth, I would deny (). Then I would introduce the term ‘metaphysical commitment’ as above. I would deny this conditional: if S says that F s exist, S is metaphysically committed to F s, and I would say that () is true when ‘metaphysical commitment’ replaces ‘on- tological commitment’ in the antecedent. And given the general truthmaker view of metaphysical commitment, when one utters a sentence, one is metaphysically com- mitted to there being an x such that that x makes that sentence true.
For the rest of the paper I’ll assume that the link between quantification and ontological commitment is not analytic, and that there is room to disagree about whether a theory is ontologically committed to the things over which it quantifies, and that I am objecting to (). But those who think I’m objecting to an analytic truth may substitute “metaphysical commitments” for “ontological commitments” in the remainder of the paper and classify me as objecting to ().
. Two Ways of Understanding Truthmaker Views
The truthmaker theorist says that one can affirm “statues exist” without being ontologically committed to statues. There are (at least) two ways to justify this. The
Where ‘S quantifies over F s’ means that S accepts (in her most reflective and philosophical moods) a sentence that quantifies over F s as being strictly and literally true.
best way of bringing out the distinction between the two is to look at the following argument against truthmaker views:
. If S affirms “statues exist”, then S believes that statues exist.
. If S believes that statues exist, then S is ontologically committed to statues.
. Therefore, if S affirms “statues exist”, then S is ontologically committed to stat- ues. (from ,)
The truthmaker theorist wants to deny (), since she thinks our ontological com- mitments are to there being truthmakers for “statues exist”, and the truthmakers might not be statues. Since the above argument is clearly valid, the truthmaker the- orist must deny () or (). In this section, I shall discuss each of these options.
.. Denying ()
One way of understanding truthmaker views is as a claim about the relationship between sentences—ones that seemingly express the existence of a thing—and the existence of a thing. One could put this in different ways. One way would be to say that the disquotational principle—if a subject S assents to “p”, then S believes that p—fails, either in general or just in the case of sentences that ascribe existence to something. There are well-known problems with the disquotational principle, so it might not be so bad if the truthmaker theorist has to deny it. But I do not think truthmaker views should rise or fall with the truth of the disquotational principle.
And a better argument can be run a bit differently.
One could also accept the disquotational principle above but reject a closely re- lated principle: For any sentence S, if ⌜S⌝ is true, then ⌜S⌝. This is one direction
The principle was named by Kripke in his (), and he poses the most famous problem for it as well; namely, that a person might believe “Londres est jolie” and “London is not pretty”, and therefore that London is pretty and that London is not pretty.
of the Tarskian biconditional (⌜S⌝ is true iff ⌜S⌝). One might think that if one affirms “statues exist”, then one believes that “statues exist” is true (accepting the disquotational principle), but deny that “statues exist” is true if and only if if statues exist.
Denying the T-schema has some appeal for the truthmaker theorist inasmuch as it allows her to deny (), which is a premise in an argument against a truthmaker view of ontological commitment. And she might independently motivate the denial of the T-schema by pointing to the liar paradox (is “this sentence is not true” true?) and suggesting that we need to re-interpret our understanding of truth-conditions anyway. This is an interesting avenue, but I will not pursue it for two reasons. First, I do not think that the truthmaker view rises or falls with the truth of the T-schema.
Second, I think there is a better response to the argument—deny ().
.. Denying ()
On my view, the truthmaker theorist ought to deny (): if S believes that statues exist, then S is ontologically committed to statues. She should think that existence claims come apart from ontological commitments, rather than thinking that seeming existence claims aren’t in fact existence claims. The best way to deny () is to think that we are only ontologically committed to the fundamental, and that all and only the truthmakers are fundamental. Talk of fundamentality, fundamental things, and fundamental language (or lan- guages) has taken center stage in metaphysics in recent years. A number of meta- physicians have defended the view that what matters in ontology is not the question of what exists, but rather the question of what is fundamental. For some, the
Quine () famously used “‘S’ is true if and only if S” as a “theory” of truth, but one needn’t do so to endorse the T-schema—neither the conditional nor the biconditional tell us what truth is.
See, e.g., Schaffer (a). Fine () says we should investigate the question of what really exists.
answer to the question is mereological simples. For others, it’s the world. No- body says that tables are fundamental, but all agree that they exist. The truthmaker theorist thinks that there are many things that our English sentences say exist, but these things aren’t the truthmakers for those sentences. Rather, some other things makes those sentences true, and those things—the truthmakers—are the fundamen- tal things, in virtue of which true English sentences are true; this is the version of the truthmaker view that I accept.
We can introduce a quantifier that ranges over all and only the truthmakers. Since
I take it that the fundamental things are the truthmakers, I shall call the quantifier
that ranges over them ‘the fundamental quantifier’. I shall use ‘∃F ’ for the funda-
mental existential quantifier, and ‘∃E’ for the English existential quantifier. The truthmaker theorist thinks that what is fundamental are the truthmakers. So, ∃F has in its domain all and only the truthmakers of true English sentences. Since all and only the truthmakers existF and in order to be ontologically committed to something one must think it existsF , we can use ∃F as the quantifier of ontological commitment.
See Cameron (b), Cameron (), and Sider ().
See Schaffer (b).
Again, the truthmaker theorist might deny this, saying that “there are F s” is made true by things that are neither fundamental nor F . That project strikes me as much more difficult to motivate.
Most who think there is a fundamental quantifier think that it cannot be a restriction on the ordinary English quantifier (‘∃E’). Presumably their reason is that when we do ontology, we want to talk about everything (wave the hands wildly for emphasis), and restricted quantifiers don’t range over everything. McDaniel () is a notable exception, though he thinks there are multiple fundamental quantifiers. I also disagree, but for different reasons; I defend the view in Chapter .
I shall affix the subscript ‘E’ to quantificational expressions to denote ordinary English quantifica- tion, and affix the subscript ‘F ’ to quantificational expressions to denote fundamental quantification. I’ll continue to use ‘exists’ and ‘∃’, and I intend them to be ambiguous between ‘∃F ’, ‘∃E’, or some other existential quantifier.
My usage of ‘the fundamental quantifier’ may differ from that of Sider () and others, since they think that fundamentality is primarily a property of ideology. Saying that “in the fundamental sense of the word ‘exists’, only fundamental things exist” is a substantive thesis; I accept it, but Sider and others deny it.
In order to show that something x existsF , we have to show that x existsE, and that it does some truthmaking work—perhaps by being the best or only candidate for making true the English sentence “x exists”.
The truthmaker theorist thinks that at least some sentences with ‘exists’ or ‘there are’ aren’t made true by the objects quantified over, and that “there are tables” is one such sentence. The logical form of the sentence is ‘∃Ex(Table)x’. This sentence quantifies over tables. So, the one who affirms the sentence affirms the existenceE of tables. So according to the Quinean, the one who affirms the sentence is onto- logically committed to tables. But some truthmaker theorists think that in affirming sentences with ‘existsE’, we aren’t ontologically committed to the things in the do- main of ∃E; we are just committed to whatever makes the sentence true. And the general truthmaker theorist thinks that in affirming sentences with ∃E, we are just committed to there existingF something (or some things) that makes (or make) them true. We need an additional argument that it has to be tables.
So then, what allows us to say that tables existE? In short: tables do exist; just look around you! To say more, the sentence “tables exist” is true, and it’s made true by something (or some things). Since it’s true, tables are in the domain of ∃E.
Since it’s made true, whatever makes it true is (or are) in the domain of ∃F . What enables one to say that tables and chairs do not existF ? It’s that tables don’t make true “tables exist”; rather, something (or some things) more fundamental than tables do. In our English assertions we quantify over tables, and our assertions are true, but in the fundamental language we won’t need to. The fundamental quantifier ranges over only the fundamental things, the fundamental things are the truthmakers for our English sentences, and tables are not truthmakers or fundamental things. This
This entails that it’s not the case that there isF a truthmaker for some sentence that isn’t ranged over by the English quantifier. I defend this claim in Chapter .
is why they don’t existF .
. The Meinongian Contrast
One might object, “Isn’t this just Meinongianism in sheep’s clothing? The Meinon- gian says that there are some things that don’t exist, and so do you.” By way of reply, on my framework there are four ways of reading the Meinongian claim.
. There areE some things that don’t existE.
. There areE some things that don’t existF .
. There areF some things that don’t existE.
. There areF some things that don’t existF .
The Meinongian, in making a distinction between what there is and what exists, accepts (), and perhaps would accept () if presented with it. I deny both () and
(), and I also deny (). I do accept (). If one has objections against Meinongianism that tell against the truth of (), she is more than welcome to offer them. But my suspicion is that non-Meinongians object to (), and perhaps (). I do not think the standard objections to Meinongianism tell against the denial of (), or of (). So the truthmaker theorist is not a Meinongian.
. The Quinean Contrast
At this point one might wonder just how different the truthmaker view is from
Quineanism. van Inwagen () lays down five theses that the Quinean accepts.
They are:
This assumes that tables are not fundamental. If the reader thinks they are, she is invited to pick as an example something else that exists but is not fundamental.
This objection is due to Amy Seymour.
I am thinking of the Quineanism of van Inwagen (), which has its ancestry in Quine (), Quine (), Quine (a), Quine (b).
. Being is not an activity
. Being is the same as existence
. Being is univocal
. The single sense of being or existence is adequately captured by the existential quantifier of formal logic
. Quine’s criterion of ontological commitment, which van Inwagen explicates as follows:
One takes sentences that the other party to the conversation accepts, and by whatever dialectical devices one can muster, one gets him to introduce more and more quantifiers and variables into those sentences…If, at a cer- tain point in this procedure, it emerges that the existential generalization on a certain open sentence F can be formally deduced from the sentences he accepts, one has shown that the sentences that he accepts, and the ways of introducing quantifiers and variables into those sentences that he has endorsed, formally commit him to there being things that satisfy F. (p-)
The truthmaker theorist may agree with () and (). She ought to disagree with a certain way of thinking about (); she should say that sometimes ‘being’ means existenceE, and sometimes ‘being’ means existenceF . If you ask whether existenceE or existenceF is being, the truthmaker theorist says that they are two distinct notions and being is ambiguous between the two. If being is the thing that objects must have in order to figure in the fundamental description of the world, then being is existenceF . If being is the thing that some thing x must have in order for the sentence
“x exists” to be true, then being is existenceE. The truthmaker theorist invites the believer in the univocity of being to say which of existenceE or existenceF being is. The truthmaker theorist takes issue with () for the same reason she takes issue with ()—she thinks there is not a single sense of ‘existence’. She agrees that each sense of ‘existence’ can be captured by the existential quantifier of formal logic, in that each sense of existence obeys the introduction and elimination rules of the ex- istential quantifier of first-order logic. If it is true that “a is F ”, then it is true that
“∃ExF x”. And if ‘a’ names something in the fundamental language and a is F , then it is true that “∃F xF x”. But since we speak English, regimenting our ordinary dis- course into first-order logic is done using the English quantifier. It’s not clear how ordinary language maps onto the logic of the fundamental language, but certainly
“a is F ” expressed in English does not license one to infer that ∃F xF x. The truthmaker theorist also denies Quine’s criterion of ontological commit- ment, and this is the biggest departure from Quineanism. One could perhaps be a Quinean and grant all the above points about the English quantifier. She would do so by saying that speakers of English very often use ‘there is’ or ‘there exists’ idiomatically, and not to express existence. This, she might say, is what the truth- maker theorist is trying to describe with the invocation of existenceE. Rather than think ‘existence’ often expresses existenceE, this Quinean would say that ‘existence’ is often used idiomatically and not to express the single sense of existence.
That is all well and good, but one oft-touted advantage of Quineanism is its help in saddling with ontological commitment to abstracta those nominalists who say things that seem to be inconsistent with nominalism and then insist that they’re using the quantifier idiomatically so as not to express existence. In this way, the nominal- ist hopes to dodge ontological commitment to non-nominalist-friendly things. But
Quine mandates that, in all such cases of idiomatic usage of apparently quantifica- tional expressions, one paraphrase one’s sentence into a sentence that doesn’t use a quantificational expression. If she can’t do so, Quine insists, then she is ontologi- cally committed to the things over which she’s quantified. And this the truthmaker theorist cannot accept. The truthmaker theorist thinks that one can utter “there are numbers” and still be a nominalist, thinking that the sentence is made true not by numbers but by other things; she needn’t paraphrase away the sentence, because she
She would accept it as a criterion for existential commitment, but she wouldn’t think that onto- logical commitment is existential commitment, and she wouldn’t care about existential commitment qua metaphysician or ontologist.
can take it to be strictly and literally true. Nominalism on the truthmaker view, then, isn’t a view about what existsE, but rather about what makes true sentences seem- ingly about abstracta—namely, that such sentences aren’t made true by abstracta.
. Advantages of Truthmaker Views
There are three main advantages of truthmaker views. The first is that we can say that sentences that quantify over tables and the like are strictly and literally true without populating our ontology with what some consider untoward entities. We can say that “tables exist” is true, but not be ontologically committed to tables; and if we’re not ontologically committed to tables, our ontology doesn’t contain tables. This is because, on the general truthmaker view, we are only ontologically committed to there existingF something (or some things) that makes (or make) true the sentence “tables exist”. One candidate is simples arranged tablewise. If one thinks that simples arranged tablewise make true “there are tables”, then one can affirm “there are tables” without even considering being ontologically committed to tables; we get the best of both worlds. (Of course, nobody who affirms “there are tables” is ontologically committed to tables simply in virtue of affirming it.) Cameron puts the point nicely: “…the nihilist is right about the ontology but the universalist is right about what sentences are true” (Cameron ). In other words: the nihilist is right about what existsF , but the universalist is right about what existsE. Or Sider: “We’re trying to find our way in a world with a minimal ontology, and we don’t know much about particle physics” (Sider MS). The principle thought is that we’ve introduced words, some of them quantificational, to describe the world around us. And we’ve said true things, even when describing what things there are.
But what existsF are the things that make those sentences true.
Of course, not certain sentences, like “nihilism is false”. Just sentences about what exists.
I think “there are tables” need not be made true by tables. But my view leaves open the question of what the truthmaker or truthmakers for the sentence “there are tables” is or are. It could very well be tables, or it could be simples. But we are not able to distinguish between whether tables or simples-arranged-tablewise are the truthmakers for sentences about tables. And our ontological commitments are to there beingF truthmakers. So instead of arguing about whether or not tables exist
(since all it takes for tables to exist is for “tables existE” to be true), metaphysicians ought to argue about whether simples make true sentences about tables.
Truthmaker theorists think that Quineans rely too much on the surface form of language in determining someone’s ontological commitments. The second advantage of truthmaker views is that they allow us to resolve ontological questions by doing metaphysics, and not by investigating our use of language. We say that the sentence
“tables exist” is true. The logical form of this sentence is ∃x(Table)x. Therefore, there are tables; that is, tables number among the things in the world. According to the Quinean view, the only way to avoid this ontological commitment is to para- phrase the sentence into one that doesn’t quantify over tables. If we can’t do so, we’re stuck with an ontological commitment to tables. But the paraphrase is still being done at the level of sentences. Why think that English sentences are ontolog- ically perspicuous? And why think that the truth of those sentences ontologically commit us to tables? In order to answer these questions, the Quinean must make more substantive assumptions about the relationship between sentences and truth
(and I daresay truthmaking) than the truthmaker theorist—something like the sur- face form of the sentences indicating their nature, and the surface form of the sentence
It could not, of course, be three-legged unicorns; there is a limit as to what can do the truthmaking for sentences. This seems obvious, but you might wonder why it’s true. If we don’t say anything about what the truthmakers are, what eliminates unicorns as candidates? The answer is that I don’t have an argument against unicorns making true sentences about tables. If you were to press me on the point, I would respond with glee. After all, the truthmaker theorist thinks that this is just the sort of debate we should be having—not over whether “there are unicorns” is true, but about whether unicorns do any truthmaking.
determining what makes it true if it is true. The third advantage can be brought out by modifying a story authored by Ted
Sider (, p). Sider describes a world created by a god named Nihilo. When
Nihilo created the world, he created only simples ex nihilo. Then he moved them around in certain ways; but none of them composed anything. Eventually he got lonely and moved some simples around in ways to get them to be arranged in such a way as to look and behave much like us. He then taught them metaphysics, so they could talk precisely about the world around them. But they were not intelligent, and they had a hard time talking this way. So Nihilo taught them shortcuts; when they see simples-arranged-tablewise, they say “there’s a table”. And so on for other simples-arranged-certain-ways. They are now no longer speaking Nihilo’s language
(which we suppose is the fundamental language), but some other language. So, they are not speaking metaphorically or non-strictly; they intend their sentences to be true in the their language. Here are two questions we might be interested in answering: Do they speak truly? Are they ontologically committed to composite objects that are tables?
Let’s add to the story as follows: Nihilo continues to converse with his minions, and he does so using the new shortcut words, in order that his minions might un- derstand him. He says things to his minions like “There are three tables in the next room”. Here are two questions we might be interested in answering: Does he speak truly? Is he ontologically committed to composite objects that are tables?
Suppose that after a while Nihilo gets bored with his minions and stops talking to them, and then leaves them alone for a few thousand years. They get a bit smarter, but not too much, and they continue to talk in the shortcut way he has taught them,
Take ‘them’ and ‘they’ to be referring to a plurality of pluralities.
Normally we can introduce new words into a language, but this isn’t the case with the fundamental language.
saying things like “there are three tables in the next room”, vaguely aware because of their oral mythology that a god once tried to teach them to speak more precisely.
Again, two questions: Are their sentences true? Are they ontologically committed to composite objects that are tables?
Suppose that after a few billion years the minions get much, much smarter, and they stop believing that simples ever compose anything. But they’re used to talking a certain way and it’s a whole lot shorter and their children catch on easier, so they keep saying “there are three tables in the next room” and the like. Again the two questions: Are their sentences true? Are they ontologically committed to composite objects that are tables? I want to say “yes” and “no” respectively to all four sets of questions; the minions are speaking truly, and they are not ontologically committed to tables. I hope many readers think it would be nice if we could answer the questions that way. Truthmaker views provide a principled reason for doing so. Quineanism answers the questions exactly opposite. Quineanism says that if one of the minions asserts “there are three tables in the next room”, the minion speaks falsely (given the description of the world as containing no composites). Quineanism also says that if anyone affirms ‘there are three tables in the next room’ as strictly and literally true, she is ontologically committed to tables. But what if the sentence is true, but it’s not made true by tables? Then it might be the case that the sentence
Sider says it’s an open question whether the minions speak truly in the first case (though he thinks they don’t), and since in his story Nihilo doesn’t speak, he doesn’t discuss whether Nihilo would speak truly were he to talk about tables. He also says the minions certainly speak correctly, where ‘correctly’ is a technical term for something that is either (i) true or (ii) close to true and also useful or advantageous or something. I shall avoid this, because I don’t know what it means. If we can give a theory whereby the sentences are true, I think that theory is better—it has fewer primitives and respects the intuition that the minions are doing something right.
Why not answer the sets of questions differently? Well, the sentences in question have the same words (“There are three tables in the next room”), and they are spoken in the same language. So presumably they have the same semantic content. And it would be odd if a sentence with the same se- mantic content had different truth values and bestowed different ontological commitments depending on who said it.
is true and there are no tables, since whatever makes the sentence true exists. The Quinean thinks this is impossible. Perhaps it’s because she thinks tables are required to make true our sentence “there are three tables in the next room”; and if one isn’t ontologically committed to tables, then one can’t provide a truthmaker for “there are three tables in the next room”. But if we were in a world like Nihilo’s, “there are three tables in the next room” would be true, and the truthmaker(s) wouldn’t be a table or some tables. The moral of the story, then, is that some quantificational sentences are true, but they’re not made true by the things quantified over. Thus, one who asserts one of them isn’t and needn’t be ontologically committed to the things over which she quantifies. This suggests that the Quinean criterion for ontological commitment is false.
The Quinean thinks that the existence claims of the theory must be made true
(if they’re made true at all) by the things quantified over; if she thought “P s exist” could be true and made true by things other than P s, then she would not insist that one has to be ontologically committed to P s if one says they exist. The truthmaker theorist thinks that this needn’t be the case: “there are P s” can be made true by things that aren’t P s. So, “P s exist” is true (as the theory says), but saying so doesn’t ontologically commit us to P s, only to there being truthmakers for “there are P s”. The Quinean responds, “If that’s the case, you must paraphrase away your com- mitment to P s.” To quote Quine:
When we say that some zoological species are cross-fertile we are com- mitting ourselves to recognizing as entities the several species themselves,
Perhaps she would claim not to understand “makes true” or “truthmaker”, and might resist phrasing her view in this way. But the thought would be something like what I’ve characterized her as thinking. Quine thought that “nothing is true but reality makes it so” (, p), but modern Quineans tend not to talk much about truthmaking.
Compare “there are water molecules” being made true by two hydrogen atoms covalently bonded to a single oxygen atom.
abstract though they are. We remain so committed at least until we de- vise some way of so paraphrasing the statement as to show that seeming reference to species on the part of our bound variable was an avoidable manner of speaking. (Quine (), p, emphasis mine)
The truthmaker theorist responds by denying the need to paraphrase in order to avoid ontological commitment to P s. When paraphrasing away existence claims, one gives another English sentence which quantifies over different things than the original sentence. The classic example is the mereological nihilist who denies the existence of tables but feels free to assert sentences like “this table is white” in some contexts.
If pressed, she would give one of a number of responses. One response is that she was asserting a sentence that is ontologically neutral, so to speak. She would then paraphrase, “There are some simples here arranged tablewise and whitewise”. In this way, the Quinean story goes, the nihilist dodges an ontological commitment to tables.
But why rest so much on the surface form of language? Why care about whether we’re clever enough to avoid speaking a certain way? There are ingenious proposals to paraphrase our sentences in a way that’s consistent with ontological nihlism—the view that nothing exists. Ontological nihilists should not be considered to have a more ontologically parsimonious theory just because they’ve come up with some linguistic and logical tricks to avoid affirming the existence of anything. And those who recognize the power of the arguments for mereological nihilism but cannot for the life of them come up with paraphrases for sentences about tables should not be saddled with ontological commitment to tables in virtue of their lack of creativity.
Suppose someone (call him ‘Tom’) says, “The average family has . children”.
The Quinean responds, “You think there is an average family? Well, then you’re on- tologically committed to an average family.” What if Tom is not sufficiently clever
She might also say that what she said wasn’t in fact true, but quasi-true, or correct, or something else indicating falsehood but usefulness. But I’m less interested in these responses as in ones that maintain the truth of the assertion.
See Hawthorne and Cortens () and Turner ().
enough to think of a way to paraphrase the sentence so that it doesn’t quantify over average families? He may very well know that there’s no such thing as an aver- age family (since he knows that it’s impossible to have . children), but he knows he’s saying something true, so he affirms the sentence. And since he doesn’t have a paraphrase but he knows it true, he affirms it as being strictly and literally true. After all, if a Quinean says, “You think the average family has . children. So you think there are such things as average families?” Tom might respond, “Yes”, to which the Quinean says, “So there is something that is an average family?” Tom ought to say no, because he knows what’s coming, and he knows that there’s no family that has . children. So he retraces his steps and says that there are no average families. But then the Quinean wants to know what Tom means by saying,
“The average family has . children.” Tom knows he’s saying something true, and he knows that it doesn’t entail that there’s a family with . children. But he’s not sure exactly how to paraphrase it. The Quinean says that he must either take it back, or supply a paraphrase. He’s not inclined to do either.
So the Quinean is forced to say that Tom is ontologically committed to an aver- age family. The general truthmaker theory says that the nihilist and the no-average- familyist needn’t be able to paraphrase their sentences in order to avoid ontological commitment to tables or average families; by saying “there are three tables in the next room” and “the average family has . children”, she is just committed to
It’s not as easy as it seems.
Perhaps the Quinean would say that Tom isn’t smart enough to ontologically commit to any- thing. But this would require a modification of the Quinean position in the form of an additional condition that a person must satisfy in order to be ontologically committed; e.g., “S must understand the sentence she affirms”. But of course Tom understands “the average family has . children”, and he really believes that it’s true. It seems unfair that he can dodge the commitment with which the rest of us are saddled by virtue of not being intelligent enough. I can’t see what the Quinean would want to add that would allow Tom to dodge commitment to average families that wouldn’t unacceptably generalize.
those sentences being true! The nihilist is ontologically committed, then, to there being something that makes it true that this table is brown—it may or may not be a table. The good neo-Quinean nihilist thinks it’s simples, so she paraphrases her table- sentence into a simple-sentence, thus allowing her to ontologically commit only to simples, and not tables. And the no-average-familyist is ontologically committed to there being something that makes it true that the average family has . children— it may or may not be an average family. The neo-Quinean no-average-familyist thinks it’s simples or people and some facts about numbers, so the intelligent neo-
Quinean no-average-familyist offers a paraphrase: “The total number of children had by families divided by the total number of families is ..” But the less intelli- gent neo-Quinean no-average-familyists are stuck being ontologically committed to an average family. All this work is unnecessary, on the general truthmaker theory.
. Other Truthmaker Views
Thus far I have explained and argued for the general truthmaker view of onto- logical commitment, and made clear its advantages over the Quinean view. But the general truthmaker view is not the only truthmaker view on offer, and many of the advantages of the general truthmaker view are shared by other truthmaker views. However, there are other reasons to prefer the general truthmaker view to other truthmaker views. I’ll spend the remainder of the paper explaining and critiquing other truthmaker views and showing the advantages that the general truthmaker view has over them.
The specific truthmaker theory also says that she needn’t paraphrase (or be able to paraphrase) her sentence; she is just committed to the existence of the truthmaker.
And now it looks like she’s ontologically committed to total numbers!
.. The Specific Truthmaker View
The specific truthmaker view says that when one affirms a sentence, one is onto- logically committed to whatever happens to make true the sentence. I am not sure if anyone holds the specific truthmaker view, because proponents of truthmaker views have not yet filled in enough details; they have never made clear just what they take our ontological commitments to be. They talk about our ontological commitments being to the truthmakers, but that’s not the general truthmaker view. First, people ought to incur some ontological commitment by uttering false sentences. On the specific truthmaker view, someone who says, “There are ℵ0 unicorns” occurs no on- tological commitment, because the sentence is false and thus has no truthmaker. But most of us want to say that they do incur some ontological commitment. If our onto- logical commitments are to the truthmakers the sentence would have if it were true, then what about necessarily false sentences? For example, what are my ontological commitments when I affirm “There are ℵ0 unicorns and 2 + 2 = 5”? Again, it seems I ought to incur some ontological commitment, but on the specific truthmaker view I do not.
Second, suppose Jonathan Schaffer (b) is right; truthmaker monism is true, and the truthmaker is the world. The specific truthmaker view says that we are ontologically committed, then, to the world—and this is the case even if we think that the truthmakers are simples, or ordinary objects, or we don’t believe in truth- makers at all. I disagree. We are not ontologically committed to the world when we say “tables exist” and when we say “there are a few colors”, especially if we emphatically deny that the world is the truthmaker for those sentences. But that’s what proponents of the specific truthmaker view are committed to. I like the general view—we’re only committed to there being truthmakers. So, by saying “tables ex-
Truthmaker monism is the view that there is one truthmaker. According to Schaffer (b), the leading (and perhaps only) proponent of the view, the one truthmaker is the world.
ist”, we’re not ontologically committed to the truthmakers; we’re just committed to there being truthmakers. Namely, we’re committed to the sentence being true and having a truthmaker (or several). This sounds eminently reasonable to me, and it is good reason to prefer the general truthmaker view to the specific truthmaker view.
There are not many who have held truthmaker views. Though contemporary talk of truthmaking has its origins in , most of the discussion of truthmak- ing has been attempts to formulate an adequate truthmaker principle, discussions of which ontological category truthmakers belong to, and accusations that certain people (e.g. nominalists, presentists, actualists) cannot provide truthmakers for the sentences they so freely affirm. It is widely thought that John Heil was the first to accept a truthmaker view of ontological commitment, and he has been followed by
David Armstrong. Ross Cameron has recently articulated his own truthmaker view in a series of papers. I will attempt to formulate each person’s criterion of ontolog- ical commitment and pose problems for it.
.. John Heil’s View
John Heil () was the first to allude to a truthmaker view of ontological com- mitment. He seemed to take it for granted that someone who placed a lot of em- phasis on the truthmaker principle would hold a truthmaker view of ontological commitment, so he did not take great pains to show how much of a departure this was from orthodoxy, nor did he explicitly state or defend the view. Nevertheless, one gets a foretaste of truthmaker views, though with almost no detail. Heil’s whole book, after all, is an argument against the thought that figuring out what there is
The paper to which I’m referring is Mulligan et al. (a), who cite as inspiration the Tractatus.
See Heil () and Heil (, §.), Armstrong (, §.), Cameron (b), and Cameron ().
And Ross Cameron () cites Heil (, §) as an inspiration.
can be done by reflecting on the way we talk about the world. Time and again Heil resists the move from “we talk about F s” to “therefore, there are F s”, and he does so by asking what the truthmakers for our discussion of F s are. Only when we’ve given the truthmakers have we told “the deep story”. This thought, while perhaps not entailing a truthmaker view of ontological commitment, certainly supports one. While there is not much explicit discussion of such a view in Heil, there are a few quotations which lend support to thinking of him as holding a truthmaker view of ontological commitment, though it is less clear what kind of truthmaker view he holds.
The first occurs in the introduction, where he says, “Truth-makers for claims about statues or people could turn out to be configurations of the atoms in the void.
This, however, while providing what might be thought of as the deep story about statues and people, falls well short of establishing that there are no statues or people”
(). It is natural to read this as an expression of a truthmaker view of ontological commitment; when one finds out the truthmaker(s) for claims about F s, one is on- tologically committed to those things—but F s still exist. However, I don’t think it’s that simple. It’s not entirely clear that Heil equates “the deep story” with our onto- logical commitments. That is, I take it that someone like Jonathan Schaffer would think that the truth-maker for claims about statues and people is the world, the world provides the deep story about statues and people, and there are statues and people; but Schaffer still thinks we’re ontologically committed to statues and people. So it’s not totally clear just from this that Heil holds a truthmaker view of ontological commitment. Though he certainly holds a truthmaker view of “the deep story”— that is, when you find out the truthmaker(s) for claims about F s, you have found the deep story about F s. But this is about the importance of finding out truthmakers, not about ontological commitment.
See Schaffer (), where he says that we are ontologically committed to what we think exists.
The second is in §., where he wonders just what exactly realism is. “What I should like to challenge is the idea that realism about an object answering to a sortal obliges us to suppose that the sortal designates an object or a class of ob- jects in a metaphysically robust sense of object” (p). So, one might be a realist about an x that is an F but not think that F s are objects in a metaphysically robust sense of object. Or, one can be a realist about F s but not think F s are objects in a metaphysically robust sense of object. Realism, as Heil understands it, is a claim about mind-independence. To be a realist about F s is to think that F s are mind- independent. So, the above is to be understood as saying that one can think that F s are mind-independent but not think they are metaphysically robust. This is because in some cases it depends on us what things we pick out when we talk using ‘F ’, but the F s exist regardless of how we use the term. Once the quotation is fully cashed out, it’s not clear that this is at all a claim about truthmaking or ontological com- mitment, but rather whether a certain view of how sortal terms connect up with the world counts as realism.
Third, Heil asks:
What do we require in order to say that statues (or lumps) exist? …God will need to create the atoms and the void (the elementary particles, or the fields, or what have you), and arrange them appropriately…Once this is accomplished, God will have created a world containing statues…it will be true, literally true, that there are statues (and, for that matter, that there are lumps of bronze). (p)
There are a few ways to read this. One way is that Heil thinks that composi- tion supervenes on the qualitative nature of the relata. Necessarily, if God creates atoms and the void and arranges them appropriately, then composition occurs. This is a reasonably moderate view. After all, anyone who wants to answer the Special Composition Question has to say something like this; answers to the Special Com- position Question are just attempts at specifying what it takes to arrange the atoms
appropriately. This is pretty standard fare, and it’s all that a strict reading of the text allows.
But there’s another potential interpretation. Notice that the above quotation is in the spirit of what at least some proponents of the view that composition is identity want to say: a statue is nothing and above the atoms; what it is for the statue to exist is for the atoms to exist and be arranged a certain way; if you already think the atoms exist, the statue is no addition to being. But composition as identity neither entails nor is entailed by a truthmaker view of ontological commitment.
A third way of reading this is that composition doesn’t occur even when God creates the atoms and arranges them, but even though composition doesn’t occur, the world still contains statues. But how could that be? Given his other views, it’s natural to read Heil as thinking that we are allowed to say that statues exist, because our concept of a statue is such that when we see in front of us this, then our concept of statue applies, and we can say “there’s a statue in front of me”. Heil doesn’t think it matters whether we think there are genuine entities that are statues, or just modes, or just atoms in the void—we still speak truly when we say “there are statues”. By holding these other views, what we’re saying is that we’ve uncovered the deep story about statues. That is, we’ve discovered the truthmakers—the things out there in the world—that make true our sentences about statues. Heil continues by asking us to suppose that “the deep truth about objects like statues and lumps of bronze would be that such things are in fact modes. Is our ordinary talk of states and lumps of bronze at odds with this possibility? Again, I do not see why we must think so” (p). So, even if statues and lumps are modes and
The Special Composition Question is posed in van Inwagen ().
But Heil explicitly disavows composition as identity, saying that our concepts of statues and lumps have historical constraints that forbid us from identifying the two. Of course, this would be constitution as identity, not composition as identity. But the doctrines are quite similar, and if anything, constitution as identity is the more plausible. So it’s doubtful that Heil has anything like composition as identity in mind.
thus not composite objects, their being so is consistent with our ordinary discourse. But as Heil sees it, this is more a comment about the fluidity of our concepts of things than it is about ontological commitment. He goes a bit further when he asks us to
“Suppose that trees, mountains, human beings, and the rest are modes: ways the ultimate stuff is. Does this mean that macroscopic objects do not exist (or do not really exist)? Only a philosopher would want to say this” (p). Of course, Heil is a philosopher, but in this case one gets the feeling he’s attempting to distance himself from the rest of us. He holds the commonsense view—macroscopic objects exist, and indeed they really exist, but they are (ultimately? really?) modes; this is what we learned in th grade science. But this strikes me as wrong. If I were to find out that the deep truth about statues involved modes, I wouldn’t want to identify the statues with the modes. I’d rather say that there are statues and there are modes, and statues are not modes, but modes are the truthmakers for statements about statues. I’ve thought all along that by saying “there are statues” I am not ontologically committed to statues; if I become convinced that modes are the truthmakers for statements about statues, then I should think that I’m ontologically committed to there being truthmakers for “there are modes” and “modes are the truthmakers for statements about statues”.
These are the things Heil says that might cause one to classify him as holding a truthmaker view of ontological commitment. While he says many things that a truthmaker theorist would say, I’m not convinced that these quotations are enough to establish that he is. I think that a truthmaker view is likely consistent with what he says (although I worry about what he means when he says macroscopic objects
“really” exist), and indeed it fits quite nicely with his desire to make ontology be about what there is and not how we talk; and of course, there is his commitment to the importance of truthmakers in general. But as far as what he in fact says, he might hold this conjunction: (a) statues exist, (b) when we say that statues exist, we are
ontologically committed to statues, but (c) the deep story about statues is in terms of atoms arranged certain ways. If that is his view, I urge him to abandon (b). He should think that his ontological commitments are to there being things that make true ordinary English sentences, and they are the things referred to in the true deep stories. And he should consider the conjunction of all the deep stories, identify what objects that conjunction is talking about, and have all and only those things in his ontology.
.. David Armstrong’s View
Armstrong seems to have been the first to say that if one postulates truthmakers for all the things one takes to be true, then, by doing so, one has has an ontology.
That is, he seems to be the first to realize that truthmaking could be used as a cri- terion for ontological commitment. He says, “To postulate certain truthmakers for certain truths is to admit those truthmakers to one’s ontology. The complete range of truthmakers admitted constitutes a metaphysics…” (p). Of course, he does not explicitly say that one’s ontology consists only of what one takes truthmakers, but that seems to be his intent. He saw his view as starkly opposed to Quine’s, and thought that “the great advantage, as I see it, of the search for truthmakers is that it focuses us not merely on the metaphysical implications of the subject terms of propo- sitions but also on their predicates” (p). Quine thought that when we affirm “a is F ”, we have to admit into our ontology only a. Armstrong thought that, since a is only a partial truthmaker for “a is F ”, we must admit more into our ontology.
Quine considered predicates ideology, but Armstrong thinks that, without admitting into our ontology something “corresponding” to the predicate, we can’t provide a truthmaker for “a is F ”. Armstrong thought that requiring ontological commit-
One wonders if Armstrong is surprised at how the truthmaker view of ontological commitment is being used both here and in Cameron—not to force people into admitting into their ontology more
ment to truthmakers “leads us to consider whether we do not require at least selected properties and relations in our ontology” (p). He, of course, thought that we do.
And indeed, he thought that we also need facts or states of affairs, both negative and general, to make true contingently true propositions.
This is all Armstrong says in the direction of a truthmaker view of ontological commitment. Of course, we could conjoin this view with his views about the truth- maker principle itself and get a pretty good idea of what Armstrong took to be his ontology. But it’s difficult to tease out a more nuanced position of his criteria of on- tological commitment. That said, I think we can say a few things for certain. First,
Armstrong rejects Quine’s criterion of ontological commitment. Second, he thinks we are ontologically committed to all and only the things we postulate as truthmakers for the propositions expressed by the sentences we affirm. His view, then, is neither a specific nor a general truthmaker view. If the way we postulate truthmakers is by affirming sentences like “I postulate a as a truthmaker for the proposition expressed by ‘a is F ”’ (or the simpler “a is the truthmaker for the proposition expressed by
‘a is F ”’), then the general truthmaker view says that we are ontologically commit- ted to there being something that makes true the proposition expressed by “a is the truthmaker for the proposition expressed by ‘a is F ”’; and the specific truthmaker view says that we are ontologically committed to whatever makes true the propo- sition expressed by “a is the truthmaker for the proposition expressed by ‘a is F ”’.
Armstrong’s view has already come apart from the general truthmaker view. And if the truthmaker for the proposition expressed by “a is the truthmaker for the propo- sition expressed by ‘a is F ”’ is not a, then Armstrong’s view also comes apart from the specific truthmaker view. We might also wonder what Armstrong would say about our affirmation of sen- tences for which we don’t postulate truthmakers. The general and specific truth- than Quine thought they should (as seems Armstrong’s intent), but in fact less.
maker theorists both have things to say. But Armstrong seems to think that onto- logical commitment is something that only happens when one postulates a truth- maker. And it seems he doesn’t think that we postulate truthmakers by affirming sentences like “a is F ”—only by postulating a truthmaker do we ontologically com- mit to anything. This is a problem. For on this view, only truthmaker theorists are ontologically committing to anything at all. And even then, we’re not ontologically committing to very much—just the things that we say make true the sentences that have been disputed by our opponents, and the things that we appeal to in our exam- ples of truthmaking. That is, of course, too sparse an ontology. One needn’t perform an act of truthmaker postulation in order to incur ontological commitment.
.. Ross Cameron’s View
Ross Cameron has offered the most sustained explication and defense of a truth- maker view. He sees an ancestor of his truthmaker view in Heil, and his two recent papers (b and ) attempt to develop the view in much greater detail. The most natural reading of Cameron is as holding the specific truthmaker view; in this section I’ll show why, as well as offer some objections to his view.
Cameron says, “It is true to say that there are such things [as tables and chairs], but that it is true does not commit us to admitting such things into our ontology” (, p). This brings up a natural question: is it also true that there are such things, or is it just true to say that there are? That is, does the truth of sentences come apart from truth of the propositions they express, or does existence come apart from ontological commitment? Cameron wants to endorse the latter, since he wants to retain disquotation (b, p). He wants to say that by uttering, “The Taj Mahal exists”, we affirm the existence of the Taj Mahal, but we do not ontologically commit to it. I agree.
It sounds legitimate to say, “It is true to say that tables exist, even though tables don’t exist.”
Cameron also says, “If you want to hold that ‘there are Xs’ is strictly and literally true whilst resisting ontological commitment to the Xs, you should show that one can provide grounds for the truth of such claims without appealing to the Xs…” (, p). Here we begin to differ. While I agree that you should eventually show (or at least argue) that something else can make true sentences about Xs if you don’t want to be ontologically committed to Xs, I think you don’t have to. That is, you needn’t show that you can provide grounds for “there are Xs” in order to maintain that
‘there are Xs’ is strictly and literally true while not ontologically committing to Xs.
Cameron seems to disagree; he also says, “To resist commitment to tables I do not need to reject the truth of table-talk but rather show that table-talk can be made true by something other than tables” (, p, emphasis mine). Saying, “I don’t need to X, but rather Y ” implies that “I need to Y ”. If that’s true, then Cameron thinks that to resist commitment to tables, he needs to show that table-talk can be made true by something other than tables. This is, of course, a nice advance over Quineanism, which says that he needs to paraphrase his sentence into one that doesn’t quantify over tables; Cameron just says he needs to provide truthmakers that aren’t tables.
But the spirit of the demand for truthmakers is very much the same as the demand for paraphrase. On my view, not only does Cameron not have to show what the truthmakers could be, he doesn’t even have to say what he takes them to be. He ought to, qua ontologist, be in the business of investigating what the truthmakers are/must be/could be for various sentences. But it’s not the case that the only way to resist ontological commitment to F s is by offering a different truthmaker for sentences about F s. It’s not clear what Cameron thinks about this. He talks about resisting ontological commitment to tables when we say “tables exist” because simples are all that’s required to make it true. What if we had no idea that simples exist? Would we then be ontologically committed to tables? I say no—we’re just committed to the sentences having truthmakers, and it’s the ontologist’s job to find out what they are.
Perhaps it’s the world, perhaps simples, perhaps tables, or perhaps something else. Every time Cameron says, “We aren’t committed to Xs”, he immediately supplies a truthmaker, “All that sentences about Xs commit us to are Y s”. But on my view, we are not committed to Xs if we cannot supply Y s as candidate truthmakers.
Throughout his papers, Cameron says things like, “A theory’s ontological com- mitments are to what must exist to make true the sentences of that theory” (for the
first time on b, p, emphasis mine). As I see it, there are three ways to make sense of Cameron’s statement. The first is to say that it’s not the case that tables must exist for the sentence “tables exist” is to be true; rather, some other things exist and make it true. The second is to say that of course tables must exist for the sentence “tables exist” to be true, but tables aren’t the truthmakers for the sentence, and thus the theory is not ontologically committed to them; it’s only ontologically committed to the truthmakers. The third is to say that tables must exist for the sentence “tables exist” to be true, but that the theory isn’t ontologically committed to them—it’s only ontologically committed to there being something that makes “tables exist” true.
I don’t know which of these Cameron intends. Sometimes he seems to favor the
first option. But at other times he makes a distinction between existence and “real being”, and says that tables must exist for “tables exist” to be true, but tables don’t have to have real being for “tables exist” to be true; and we’re only ontologically committed to things we think have real being. On that basis, I think we can rule out the first option. And he thinks that we can ontologically commit to particular things, so option two is still on the table. But with respect to this particular case,
I cannot tell whether he means option two or three. I think that the most sensible thing for the truthmaker theorist to think is that existence and real being come apart.
Compare the following two quotations, which seem to be in tension: “I hold that the ontological commitments of a theory are just those things that must exist to make true the sentences of that theory” (TOC ) and “the ontological commitments of a theory are those things whose existence its truth entails that have real being” (RMO ).
I think she should say that “F s exists” requires the existence of F s but might not be made true by F s; so all we’re ontologically committed to when we affirm “F s exist” is the “real being” of something or other that makes it true, even though we do affirm that F s exist. And I think the way of making sense of “real being” is to understand it in terms of fundamentality: x has real being=df x is fundamental. Second, what does ‘must’ mean in this context? Is it that the ontological commit- ments are to things that entail the truth? Or the things that in fact make it true? The most natural reading is that ‘must’ here is a modal operator. But in that case, our ontological commitments might very well be disjunctive; if “tables exist” is true, then what must exist to make it true is either tables or simples or thoughts or the world or distributional properties or…So if every sentence is made true by different things in different worlds, then the most natural reading of Cameron’s view is as a specific truthmaker view, but of a modal sort. He says that our ontological commitments are to a certain disjunction of things (truthmakers at various worlds). In a similar vein, he says, “We should make a distinction, as indeed anyone must, between a sentence bringing an ontological commitment to some particular thing(s), and it ontologically committing you to some things or other. I say that a sentence
S commits you to some particular thing A when A has to make S true if it is true”
(, p). This is great progress toward the general truthmaker view. But it is not the general truthmaker view, because one might think that very often there are sentences such that what makes them true has to make them true. So the difference between this view and the general truthmaker view turns on one’s view about how often there’s a particular sentence and object such that the sentence could have no other truthmaker than that object. Similarly, Cameron says, “the truth of ‘Beethoven’s ninth exists’ is actually grounded in Beethoven’s having indicated a certain abstract sound structure, and that is com- patible with the fact it might not have been so grounded” (, p). This makes
one wonder what our ontological commitments are: one of the things that might have grounded it, but no particular one thing? Or the thing that actually does ground it?
Or some thing or other? It’s not clear.
There are things with which I disagree more strongly. Cameron says that “if
‘there are denumerably many electrons’ is true, then we aren’t committed to a par- ticular plurality of electrons, but rather some denumerable plurality of electrons”
(, p). This seems starkly at odds with a truthmaker view of ontological commitment. Why are we committed to some denumerable plurality of electrons, rather than to the truthmakers of that sentence, or there being some truthmakers?
After all, what if I believe that “there are denumerably many composite objects” is true? Am I ontologically committed to some denumerable plurality of composite objects? The truthmaker theorist wants to say no; “there are denumerably many composite objects” might be made true by denumerably many other things. So why not with electrons? If we’re only ontologically committed to the truthmakers (or to there being truthmakers), why are we committed to some denumerable plurality of electrons by uttering “there are denumerably many electrons” but not some de- numerable plurality of composite objects by uttering “there are denumerably many composite objects”?
I’ll conclude this section with a prime example of Cameron’s seeming commitment to the specific truthmaker view: “Perhaps what makes it true that there is a one- to-one correspondence between the F s and the Gs are numbers; but in that case the stipulation of Hume’s Principle isn’t bringing about any new commitment—we were already committed to the existence of numbers in claiming such a one-to-one correspondence” (b, p). But I disagree. In saying, “there is a one-to-one correspondence between the F s and the Gs”, we were committed to there being a truthmaker for that sentence. Perhaps numbers, perhaps some particular function mapping the F s to the Gs, perhaps the world, perhaps…But we are not ontologically
committed to any of those particular things, even if it turns out that the numbers make it true that there is a one-to-one correspondence between the F s and the Gs.
. Conclusion
On the general truthmaker view, one’s ontological commitments are to there beingF entities which make true the sentences one affirms. The sentences one af- firms will include sentences like “a exists”, “P s exist”, and the like. So, the everyday
English quantifier, ∃E, has in its domain a, things that are P , and the like. One’s ontological commitments are to there beingF entities that make those sentences true. There are three advantages of the general truthmaker view. One is that it allows us to make sense of cases like the Nihilo case. Another is that it allows us to rely less on language to determine what we ought to be ontologically committed to. And a third is that it allows us to say that English sentences that nearly everyone accepts are true, but without the ontological baggage that the Quinean view requires. These are good reasons to accept the general truthmaker view. There are putative reasons not to accept the general truthmaker view, but I hope to have shown why they are not good reasons. Truthmaker views are better than the Quinean view, and the general truthmaker view is the best of the truthmaker views.
CHAPTER
TRUTHMAKERS AND SUBSTANCES
. Introduction
In this chapter, I present and defend a meta-ontology. A meta-ontology, roughly, is a way of thinking about what someone is doing when she’s doing ontology. Put another way, it is a method or schema for giving an ontology. One gives an ontology by giving an answer to “the ontological question”. Because there is no agreed-upon ontological question, and each ontologist is attempting to answer that which she considers the ontological question, ontologists are not all doing the same thing when they’re doing ontology. Some are in the business of saying what there is, or what kinds of things there are. Some are trying to give an account of the structure of reality. Some are trying to tell the deep story of the world. What an ontologist thinks the ontological question ought to be will determine what she’s up to when she does ontology.
Quine () thought the ontological question was, “What is there?” So Quine was in the business of saying what things there are. He didn’t do so by listing them all, but by figuring out the predicates of our best theories. The extensions of those predicates are sets, and the members of those sets are the things there are. Recently,
Though presumably there’s something in common with what they’re all doing in virtue of which we all agree that they’re doing ontology. To say what it is is a project for the future.
See Quine () and its many ancestors.
See Sider ().
See Heil ().
Schaffer (a) has argued that the ontological question is “What grounds what?” So Schaffer is trying to say what things are the grounds, and what things those things ground. Fine () argues that the ontological question is “What is real?” So he is trying to list the things that are real; there are some things that are not real. (Sider,
, p viii) thinks “the goal of metaphysics is to give a fundamental description of the world”; this suggests that for him the ontological question is, “What things show up in the fundamental description of the world?”
On my meta-ontology, there are fundamental things, and there are non-fundamental things. One’s ontology is what one takes to be the fundamental things. The funda- mental things ground the non-fundamental (or derivative) things. Propositions are true if and only if something makes them true. Truthmaking is a kind of grounding— grounding the truth of a proposition. Since only the fundamental things are in one’s ontology, only they are suited to be truthmakers. So, only those things are the truth- makers for our ordinary English sentences. The ontology has one primitive: ‘grounds’. On my view, ground is a genus of which the other priority relations of metaphysical dependence (truthmaking, onto- logical dependence, reductive analysis, metaphysical explanation, and the like) are species. So, ground holds between a variety of relata. The following are some defi- nitions cast in terms of ground. x is fundamental if and only if it’s not the case that there’s a y such that y grounds x. x is a truthmaker for y if and only if x grounds the truth of y. x is an ultimate truthmaker if and only if there exists a y such that x is a truthmaker for y and it is not the case that there exists a z such that z grounds x. x is a substance if and only if x is fundamental.
Because this meta-ontology characterizes ontology and the ontological question
One upshot of characterizing things this way is that if one denies truthmaker maximalism, the view that all truths have truthmakers, then one is forced to say that some truths of propositions are fundamental. If truthmaker maximalism is false, there is at least one proposition p such that p is true but nothing grounds its truth. But if nothing grounds x, then x is fundamental. So, the truth of p (whatever that is) is fundamental.
in terms of ground and fundamentality, it has the virtue of allowing for a simple on- tology. The ontology contains only one kind of thing: substances. Most ontologies that contain only one kind of thing (states of affairs a la Armstrong (), prop- erties a la Paul (MS)) have the disadvantage of conflicting with ordinary ontological beliefs (that there are tables and chairs and other people) as long as we think those ontological beliefs are not subject to too much revision, e.g. that tables and chairs and other people are really states of affairs, or properties, or something. My one- category ontology, despite being similarly minimal, does not conflict with common sense. It affirms the existence of all the things we ordinarily take to exist (tables and chairs and people and such), and does not admit anything we ordinarily don’t take to exist (incars and outcars and trout-turkeys and such). Usually such ontologies also can’t provide enough things to satisfy the demands of the metaphysicians; but because my meta-ontology is cast in terms of grounding and truthmaking, I can do that as well. This paper is largely a defense of the last claim—that my meta-ontology allows my ontology to satisfy the demands of the metaphysicians. I characterize the de- mands and how my meta-ontology attempts to meet them in §-, and I respond to objections in § and . But I begin with a positive argument that substances are truthmakers.
Those who have a different meta-ontology will, of course, disagree.
Clearly I make a distinction between affirming the existence of x/F s and admitting x/F s into one’s ontology. I take “positing x/F s” to be the same as affirming the existence of x/F s.
. The Argument
The part of the meta-ontology that I want to defend in this paper is that substances are the ultimate truthmakers. Here is the argument:
. For any x, if x is an ultimate truthmaker, then x is not grounded in anything.
. If x is not grounded in anything, then x is a substance.
. Therefore, for any x, if x is an ultimate truthmaker, then x is a substance.
Both () and () follow from the characterizations given at the end of the last section, so the conclusion isn’t that surprising. The crucial move is arguing that there are propositions that have ultimate truthmakers—conditionals aren’t worth much unless there are things satisfying the antecedent. The most promising way of arguing for it is arguing that if every proposition has a truthmaker, every proposition has an ultimate truthmaker. The antecedent of this is truthmaker maximalism, which enjoys widespread acceptance. So, I’ll argue that if truthmaker maximalism is true, every proposition has an ultimate truthmaker. Every truthmaker is either an intermediate truthmaker or an ultimate truthmaker. For any x such that x is an intermediate truthmaker, there exists a y that grounds x; either y is a substance, or y is not a substance. If y is a substance, then y is ungrounded; so y is not an intermediate truthmaker, and thus y is an ultimate truthmaker. If y is not a substance, then there is a z such that z grounds y; so y is an intermediate truthmaker. Either z is a substance, or z is not a substance. And so on. So, for every proposition, if it has a truthmaker, it has an ultimate truthmaker. And this ultimate truthmaker is not grounded in anything else. If the ultimate truthmaker is not grounded in anything else, then it is
Other parts I defend in other papers, and still other parts have been given adequate defense by others.
This entails that grounding is well-founded, which is a standard assumption, though not without its detractors. More on this in a few paragraphs.
a substance. Here’s another argument. Suppose all truths have truthmakers. Then, for every truth p, there’s an x that makes p true. Either x is grounded, or x is ungrounded. If it is ungrounded, it is an ultimate truthmaker. If x’s existence is grounded in something else, then there exists a y that grounds x. Grounding is usually taken to be transitive; so, if x grounds the truth of p and y grounds x, then y grounds the truth of p. Either y is a truthmaker for p, or it is not. If it is not a truthmaker for p, then it grounds the truth of p, but it’s not a truthmaker for p. But truthmaking is just a particular kind of ground, so what other kind of ground would y stand in to p? The most reasonable thing to think is that it’s a truthmaker. If y is ungrounded, then there’s no more fundamental thing that grounds the truth of p, so y is an ultimate truthmaker for p. If y is grounded, say in z, then z is also a truthmaker for p (for the same reason that y is), and if z is ungrounded, it is an ultimate truthmaker for p. And so on.
Finally, a reductio. Suppose it’s not the case that every proposition has an ultimate truthmaker. Then there is a proposition p that has a truthmaker x, but x is grounded in some thing y, and y is not a truthmaker for p. (If x is not grounded in some other thing, then x is an ultimate truthmaker, contra the supposition.) And if x is grounded in y and y is a truthmaker for p, then either y is ungrounded or grounded.
If y is ungrounded, then it is an ultimate truthmaker for p, contra the supposition. If y is grounded, then there is some thing z that grounds y. z is either grounded or ungrounded. If it’s ungrounded…
This assumes that grounding is well-founded. A relation R is well-founded if and only if there are no infinite descending chains such that xRy, yRz, zRz1, z1Rz2…There is an intuitive thought that grounding isn’t the kind of relation that can fail to termi- nate; much like proper parthood, there have to be some minimal elements. But with
This entails that if there is at least one true proposition, then there are substances. But it does not entail that, necessarily, if there is at least one true proposition, then there are substances; that only follows if truthmaker maximalism is a necessary truth.
the possibility being raised of gunk—objects with infinite mereological descent—why not think something similar is possible in the case of grounding?
As Bennett (a, fn) says, “It is interestingly difficult to argue that grounding is well-founded”. But in the words of Schaffer (c, p) , if grounding is not well- founded, then in worlds in which grounding chains do not terminate “being would be infinitely deferred, never achieved”.
Here is one way to put the thought. If x partly grounds y, then x is partly respon- sible for the existence of y. And if x fully grounds y, then x is fully responsible for the existence of y. If z fully grounds x and x fully grounds y, then z fully grounds y, and z is fully responsible for the existence of y. If z is fully grounded, and the thing that grounds z is fully grounded, and so on ad infinitum, then nothing is responsible for the existence of y.
Unfortunately, it’s hard to give such arguments without resorting to metaphor or loose talk, which is perhaps why not many have given them. However, it’s impor- tant to note that nobody has argued for the contrary either. Though some deny that grounding is well-founded, they simply cite intuition, or respond to arguments that grounding is well-founded. We can talk about infinite chains of dependence, or explanation, or what have you, but anyone who doesn’t have the intuition that there can’t be infinite chains of grounding will presumably lack the intuition that there can’t be infinite chains of those things either. For example, Bennett: “It is an inter- esting and delicate question just which infinite series set off the regress alarm (see
Nolan ()). Nonetheless, this seems like a good candidate. It yields an infinitely expanded ontology of fact upon fact upon fact…” (, p). The thing to do in this scenario is to proceed with work under both assumptions and see what shakes out. I’m confident that the models that have theories with well-founded grounding
See Rosen (Forthcoming, p), who says that though well-foundedness is “natural to suppose” we should “leave it open” that it’s false, and Morganti (), who gives arguments against Schaffer’s arguments for well-foundedness.
will yield better results, so that’s the assumption under which I choose to proceed. So, if one accepts truthmaker maximalism, that truthmaking is a kind of ground- ing, and that grounding is well-founded, then the terminating point of every ground- ing chain that starts with a proposition ends with a substance. Thus, substances are the ultimate truthmakers. The upshot is that accepting certain meta-ontological commitments makes it so that we don’t need to admit into our ontology facts or any- thing else to serve as truthmakers, since even if we think they exist, they are grounded in substances; we only need to admit substances into our ontology.
In the final section, I’ll defend the conclusion against four prominent objections.
In order to do so, I’ll begin by discussing truthmaking, grounding, and substance.
. Truthmaking
A natural thought is that what is true depends on the way the world is; everything couldn’t be exactly the way it is and yet different things be true. There are other ways of stating this intuition; most of them are slogans, like “truths require truthmakers”,
“truth supervenes on being”, “truths don’t float free of the world”, “truths must be tied down”, or the like. For any slogan, making it precise has been a process fraught with difficulties. Yet many are not willing to give up; it seems that something in the neighborhood is true. Because of the ubiquity of supervenience talk and the work supervenience was made to do in the s, metaphysicians again looked to supervenience (plus logical relations) to help explicate truthmaking—any two worlds in which the same things exist are worlds in which the same things are true. That is:
S-Truthmaking: x makes T true=df. x exists, T is true, and necessarily, if x exists, then T is true.
A precise attempt was: it couldn’t be that everything is exactly the way it actually is and yet dif- ferent things be true. But modal co-variation doesn’t seem to capture everything that the dependence language in the slogans is supposed to.
See Fox () and Mulligan et al. (a).
A thing x makes true all and only those propositions that are true in any world in which the thing exists. It is worth noting that S-Truthmaking doesn’t guarantee the intuition that truth depends on being—that the mere existence of x is the truthmaker for T . S-Truthmaking merely asserts a sufficient condition for T ’s being true—x’s existing. But this doesn’t say that T is true because x exists. x’s existence entails T ’s truth, but for all S-Truthmaking says, x might make T true by doing many more things other than existing; perhaps in each world, x does something, or has certain properties, that makes T true. For all S-Truthmaking says, it’s possible that in one world x makes p true by being to the left of y, and in another world x makes p true by eating ice cream, and so on. Indeed, in every world in which x exists, x has all its essential properties; so for all S-Truthmaking says, it’s x’s existence and x’s having of its essential properties that makes T true.
Armstrong endorses S-Truthmaking, and gives the following argument for it.
Suppose x exists and makes p true, but does not necessitate p. So p is false in a world W in which x exists. But then there must be something else required to make p true—either another proposition q, or another thing y. But then x doesn’t make p true—x and y, or x and q, do. So x must not be making p true.
But it doesn’t take long to see that argument won’t stand, because it begs the question. It says that because x doesn’t make p true in some world in which x exists and p is true, x doesn’t actually make p true. But this assumes S-Truthmaking. There is another problem with S-Truthmaking. For consider my nose and the truth that there are more than five prime numbers. Necessarily, if my nose exists, then it is true that there are more than five prime numbers; after all, it is necessarily true that there are more than five prime numbers. And so on this characterization it turns out that absolutely everything is a truthmaker for every necessary truth. And impossible things are truthmakers for everything. This shouldn’t be.
See Armstrong (), p-.
Characterizing truthmaking as supervenience was a project bound to fail; super- venience doesn’t have the right structure, formal or otherwise. It is worth investigat- ing other options. And there are many in the literature.
• Truthmaking is truthgrounding: the truthmaking relation is the relation of grounding between substance and truth. (Schaffer, b, p) • Necessarily, if p is true, then there is some entity in virtue of which it is true. (Rodriguez-Pereyra, , p) • For every sentence which is true there must be some explanation of why it is true. (McFetridge, , p) and (Liggins, , p) • A proposition is made true by some things, the Xs, if and only if it is the brutely true pure existence claim that the Xs exist or it is true in virtue of the brutely true pure existence claim that the Xs exist. (Cameron, Forthcoming, p) • p (a proposition) is true if and only if there exists a T (some entity in the world) such that T necessitates that p and p is true in virtue of T . (Armstrong, , p). This approach combines S-Truthmaking and Rodriguez-Pereyra’s for- mulation using ‘in virtue of’. • x makes p true iff x is intrinsically such that p. (Parsons, , p).
None of these are equivalent to S-Truthmaking, at least as long as ‘x in virtue of y’, ‘y grounds x’, and ‘y explains x’ don’t mean ‘y supervenes on x’.
There obviously is not widespread agreement as to the correct statement of truth- making, so there’s nothing with which we can, without reservations, replace S-Truthmaking.
What we can do, however (and what many have in fact done), is make the definiens of S-Truthmaking into a necessary condition on truthmaking. This is what’s known as ‘Truthmaker Necessitarianism’.
T N: x makes p true only if, necessarily, if x exists, then p is true.
Truthmaker Necessitarianism has been very attractive to truthmaker theorists; indeed, many think it’s partly constitutive of truthmaking. The main objection to my view is that it allows a denial of Truthmaker Necessitarianism; I shall respond to this objection at the end.
I think Truthmaker Necessitarianism is false. Truthmaking is most closely related to grounding, and recent work on grounding should be used as a guide to formulating a truthmaker principle and applying it to particular cases.
. Truthmaking and Grounding
Contemporary metaphysics literature is replete with talk of grounding. Ground- ing is that relation that holds between all of the following pairs: a singleton set and its member, an existential generalization and each of its instances, wholes and parts
(though which grounds which is up for debate), holes in a piece of cheese and the piece of cheese, mental facts and physical facts, and the like. Often “x grounds y” is intended to mean the same thing as would “y depends on x” or “y in virtue of x”.
Grounding is sometimes called “non-causal dependence”. Schaffer says: “Ground- ing is an unanalyzable but needed notion–it is the primitive structuring conception of metaphysics. It is the notion the physicalist needs to explicate such plausible claims as ‘the fundamental properties and facts are physical and everything else obtains in virtue of them”’. (Schaffer, a, p)
Given that grounding is thought of as non-causal dependence, and given that truthmaking is supposed to capture the intuition that what is true depends (presum- ably non-causally) on the world, one might wonder whether we can characterize truthmaking in terms of grounding, or grounding in terms of truthmaking. Kit Fine
(a) has made a persuasive case that grounding cannot be characterized in terms of truthmaking. But it remains to be seen whether truthmaking can be character- ized in terms of grounding. I think it can.
Grounding and truthmaking share a number of features, in addition to being kinds of non-causal dependence. Both are cross-categorial relations; grounding can
Though since he characterizes grounding as holding between sentences, someone who doesn’t do so might find the arguments less compelling.
seemingly hold between any kinds of things, and though truthmaking must have a truth-bearer on one side (a proposition or sentence or whatever), the other side can be any kind of thing. And if the current literature on grounding is correct,, they share a number of formal features: asymmetry, irreflexivity, non-monotonicity, factivity, and counterfactuality. Grounding relationships are often stated in the form of “A grounds B”, as I did above. But just as often, we talk about grounding in form of “that A is F grounds that B is G”. For example, that the ball is round grounds that the ball has a shape.
Or, that Sam exists grounds that Sam’s hand exists. One could also put the same point differently: Sam’s existing grounds his hand’s existing. There is reason to think it isn’t always two objects that are the relata of the grounding relation. Indeed, Fine (a) sees grounding as a relation between two sentences, and Trogdon (Forthcomingb) sees grounding as a relation between facts.
Given the similarities between grounding and truthmaking and a desire for few primitives, it seems fruitful to attempt to explain truthmaking in terms of grounding.
Indeed, truthmaking can just be seen as a case of grounding with the truth of a proposition as a relatum. I suggest:
G-Truthmaking: x makes T true=df. x grounds the truth of T .
This will leave open whether Truthmaker Necessitarianism is true, since it is an open question whether Grounding Necessitarianism is true. Whereas Truthmaker
Necessitarianism has very few detractors, grounding theorists are just about split
Though I doubt that it is, for the reasons I give in Chapter .
This is very similar to Schaffer (b).
See Trogdon (Forthcominga) and Fine (a). Grounding Necessitarianism is the thesis that for any fact [p], if there are some facts the Ds that ground [p], then for all the propositions the qs that correspond to the Ds, the qs entail p.
down the middle with respect to Grounding Necessitarianism. I think we have good reason to deny Grounding Necessitarianism; namely, many of the paradigm cases of grounding hold contingently: an object and its shadow, a hole and its host, and a whole and its parts. To retain Grounding Necessitarianism, one would have to deny that these are in fact cases of grounding, or maintain that they hold of necessity. Neither of these options is palatable. Since there is good reason to understand truth- making in terms of grounding, and since there is good reason to deny Grounding
Necessitarianism, this is an additional reason to deny Truthmaker Necessitarianism.
For the remainder of the paper, I will assume that G-Truthmaking is the correct account of truthmaking. If it is, then reflection on the nature of grounding can help illuminate the nature of truthmaking. If truthmaking is grounding the truth of a proposition, then principles about grounding are also true of truthmaking. For the remainder of the paper, I shall be interested in saying what the nature of grounding can tell us about the nature of truthmaking. In particular, I’ll be interested in saying what thinking of truthmaking as a kind of grounding can tell us about what sorts of things are truthmakers.
One might wonder how this coheres with my view from Chapter —that ground is a genus and truthmaking is a species of ground. First, it is compatible with truth- making being a species of ground that ground is more fundamental than truthmak- ing. So it might be that there are multiple species of ground, and ground is more fundamental than each of them. If that’s the case, then certainly reflecting on ground is useful for understanding truthmaking. Second, even if a genus is less fundamental than a species of it, sometimes it’s helpful to reflect on the characteristics of the genus
In general, proponents include those who think that grounding holds between facts (Fine and Rosen), and detractors include those who think grounding holds between objects (Skiles and Schaffer). On this, see Trogdon Forthcominga.
On this, see Wilson (). Wilson casts her project in terms of determinables and determinates, but the same reasoning applies. She thinks mass and charge are more fundamental than any of the ways of having mass or charge, e.g. having gram mass, or having positive charge.
in order to illuminate the species. For example, figuring out what colors are like is at least somewhat helpful in figuring out what red is like, and figuring out what animals are like is at least somewhat helpful in figuring out what humans are like. We look at the characteristics that the genus has as a guide to figuring out what characteristics the species have. It’s not that every species will have only the features of the genus, but it’s a good starting point—especially when there’s promising work being done in analyzing the genus. So, I think casting truthmaking in terms of ground is still helpful and interesting, even if truthmaking is a species of ground.
. Truthmaking and Substances
.. The Criteria of Substancehood
The notion of substance has its genesis in the pre-Socratics, but was made popu- lar by Aristotle. Aristotle () says: “So if the primary substances did not exist it would be impossible for any of the other things to exist” (; Cat.b-; c.f. : ; Meta.a-). Jonathan (Schaffer, a, p) calls substances “the fun- damental units of being”.
For Aristotle of The Categories, the substances are independent, and they are the things that can neither be said of other things nor are in other things. I am neither in anything or said of anything, nor is my desk; so for the Aristotle of The Categories, both of us are substance. Humanity is said of me, so it is not a substance. The color purple is in the desk, so it is not a substance. Things that are said of things or that are in things, Aristotle thought, depend on the things of which they are said and the things they are in. Humanity depends on me (at least, my particular instance of humanity does), and the color purple depends on the desk (at least, its particular instance of purple).
So, Aristotle thought the following three are equivalent: (i) x is a substance, (ii) x
doesn’t depend on anything, and (iii) x is neither said of anything nor in anything. But certainly, for some people (including the later Aristotle), (i) and (ii) and (iii) will come apart. Some will say that there are things that are neither said of things nor in things that are not independent (perhaps my hands), and some will say there are things that are said of things or in things that are independent (perhaps platonic universals). For such people, which things are substances—the independent things, or the things that are neither said of things nor in things? I suspect that “x is a substance if and only if x doesn’t depend on anything” is Aristotle’s analysis of substance, and he thought the things that satisfy it are the things that are neither said of things nor in things.
I find it unlikely that these are meant to be definitions of ‘substance’. If they are, then it would be impossible to disagree with them; but many have done so. More likely, these are attempts to analyze a concept we all share. But this is a slightly different case from ‘knowledge’ and ‘humility’ or other concepts we try, as philoso- phers, to analyze. In those cases, there is widespread agreement about which things we know and which actions are displays of humility. But there is no such widespread agreement about which things are substances. There is some agreement, however; most people agree that if God exists, God is a substance. Most agree that electrons, if they exist, are substances. And when Jonathan Schaffer (b) says that the Cos- mos is the only substance, people try to argue with him, presumably thinking they and he are using ‘substance’ to mean the same thing; and most of us think that they are disagreeing with him.
So in this sense, ‘substance’ seems more like ‘abstract’ or ‘concrete’ or ‘intrinsic’ than it is like ‘mereological simple’. And giving an analysis of ‘x is a substance’ is more like giving an analysis of ‘x has F intrinsically’ than giving an analysis of ‘x is a mereological simple’. And giving the necessary and sufficient conditions for being
Since “x is a mereological simple” is defined as ‘x lacks proper parts’. Of course, it’s a further question which things lack proper parts.
a substance is more like giving the necessary and sufficient conditions for having a property intrinsically than it is like giving the necessary and sufficient conditions for being a mereological simple. In the former case, there is a concept that we all share to at least some degree, and we are trying to figure out what sorts of things answer to that concept. In the latter case, we have a definition (x is a simple =df x lacks proper parts), and we’re trying to figure out what sorts of things satisfy the definition. But we don’t agree upon a substitution instance for p in the following schema: x is a substance=df p.
There are several proffered analyses of substancehood. E.J. Lowe offers the fol- lowing account of substance: “x is a substance if and only if x is a particular and there is no particular y such that y is not identical with x and x depends for its ex- istence on y”. Lowe defines ‘x depends for its existence on y’ as ‘Necessarily, x exists only if y exists.’ So, substances are particulars that are such that there isn’t anything that it’s impossible that they exist without. Michael Gorman offers a similar definition, but makes a few changes. He defines substance in the following way: “x is a substance=df x is a particular, x is unified in the right way, and there is no particular y such that y is not identical with x, y is not one of x’s parts, and the identity of x depends on the identity of y.” He adds the unity clause and allows for objects to depend on their parts. This is so as to allow hylomorphic compounds, garden-variety composite objects, and the like to be substances.
Koslicki argues that neither of these accounts allow for non-particulars, proper
(Lowe, , p). I’ve substituted “if and only if” for “=df”, because Lowe offers this as a substantive analysis.
(Lowe, , p).
One reason to reject this modal analysis is that if there is more than one necessary being, nothing is a substance; and if there is one necessary being, it is the only substance.
(Gorman, , p).
parts, or hylomorphic compounds to be substances, and that a theory of substances shouldn’t automatically rule these out. She thinks that Gorman was on the right track in adding “x is unified in the right way”, and suggests that the way forward for theories of substance is to abandon talk of independence and instead frame the criteria in terms of unity. Of course, this is a break from history. Hoffman and Rosenkrantz: “…Aristotle,
Descartes, and Spinoza, have tried to characterize substance in terms of some sort of independence criterion, but the consensus is that none of them has provided an adequate account of the requisite notion of independence” (, p). That is, most think that, even though we can’t define “x is independent”, independence is the right criterion for substancehood. But if we accept talk of ground, then ‘x is indepen- dent’ can be defined: ‘x is independent if and only if nothing grounds x’. If we accept that definition, then at least one roadblock to an independence criterion of substancehood—the notion of independence isn’t well enough understood—can be resisted.
Hoffman and Rosenkrantz also offer arguments against independence criteria of substancehood, giving what they take to be counterexamples. For example, a stone arguably couldn’t exist without its parts, surface, properties, and location. And a donut arguably couldn’t exist without holes existing. And so on. These arguments rely upon an assumption that many now think is mistaken: that ‘x depends on y’ means, or at least entails, ‘x could not exist without y’. But it is far from clear whether this is true. Things can depend on their parts even though they could have
We might still want to define ‘x is independent’ differently, but the point is just that we can define it, contrary to the prevailing opinion.
See (Hoffman and Rosenkrantz, , p-), which arguments are reproduced in Hoffman and Rosenkrantz () and Hoffman and Rosenkrantz ().
See Trogdon (Forthcomingb) and Skiles (MSa) for discussion of this, where ‘depends’ is replaced with ‘grounds’.
lacked some of them. That is, it may well be that (i) x is a part of y (ii) y depends on x, and (iii) it is possible that y exists and x does not exist. At any rate, the denial of the conjunction of (i)-(iii) is a substantive assumption.
I think independence (understood in terms of grounding) is the right criterion for substancehood. The substances are the grounds of all other things, and grounding goes in the same direction as parthood: if x is a proper part of y, then x partly grounds y. So things with proper parts are partially grounded and thus are not substances.
One might disagree that partial grounding goes in the direction of parthood, either by thinking that parthood bears no interesting relation to grounding, or by thinking that grounding and parthood go in the opposite direction: things ground their parts. I object to the view that things with proper parts ground those proper parts. Consider an electron that has no proper parts and is not a proper part of anything: is it a substance? Suppose not. Then something grounds its existence; but there are no plausible candidates. Suppose it is a substance. When it becomes a part of an atom, it ceases to be a substance. When it becomes separated from the atom, it becomes a substance again. And so on. Not a very stable existence, and yet substances are supposed to be the metaphysically privileged things! The better thing to say is that the electron is a substance, and is always a substance.
A second objection to the thesis that wholes ground parts starts with the point that things are very often parts of many other things. For example, the electron is a part of the atom, the atom is a part of the molecule, the molecule is a part of
In light of the recent rise of neo-Aristotelian hylomorphic metaphysics, we might wonder whether the following is true: if x is a constituent of y, then x partly grounds y. Most neo-Aristotelians would deny this; substances ground their constituents, and not vice versa. This is because constituents are things like universals and tropes and the like, and those things depend on the substances of which they’re constituents. Substances can depend on their parts without depending on their constituents. For more on hylomorphic structure, see Rea () and Koslicki ().
Note that the classical theist who thinks God grounds its existence also has reason to deny that things with proper parts ground the existence of those parts, since they’ll think God grounds the existence of the thing and its parts.
the cell, the cell is a part of the hand, and the hand is a part of me. If parthood is transitive, then the electron is a part of the atom, the molecule, the cell, the hand, and me (among other things). If wholes ground their parts, which whole (of which the electron is a part) grounds the electron? The most immediate one? The biggest one?
All of them? According to this objection, there is no principled way of deciding.
.. Substances as Truthmakers
In addition to wondering what the criteria for being a substance are, we might also wonder what sorts of things satisfy the criteria of substancehood. Aristotle first thought in The Categories that every subject is a substance, and then precisified (or changed) his view in The Metaphysics. He thought that matter, form, and compound are all subjects, but that matter can’t be a substance since it could exist without form, but if it exists without form it can’t be a subject, and if it’s a subject then it can’t exist by itself. So, just the forms and the hylomorphic compounds (things composed of matter and form) are substances. And he says that the paradigm cases of substance are forms, where forms are to be understood not as Platonic universals but as particular property-instances. This fits best with his view that “some things can exist apart and some cannot, and it is the former that are substances” (Metaphysics
Book , ch).
Descartes thought there were two kinds of substances: material stuff and mental things. Leibniz thought it was monads, both uncreated (God) or created (every- thing else). Spinoza was famously a substance monist; he thinks the only substance is the Cosmos, or God. Locke talked a lot about substances, but it’s not exactly clear what he ends up believing about them. It’s likely that he accepted a sort of
See Descartes (), Volume , p.
See (Leibniz, , §).
See Spinoza (), Book , proposition .
“bare substratum” theory, where substances are nothing but the things that hold properties together; but he doesn’t seem too happy that he has to accept such things, because we can’t have any clear and distinct ideas of them—we can only have ideas of simple things (like properties), and we posit something—a substance—in which they inhere. These are some of the views of what things are substances. So, these kinds of things are the options for the ultimate grounds. And thus, if truthmaking is to be understood in terms of grounding, then one of these kinds of things are the ultimate truthmakers.
Some views of what things play the substance role will allow one to accept Truth- maker Necessitarianism and that substances are truthmakers. I still think that those who accept these views should not think that Truthmaker Necessitarianism is true as a matter of reflection on truthmaking or grounding, but rather that it just happens to be true because of the nature of substances. The views in question are mereological essentialism, hylomorphic compound essentialism, and extreme substance essential- ism.
Suppose you are a mereological essentialist who thinks that a thing is grounded by its parts. Usually we think that a thing could have had different parts, but for the
ME, the parts of a thing are essential to it. So a thing couldn’t exist without it’s parts. Suppose the xs are the truthmakers for p, where p is a proposition about what the xs compose. The thing that the xs compose–y, say— can’t exist unless the xs exist.
So, in any world in which p is true, y exists, and in any world in which y exists, the xs exist. So any world in which p is true is a world in which the xs exist. Could the xs exist and p be false? They could, if they composed something else. So the mereological essentialist in question must also think that whatever the xs compose, it is necessary that they compose that thing—not strictly entailed by mereological
See Locke (), Book II.
essentialism, but a view that goes quite naturally with it. Someone who holds these views need not deny Truthmaker Necessitarianism.
If you’re a hylomorphic compound essentialist, then you think hylomorphic com- pounds essentially have the constituents they do. If you think hylomorphic com- pounds are substances, then you think that they ground their matter and form. Since it couldn’t have been that the hylomorphic compound exist and the matter and form not exist, then grounding necessitarianism is preserved, at least with respect to hylo- morphic compounds.
If you’re an extreme substance essentialist, then you think that it’s essential to the substances that they are substances, and that they have the parts and properties they have. So, any world in which those substances exist, they have exactly the parts and properties they actually have. So at least grounding necessitarianism is preserved with respect to the substances’ parts and properties.
. Ultimate Truthmakers and Intermediate Truthmakers
If truthmaking is a kind of grounding (as I argue in Chapter ) and substances are the ultimate grounds (which they are if the independence criterion is right and independence is to be understood in terms of grounding), then it is quite a natural thought to think that substances are the ultimate truthmakers. Indeed, when one begins to think of truthmaking—when one starts having the truthmaker intuition— one usually thinks of the truthmaker role as being played by substances. And those who think that what is true is grounded in what there is normally take the grounds to be substances.
Indeed, the intuition that substances are truthmakers is so strong that even some truthmaker theorists who accept Truthmaker Necessitarianism have substances make
The classic truthmaker theorists, I’m told in conversation by Kevin Mulligan, all thought that substances were truthmakers. This includes Mulligan et al. (a) and Mulligan () .
true essential predications about them. They are forced to deny that substances can make true accidental predications because they don’t necessitate them, but even though facts also necessitate essential predications, they retain substances as truth- makers for essential predications. The best explanation for this is that they are trying to preserve as much of our intuition regarding the sorts of things that are truthmakers (substances) as they can. Since substances don’t necessitate accidental predications and most other propositions that aren’t essential predications, people end up aban- doning substances as truthmakers. These people think they need a necessitater for truths to be truthmakers, so they end up admitting facts into their ontologies to serve as truthmakers. Others admit tropes. We can accept that substances are truth- makers for essential predications and still retain Truthmaker Necessitarianism, but if we want to retain Truthmaker Necessitarianism we must admit into our ontology something else as truthmakers for accidental predications.
But once we deny Truthmaker Necessitarianism, we can accept that substances are truthmakers for accidental predications as well. For every truth T , there is a substance x such that x is the ultimate truthmaker for T . But there might be an intermediate truthmaker for T as well, and we might want that intermediate truth- maker to necessitate T . (I’m thinking the most natural intermediate truthmakers are facts, tropes, or the like.) We needn’t admit intermediate truthmakers, since propo- sitions are made true by the ultimate truthmakers. But those who like Truthmaker
Necessitarianism and want to retain the necessitation intuition might want to admit them. And we may as well, since they are grounded in the substances, and thus are
There are no assertions of this yet in print, but several of my neo-Aristotelian friends accept it in manuscripts I’m not allowed to cite yet. Schaffer (b) also accepts that substances are truthmakers, but he thinks the Cosmos is the only substance, and that is essentially the way it is; so he can also retain Truthmaker Necessitarianism and have the Cosmos make true all truths.
See Rodriguez-Pereyra (), Rhoda (), Pendlebury (), Armstrong (), (Ruben, , p), Hoffman (), Russell (), and (Cameron, c, p).
See Martin (), (Mulligan et al., a, p-), (Lowe, , p-; p-).
no addition to our ontology. This allows us to retain a necessitater for truths, but not admit that necessitater into our ontologies.
Allowing intermediate truthmakers preserves the intuition that truthmakers ne- cessitate. The intermediate truthmakers can necessitate. This might sound like we still have to admit facts or tropes or something like them into our ontology. But we don’t; we only have to admit ultimate truthmakers (the fundamentalia) into our ontology. Since the intermediate truthmakers are grounded in the ultimate truth- makers, and we only have to admit what we take to be the ungrounded things into our ontology, we can posit intermediate truthmakers. Much like we can say, “there are shadows” without admitting shadows into our ontology, we can say, “the fact that there are dogs makes it true that there are dogs”, without admitting facts into our ontology.
. Objections and Replies
.. Objection : Truthmaker Necessitarianism
Substances don’t necessitate all the things that are true., So if only substances are ultimate truthmakers, then Truthmaker Necessitarianism is false. But Truth- maker Necessitarianism is not false. So substances are not the ultimate truthmakers.
Recall Truthmaker Necessitarianism:
Truthmaker Necessitarianism: For all x and T , x makes T true only if necessarily, if x exists, then T is true.
While this doesn’t give us a fully general account of truthmaking, it does place
This depends on one’s view of what things are substances. If one thinks that Jonathan Schaffer is right that the Cosmos is the only substance, and if one added to that the thought that the Cosmos had all its parts essentially and essentially lacked any other parts, then one could think the substance necessitates all the truths.
I take it that there are ways to make grammatical sense of ‘x necessitates y’, where the object picked out by ‘x’ is a substance, such that ‘substances aren’t the right kinds of things to stand in the necessitation relation’ isn’t a deep objection.
serious constraints on what sorts of things can be truthmakers. Truthmaker Ne- cessitarianism is orthodox among truthmaker theorists; indeed, many think neces- sitarianism is partly constitutive of truthmaking. Proponents of Truthmaker Ne- cessitarianism admit that they have no argument for it, but they claim that it seems intuitive to those who think truthmaking has something going for it. But of course, we shouldn’t abandon a thesis just because we can’t think of a good argument for it. There are many philosophical positions we hold that we think don’t require an argument. Truthmaker necessitarians think that Truthmaker Necessitarianism is such a position.
I think Truthmaker Necessitarianism is false. There are several ways to argue against a thesis in metaphysics. One is to show that the thesis is false. Another is to show that is unmotivated; there is no reason to accept it. A third is to show that the thesis requires more ontology or ideology than its denial; accepting it violates
Okham’s Razor. In this section, I advance four arguments against Truthmaker Ne- cessitarianism. Three of them are arguments that Truthmaker Necessitarianism is unmotivated. But the first is an argument that Truthmaker Necessitarianism violates
Okham’s Razor.
First, Truthmaker Necessitarianism requires more ontology and ideology than its denial. Namely, it requires facts, or proposition-like things. If Truthmaker Necessitarianism is true, then for each true proposition p, there is something that exists if and only if p is true. More precisely: Necessarily, for all propositions p, if
Asay and Baron (), Armstrong (), Fox () makes the latter claim, Armstrong (), Mulligan et al. (a), (Rodriguez-Pereyra, , p).
(Cameron, c, p-), Armstrong ().
Think of the way many non-skeptics respond to Moore’s argument against skepticism.
Assuming that Truthmaker Necessitarianism is a claim about ultimate truthmakers, and that whatever one takes to be ultimate truthmakers must be in one’s ontology.
It can’t be p, since presumably p can exist and be false, and also because truthmaking is generally
there exists a world W such that p is true at W , then there exists some x at W such that for any world W ∗, if p is true at W ∗, then x exists at W ∗. This requires a lot of things! Clearly these things are nothing like you and me, or ordinary properties or abstracta; they are a very odd sort of thing indeed. Many have chosen to call them
“facts”, as though that makes them less suspicious. Normally when one says “these are the facts…”, one proceeds to state true propositions. So one might have thought that our ordinary use of ‘fact’ just meant ‘true proposition’; but that can’t be the case if truthmaking is irreflexive, since true propositions can’t make themselves true.
Alternatively, one might have thought that ‘fact’ just picked out an obtaining state of affairs, but again this cannot be; states of affairs can exist but not obtain, whereas the entities in question can only exist when their corresponding proposition is true.
So Truthmaker Necessitarianism forces one to admit into one’s ontology a new kind of entity, and an altogether mysterious one at that.
Second, Truthmaker Necessitarianism says that x makes y true only if necessarily, if x exists, then y is true. This is an instance of the following schema:
F -maker Necessitarianism: x makes y F only if there is some G such that necessarily, if Gx then F y.
But F -maker Necessitarianism is implausible. There are many cases in which something can make something else F by being G, even though the former’s being G doesn’t necessitate the latter’s being F . F -maker Necessitarianism, then, is false.
Take, for example, the situation in which F is ‘angry’. It certainly seems that I can make my sister angry, even though there’s no predicate/property such that my having it entails that my sister is angry. (In some worlds, my sister is slightly more long- suffering and never gets angry no matter what I do.) Also, my stomach’s being empty makes me hungry, even though there are worlds in which I am never hungry, despite sometimes having an empty stomach. Examples abound. F -maker Necessitarianism thought to be irreflexive.
is false. Of course, F -maker Necessitarianism’s being false doesn’t entail that all instances of it are false. But if we are to believe that F -maker Necessitarianism is false but Truthmaker Necessitarianism is true, there should be something special about having the property being true that makes Truthmaker Necessitarianism true. But there is no reason to think that there is something special about truth that explains why Truthmaker Necessitarianism is true even though the general schema, F -maker
Necessitarianism, is false.
Admittedly, it’s not clear that ‘make’ means the same thing in each of these cases.
This is because it’s not clear what ‘make’ means in either of the contexts, which en- tails that we don’t really know what ‘make’ means when we say “x makes p true”. But if we’re not relying on what we know of what it takes for something to make something have a property, then it’s not clear whether our intuitions in favor of
Truthmaker Necessitarianism lend any support to it. I have proposed a way of un- derstanding what ‘make’ means in ‘x makes p true’—‘x grounds the truth of p’. If this is the right way of understanding the making of truthmaking, then since Grounding
Necessitarianism is not at all obvious, neither should Truthmaker Necessitarianism be.
Third, Truthmaker Necessitarianism is supposed to be a response to those who want to make truth depend on the world. It’s supposed to “tie down” truths, so that, e.g., “there are dinosaurs” can’t be true unless something in the world makes it so.
But if that is the motivation to accept Truthmaker Necessitarianism, then there is no reason for a further constraint—that whatever makes it true that there are dinosaurs necessitate that there are dinosaurs. The truth of “there are dinosaurs” can be tied down by something without the thing to which it’s tied necessitating it. Again, it is admittedly unclear what “ties down” is supposed to mean in this context. But then it’s equally unclear that it means anything like “necessitates”. So it’s not at all obvious that the intuition that x must tie down the truth of p supports
the idea that x must necessitate the truth of p. And the same goes for all other truthmaking metaphors that are supposed to motivate Truthmaker Necessitarianism.
Fourth, suppose it is the case that we have the intuition that truthmakers are supposed to necessitate. Still, the necessitation intuition can be captured without
Truthmaker Necessitarianism. The necessitation intuition is a conjunction of two theses: (i) truth must depend on the way the world is, and (ii) the way the world is must necessitate the truth of the truths. As I pointed out in my second objec- tion, truths can depend on the world without the thing(s) on which they depend necessitating their truth. So (i) is relatively easily satisfied without Truthmaker Ne- cessitarianism. But (ii) can also be satisfied without Truthmaker Necessitarianism; for any truth p, the way the world is can entail the truth of p without there being some thing—the truthmaker for p—that necessitates the truth p.
For example, suppose that x is F .[x is F], then, is true. To satisfy (i), the truth of [x is F] must depend on the way the way the world is. Suppose that y is the thing in the world that [x is F] depends on for its truth. In order for Truthmaker
Necessitarianism to be false, y cannot necessitate that x is F ; so suppose it doesn’t.
But (ii) must be satisfied. The puzzle is how to satisfy (ii) without the truthmaker for
[x is F] (which is y) necessitating its truth.
The solution to the puzzle is to be found in theories of properties. Every theory of properties offers a biconditional: Necessarily, for any x and F , x is F if and only if p. And whatever it is that accounts for the truth of [x is F ] necessitates the truth of
[x is F]. For example, if you’re a realist about properties, you think that, necessarily,
[x is F] is true if and only if x instantiates F ness, and you think that if [x is F] is true, one way the world is is that x instantiates the property F ness. In such a case, x’s instantiating the property F ness entails that [x is F] is true. If you’re like Lewis, you
Andrew Bailey suggested this idea in conversation.
I use brackets around a declarative sentence to name the proposition expressed by the sentence.
think that necessarily, [x is F] is true if and only if x is a member of the set of F s; and if [x is F] is true, then one way the world is is that x is a member of the set of F s. In such a case, x’s being a member of the set of F s entails that [x is F] is true. If you’re a resemblance nominalist, you think that necessarily, [x is F] is true if and only if x resembles the other F -things, and that the world is such that x resembles the other F -things. In such a case, x’s resembling the other F -things necessitates that x is F .
And so on.
The general point is that, for any theory of properties, x’s bearing the right rela- tion to something will necessitate that [x is F] is true. So someone who doesn’t take a stand on what theory of properties is true can still respect the necessitarian intuition while denying Truthmaker Necessitarianism. She can say that there is some relation
R that x must bear to something in order for x to have the property P (where ‘x is
F ’ is true just in case x stands in R to P ), and x’s standing in R to P necessitates that
[x is F] is true. Of course, this isn’t what makes [x is F] true, because x’s standing in R to P isn’t a thing. But this satisfies (i) and (ii) without requiring Truthmaker
Necessitarianism.
One might want to say that x’s standing in R to F is also a truthmaker for [x is
F]—perhaps the only truthmaker. But of course, x’s standing in R to F is grounded in the existence of x and the existence of F . This allows us to eliminate x’s standing in R to F from our ontology. And recall that the goal of this section is not to argue that x’s standing in R to F is not a truthmaker for p, but rather that even if substances are truthmakers, the truthmaker necessitarian demand can still be met.
This general strategy even holds for someone who doesn’t think there are proper- ties, so long as she thinks that, for every true predication, there is some condition on the world that must be satisfied in order for that predication to be true. I’m thinking of someone who agrees that it isn’t just a brute fact that [x is F] is true, but who doesn’t take a stand on what theory of predication is true, or is perhaps even skepti-
cal that there is a true theory of predication. She can say that there is some condition C that the world must satisfy in order for [x is F] to be true, and the world’s satisfy- ing C necessitates that [x is F] is true. Of course, this isn’t what makes [x is F] true, because the world’s satisfying C isn’t a thing. But this satisfies (i) and (ii) without requiring Truthmaker Necessitarianism. So, the non-truthmaker-necessitarian can satisfy (i) and (ii), providing for every truth a thing in the world on which the truth depends, and having the way the world is necessitating the truth—but without what necessitates the truth being the thing that makes it true, since what necessitates the truth isn’t a thing. Indeed, the very thought that what necessitates that [x is F] is true is the very thing that makes it true that [x is F] has led to the reification of facts and the bloating of ontology and ideology. A better thought is that, rather than what makes it true that [x is F] being the thing that necessitates the truth of [x is F], what it makes it true that [x is F] is the thing that grounds the truth of [x is F]. This allows for a smaller ontology, but still maintains the existence of facts.
There are three distinct advantages in denying Truthmaker Necessitarianism. First, it allows us to eliminate facts from our ontology. This is beneficial because it makes for a smaller ontology. But not only does it eliminate a lot of things and one partic- ular kind of thing, it eliminates a kind of thing that for many of us is quite mysterious. And if one denies Truthmaker Necessitarianism and adopts the meta-ontology I’ve suggested in this paper, one can still maintain that there are facts, and facts can play all the theoretical roles they do in other ontologies.
This is not to say that there is something that necessitates the truth, but it isn’t a thing. Rather, it’s to say that there’s no thing that necessitates it, but it is necessitated. It’s similar to saying that the football team surrounded the building, even though there’s no thing that surrounded the building.
According to the meta-ontology, one shouldn’t admit more things into one’s ontology than one needs to. To put it on a bumper sticker: minimize fundamentalia, maximize existents. See (Schaffer, a, p), Armstrong (), Cameron (b), and Melia (). For a dissenting view, see deRosset (Forthcoming).
Second, denying Truthmaker Necessitarianism helps us provide truthmakers for propositions about the past and future. One persistent objection to presentism is its inability to give an account of why propositions seemingly about past and future objects are true, given that those seemingly existent past and future objects don’t actually exist. If one takes up the challenge of responding to these objections, it is incumbent on one to provide a present thing that entails, say, that dinosaurs existed— given Truthmaker Necessitarianism. If one accepts G-Truthmaking, this makes the job at least somewhat easier. Whatever makes true the propositions wholly about the past and future needn’t entail them. So as long as one can provide a story about how the putative truthmaker grounds the truth of the proposition, showing that the putative truthmaker could exist without the proposition being true is no objection.
In short, G-Truthmaking is helpful because we don’t need parts of the present to entail the truths of the past and future.
Third, denying Truthmaker Necessitarianism helps us with truthmakers for attri- butions of property instantiation. One proposition that seems true is that the phone on my desk is purple. But if this is true, then it requires a truthmaker. What makes it true that the phone on my desk is purple? A natural thought is that it’s my phone, and the property being purple. But of course, my phone and the property being purple could exist without the proposition that my phone is purple being true; this natural response runs afoul of Truthmaker Necessitarianism. Because of objections such as these, those who think that the proposition that my phone is purple is true are forced to find something that could necessitate it. They’ve come up with facts, tropes, and states of affairs—all in an effort to satisfy Truthmaker Necessitarianism.
But G-Truthmaking allows us to say that my phone and being purple make it true that my phone is purple, even though it’s possible that both exist and the proposi- tion not be true. Or, if being purple isn’t a substance, then my phone makes it true that my phone is purple. Or, if my phone isn’t a substance, the simples composing
it make it true that my phone is a substance. One might wonder how my phone (assuming it’s a substance) or the simples com- posing my phone (assuming my phone isn’t a substance but the simples composing it are substances) could make it true that my phone is purple. In response, consider the other candidate truthmakers—for example, the fact that my phone is purple, or my phone’s purple trope. Neither the fact nor the trope is a substance, so it must be grounded in some things. Presumably one of those things is my phone, and perhaps there are other things. If there are other things, then we must look at whether they are substances. If they are, then the natural thing to say is that they, plus my phone, ground the fact that my phone is purple, or ground my phone’s purple trope. Since truthmaking is a kind of grounding, why would we not say that they also make it true that my phone is purple? After all, they (the substances) are the only things in one’s ontology, so they are the only candidates to be the ultimate truthmakers.
One might still be resistant to this idea, thinking that there has to be something more than my phone to make it true that my phone is purple. I would respond that such people probably think that purpleness is a substance. So, then my phone and purpleness—both substances—make it true that my phone is purple. But some people might think that even that’s not enough—there has to be something that at- taches purpleness to the phone. This is most often expressed in an explicitly Truth- maker Necessitarian way: “the phone and purpleness could exist and the phone not be purple”. I would respond that those people either need to give an argument for
Truthmaker Necessitarianism, if that’s the motivation behind their objection, or they need to think that the instantiation relation is a substance. And I’d warn them that they should probably stop there; thinking that something grounds the fact that the instantiation relation relates my phone and purpleness gets one well on the way to- ward Bradley’s regress.
It would, of course, be helpful to give some further characterization of what it
takes for x to make p true. Truthmaker Necessitarianism was attractive for at least one reason: it said that x’s necessitating p is sufficient for x’s making p true, and we know what necessitation is. So, if Truthmaker Necessitarianism is true, then we know what truthmaking is. If it’s not, we don’t.
I have two responses. First, we don’t actually know what necessitation is, when one side of the necessitation operator is flanked by an object or the name of an object. We know that ‘p necessitates q’ means that ‘p entails q’; but entailment is not a relation that an object can stand in to a proposition, so it’s not obvious that we know what it means for an object to necessitate a proposition. Second, this might very well be a case of “understanding due to familiarity”. There was a lot of distrust of modality in the s, until Kripke gave a possible worlds semantics by which to model modal discourse. Now, because we have formal models and we talk about it a lot, we understand modal notions. We could be in the same position with dependence notions like truthmaking—more discussion and a formal model or two of grounding, and we’ll become more familiar with it and understand what it takes for x to make p true.
It may turn out that on our best models, it won’t be the case that present things can make true true propositions about the past or the future, or that properties and objects can jointly make true property attributions. But for now, we can leave it open, and that’s an advantage.
.. Objection : Explanation
According to this objection, truthmaking is closely tied to explanation. We need truthmakers because we need to explain why certain things are true. And expla- nations (at least, full explanations) entail. This is a version of the above objection that’s based on Truthmaker Necessitarianism. This provides another argument for
Truthmaker Necessitarianism: (i) truthmaking is a kind of explanation, and (ii) ex-
planations must entail, so (iii) truthmakers must entail. By way of reply, I am not convinced that either (i) or (ii) is true. I am not convinced that truthmaking is a kind of explanation. Truthmaking is a kind of grounding. And grounding is a relation that holds between many kinds of things. Sometimes those things are both propositions. And when the truth of one proposition grounds the truth of another, then those propositions might also stand in an explanation relation.
But not all cases of grounding are cases of explanation. And I see no special reason to think that all cases of truthmaking are cases of explanation. Grounding, and truthmaking, are purely matters of metaphysics. Whatever explanations are, they are not solely matters of metaphysics. I am also not convinced that explanations must entail. There is a vast wealth of literature on this topic that I don’t want to wade into. But many models of expla- nation do not require for explanations to entail. If causal explanations are expla- nations, then explanations needn’t entail. If deductive-nomological explanations are explanations, then explanations needn’t entail. If there can be probabilistic explana- tions, then explanations needn’t entail. If explanation has a pragmatic element, then explanations needn’t entail.
Anyone who wants to push an explanation-based argument that truthmakers are not substances has three options. First, one can directly argue that truthmaking is an explanatory relation and that truthmakers must entail. Second, one can argue that truthmaking is an explanatory relation and argue against the disjunction of causal, D-
N, probabilistic, and pragmatic theories of explanations. Or third, one can argue that truthmaking is an explanatory relation, and an explanatory relation of a particular kind, and that that particular kind is an entailing kind.
Liggins () has argued that truthmaking ought to be understood as explanatory; in particular, he thinks that a request for a truthmaker for p is a request for an explanation of why p is true. He is extending a line of thought from McFetridge (), who says that the truthmaker principle is just: For every sentence which is true there must be some explanation of why it is true. Smith and Simon () construe the request for a truthmaker as a request for ontological explanation, which is an
Finally, explanations are not things in someone’s ontology. At best, the things that the explanations are about are in someone’s ontology; but those things do not stand in entailment relations. So maybe this much is true: if p is a full explanation for q, then p entails q, and for any x such that p is “about” x, x is a truthmaker for q. But that is consistent with my proposal, and it doesn’t have it that x necessitates q.
.. Full Truthmaking and Partial Truthmaking
According to this objection, my view has it that at least one proposition is such that there’s nothing that’s a full ultimate truthmaker for it. Such a proposition may have a few intermediate truthmakers and a few ultimate truthmakers; but no ultimate truthmaker, taken by itself, is a full truthmaker for it. This is because there may be more than one truthmaker for p that is ungrounded, and none of them is, on its own, a full truthmaker for p. (Of course, there may be an intermediate truthmaker for p that’s a full truthmaker for p.) I am, of course, free to deny that such cases are possible. But such a move might seem unacceptably ad hoc. And in any case, I don’t see it as an objection. There are some propositions that have full ultimate truthmakers but are such that there’s nothing that’s a full ultimate truthmaker for them. This is like saying there are some four-part harmonies that are sung, but there’s nothing that sings them; rather, some people together sing them. And I see nothing wrong with that. I think the following are both true: ∃p¬∃x (x is a full ultimate truthmaker for p), and ∀p∃xs (xs are full ultimate truthmakers for p). The xs taken together are full ultimate truthmakers for p, and each of the xs is an ultimate truthmaker for p, even though no one of the xs is a full truthmaker for p. ontological posit that explains propositions.
. Conclusion
In this paper, I gave an meta-ontology in the service of allowing for a minimal on- tology. The minimal ontology is comprised solely of substances. The meta-ontology has it that the substances ground the existence of all other things and ground the truth of all true propositions. The ontology shares the advantages of other small ontologies with respect to parsimony, but it fares better with respect to fit with com- mon sense. There are several putative objections to the meta-ontology, but I hope to have shown that they are not devastating.
CHAPTER
THE FUNDAMENTAL QUANTIFIER
Within metaphysics there is ontology, and there is meta-ontology. For the last
fifty years or so, those who do ontology (hereafter ‘ontologists’) have been trying to answer the question, “What is there?” A typical ontological question schema is
“Are there xs?”, or “Do xs exist?”, where ‘xs’ is filled in with ‘tables’ or ‘temporal parts’ or the like. Meta-ontologists, on the other hand, have been trying to answer questions about ontological questions: “are ontological questions meaningful?” , “do ontological questions have mind-independent answers?”, “are ontological dis- putes substantive?”
Ontologists have usually presupposed an affirmative answer to the meta-ontological questions. But an increasing number of metaphysicians have been answering one or more of the meta-ontological questions in the negative; following Bennett (), I shall call them ‘dissmissivists’. In support of their position, dismissivists often argue that ontological debates have been raging for years, and we are no closer to resolving them than we have ever been; therefore, there must be something wrong with the enterprise of ontology. Another reason dismissivists cite in favor of their
Asked and answered in Quine () with “everything”, and then discussed repeatedly since.
Most, though not all, have treated “are there xs’?’ and “do xs exist?” as meaning the same thing.
Though Jenkins (Forthcoming) shows that the answers to the three meta-ontological questions are independent.
The dismissivist camp includes Bennett (), Carnap (), Chalmers (), Goggans (), Hirsch (), Hofweber (), Putnam (), Sidelle (), Sosa (), Thomasson () and (), and van Fraassen ().
dismissivism is that ontological questions have obvious answers; the usual example is the question of whether there are composite objects like chairs, but similar things can be said about the questions of whether there are properties, fictional characters, musical work, and more. Those who deny the existence of such things—“austere ontologists”, I shall call them—are not just wrong, but obviously wrong, according to the dismissivists. “Of course there are chairs (and properties and fictional charac- ters and musical works),” the dismissivist says, “and we needn’t take seriously any argument to the contrary.”
In another arena of metaphysics, talk of fundamentality, fundamental things, and fundamental language (or languages) has taken center stage. A number of metaphysi- cians have defended the view that the ontological question ought not be, “What is there?”, but rather, “What is fundamental?”
This paper is an exercise in meta-ontology. I will offer the ontologist a response to the dismissivist’s arguments against the fruitfulness of doing ontology. The ontol- ogist should say that the members of the two sides of the ontological debates that dismissivists have targeted are using different quantifiers, and that the austere ontolo- gist’s quantifier is a restriction of her opponent’s quantifier. The first conjunct—that there are multiple quantifiers at play in these debates—has also been argued by Eli
Hirsch. However, Hirsch’s view is much more radical; he explicitly claims that
See, for example, Schaffer (), Schaffer (a), and Williams (). Fine () says we should investigate the question of what really exists, which I take to be the same question. For some, the answer to the question is mereological simples. (See Cameron () and (forthcoming), and Sider (MS).) For others (like Schaffer (b)), the answer is the world. They all agree that there are tables, but nobody thinks they’re fundamental.
I am taking quantifiers to be semantic values of quantificational expressions, and not themselves expressions. So by ‘the English quantifier’, I mean the semantic value of the phrase ‘there is’ or ‘there exists’ when spoken or written by a typical English speaker in a normal context; this semantic value may or may not be identical to the semantic value of ‘es gibt’ when spoken or written by a typical German speaker. So, it is consistent with my view that the English and German quantifiers are identical, and it is consistent with my view that the two are distinct.
See his (), (), and ().
neither quantifier is a restriction of the other. On my view, those austere ontologists who answer the ontological questions in unintuitive ways (that is, by saying that there aren’t any tables or chairs or prop- erties or fictional characters) are restricting their attention to the things ontologists should care about—the fundamental things—and saying that tables and chairs and properties and fictional characters aren’t among them. When they say, “there are no tables” and “there are no properties” and the like, these austere ontologists are using a more fundamental quantifier (which I shall call ‘∃F ’) than the English quan-
tifier (which I shall call ‘∃E’), and ∃F is a restriction of ∃E. The reason the answers that austere ontologists give to the ontological questions seem unintuitive is that we take the austere ontologists to be using the ordinary English quantifier, but in fact they are using a more fundamental quantifier that looks and sounds the same as the
English quantifier.
Though there are many advocates of a fundamental quantifier (hereafter ‘funda- mentality theorists’), there are many others who claim not to understand what the fundamental quantifier is, or what its advocates take it to be. Some of them are dismissivists, and some are Quineans (more on Quineanism later). Fundamentality theorists have not done much to help these others understand their talk of quanti-
fier fundamentality. I aim to do better. I will explain the fundamental quantifier in terms every metaphysician can understand: ‘quantifier’, ‘quantifier restriction’, and other familiar logical notions. In this, I aim to help both those who don’t understand what the fundamental quantifier is and my fellow fundamentality theorists who don’t know how to respond to the incredulous stares they have been receiving.
While nobody has yet advocated my view, in a sense it is not very revisionary.
Though many of them would not or do not admit to this characterization of what they are doing.
I think that there are a great many quantifiers that are more fundamental than ∃E. For this paper, I need not be concerned with naming or discussing any but the quantifier than which no other is more fundamental; or if there is more than one quantifier matching that description, one such quantifier.
The notion of restricted quantification has been around for a long time, and it is rea- sonably innocuous. We know what’s going on when quantifier restriction occurs— someone is restricting her focus to a certain subclass of everything. And that is what austere ontologists are doing; they are restricting their focus to things that ontologists should care about, which are the fundamental things. They are perfectly willing to say that there are chairs, but they think that is not a metaphysically interesting truth; when we are doing ontology, we are looking for the way the world really is, at bot- tom. We’re looking for what there is, in the most fundamental sense of ‘there is’.
My suggestion is that the fundamentality theorist ought to think that what there is, in the fundamental sense of ‘there is’, is the fundamental things, and that this class of things is a subclass of everything there is.
I do not know why there has been such resistance to this thought. Thankfully, my project is not to explain why it has been rejected, but rather argue that the fun- damentality theorist should think that it is true. In what follows, I propose various ways of understanding quantifier restriction, and I argue that, whichever sense of ‘restriction’ she is using, the fundamentality theorist ought to think of the fundamental quantifier as a restriction of the ordinary
English quantifier. The ontological questions are substantive when the quantifier in question is the fundamental quantifier; the reason they don’t seem substantive is that the parties to the ontological disputes have been using quantificational expressions
(‘there is’, ‘there are’, ‘exists’, and the like) differently—one side has been using the fundamental quantifier and the other side has been using the English quantifier.
A further problem is that many disputants think that both parties are using the same quantifier.
. What is the Fundamental Quantifier?
What is it for a quantifier to be the fundamental quantifier, or for one quantifier to be more fundamental than another? For ∃1 to be the fundamental quantifier, ∃1 must figure in the most fundamental description of the world. The phrase ‘the most fundamental description of the world’ is a role, and there is room for disagreement about which description of the world plays that role. Some will say that it’s the most complete description of the world; for every sentence s such that s expresses a true proposition, the most fundamental description of the world includes s. But most will think that that’s too much; it would require too many fundamental predicates and fundamental quantifiers and fundamental variables and fundamental names, and that results in too many fundamental things. Some others will say that the most fundamental description of the world is the minimal set of sentences to express all the true propositions; but there may be several such minimal sets. Others will say that the most fundamental description of the world is the one that says all and only the true things about the fundamental things. Others will say that the fundamental description of the world is the description of the world that expresses all and only the fundamental facts. Others will say that the fundamental description of the world is the description of the world that best limns the world’s metaphysical structure.
Unfortunately, while there is much use of ‘fundamental’ and ‘fundamentality’ in the contemporary literature, there is little discussion of what they mean. There is a circle here, and it’s one that must be broken into at some point. There is ‘fundamental language’, ‘fundamental fact’, ‘fundamental truth’, ‘fundamental quantifier’, ‘fundamental predicate’, and ‘fundamental thing’. I choose to break into the circle with ‘fundamental thing’; I choose ‘is a fundamental thing’ as applied to objects as my primitive predicate, and I define the rest of the circle in terms of it. But
See Sider ().
‘is a fundamental thing’ is also a role, and there is room for disagreement about what plays it. Some will say that the fundamental things are the metaphysical grounds of all true propositions. Others will say that they are the things that physicists are talk- ing about and looking for. Others will say that they are the truthmakers for all true sentences. Still others will say they are the substances. Since I am treating ‘funda- mental thing’ as primitive, I do not mean to define it by ‘is an ultimate ground’ or ‘is a thing physics is looking for’ or ‘is a truthmaker’ or ‘is a substance’. But it might turn out that one of these is co-extensive with ‘is a fundamental thing’.
The fundamental quantifier has in its domain all and only the fundamental ob- jects. The fundamental predicates are the predicates that apply to the fundamen- tal things and are such that the true ascriptions of them to the fundamental things ground all true ascriptions of predicates to things in all languages, and such that there is no subset S of them such that the true ascriptions of the members of S to the fun- damental things ground all true ascriptions of predicates to things in all languages. The fundamental language is the language that contains all and only the fundamental quantifier and predicates and terms referring to the fundamental things. The funda- mental truths are the truths of the fundamental language, and the fundamental facts are those expressed by the fundamental truths.
So, that leaves us with the following view of the fundamental quantifier: ∃1 is the
fundamental quantifier iff ∃1 has in its domain all and only the fundamental things. We can also use the notion of ‘is a fundamental thing’ to define a notion of relative fundamentality: ∃1 is more fundamental than ∃2 iff ∃1 has the same number of (or more) fundamental things and fewer nonfundamental things in its domain as ∃2, or
∃1 has more fundamental things and the same number of (or fewer) nonfundamental
Note that in order to state the view, I had to use a quantifier. Presumably this is the ordinary English quantifier. But what if the domain of the ordinary English quantifier is smaller than the fundamental quantifier? In that case, ‘all’ wouldn’t include all the fundamental things, when ‘all’ is understood in a non-English, unrestricted sense. Below I’ll argue that all the fundamental things are in the domain of the English quantifier. Thanks to Ted Sider for raising this point.
things in its domain as ∃2. But some people deny that the fundamental quantifier has in its domain all and only the fundamental things. And this is not because there are no fundamental things
(though see Dasgupta ()); rather, it is because they think that fundamentality of ideology is not linked, in any interesting sense anyway, to fundamentality of ontology. It might be, on this view, that the fundamental quantifier has in its domain a lot of non-fundamental things. (Of course, given the previous discussion, it must not lack any of the fundamental things.) These people have a different understanding of ‘is the fundamental quantifier’; they do not define it in terms of the fundamentality of objects. Rather, they either take ‘is the fundamental quantifier’ as primitive, or take ‘is the fundamental language’ as primitive and define ‘is the fundamental quantifier’ as ‘is the quantifier of the fundamental language’.
I reject this view because on it the relationship between fundamental ontology and fundamental ideology is not at all clear. It is reasonably obvious that not all the predicates in the fundamental language have in their extensions only the funda- mental things—for example, mass might be a fundamental property, but tables are non-fundamental things that have mass. Of course, many predicates in the funda- mental language will only apply to fundamental things—for example, top/bottom, up/down, and flavor might be fundamental if quarks are fundamental, and those predicates apply only to quarks. But nobody thinks that in order for a predicate to be fundamental it must have in its extension only fundamental things. Nevertheless, there is a widely held intuition of purity of the fundamental language. Fundamen-
There is some question as to whether ∃1 is more fundamental than ∃2 if ∃1 has fewer fundamental things and fewer nonfundamental things in its domain than ∃2, or if ∃1 has more fundamental things and more nonfundamental things in its domain than ∃2. I don’t wish to take a stand on that; I think it depends on the cases. But I think one can be justified in thinking there are degrees of relative fundamentality without taking a stand on every particular case.
I’m thinking of Sider ().
Unless one thinks that fundamental things are the only things there are.
tality theorists think English can’t be the fundamental language, because it has too many predicates and too many things in the domain of its quantifier. I take it that they think it would be nice if at least part of the fundamental language is pure. Since it’s not the predicates, it would be nice if the quantifier had in its domain all and only the fundamental things. I say ‘it would be nice’, and I say it as an expression of a certain intuition that the fundamental language should be incapable of talking about non-fundamental things. To allow that there are non-fundamental things in the domain of the fundamental quantifier is to make the domain bigger than it needs to be.
I reject the thought that the fundamental quantifier might have in its domain non-fundamental things, because the other way is simpler and more elegant: the fundamental quantifier has in its domain all and only the fundamental things. Not only is this view simpler, but it makes very clear the relationship between fundamen- tal ontology and fundamental ideology. It also prompts a question: is a quantifier fundamental in virtue of having fundamental things in its domain, or are things fun- damental in virtue of being in the domain of the fundamental quantifier? On my picture, the fundamental quantifier deserves the distinction ‘fundamental’ in virtue of having in its domain all and only the fundamental things.
Thankfully, the issue of priority need not be settled in order to proceed. Regard- less of which has priority, the fundamental quantifier has in its domain all and only the fundamental things. One might choose to proceed with an investigation into the fundamental by figuring out which quantifier is fundamental, and then looking at its domain in order to figure out what things are fundamental. Alternatively, one
In fact, Ben Caplan raised this very question.
Though it seems to me that we will have an easier time figuring out which things are fundamental than which quantifier is fundamental. This is an advantage of my view; my opponents (those who think that fundamental ontology and fundamental ideology come apart) cannot figure out which quantifier is fundamental by looking at the domains of the various candidates.
might proceed with an investigation into the fundamental by figuring out what things are fundamental, and looking at what quantifier has all and only those things in its domain in order to determine which quantifier is fundamental. Either approach, if done correctly, will lead to a discovery of both which things are fundamental and which quantifier is fundamental, because of the tight connection between the two.
I propose a way of making sense of ∃F : it’s a restriction of the quantifier of
ordinary language, which for the purposes of this paper is ∃E. ∃F (probably) does not have in its domain chairs, tables, fictional characters, mereological fusions of monuments and body parts, and other such things. But the English quantifier does have those things in its domain (or at least, tables and chairs and fictional characters).
So I think that ∃F is a restricted quantifier.
I shall pause to entertain two objections against ∃F ’s being a restricted quanti- fier. First, consider the following argument. We start by introducing a hyperinten- sional notion of a restricted quantifier: ∃1 is a restriction of ∃2 iff ∃1xϕ is defined as
Of course, one might think that the fundamental things are fundamental in virtue of being in the domain of the fundamental quantifier and also think that the way to proceed is to first figure out what things are fundamental. Or one might think that the fundamental quantifier is fundamental in virtue of having in its domain all and only the fundamental things and also think that the way to proceed is to first figure out which quantifier is fundamental. The point is that one need not take a stand on this issue to start doing fundamental ontology.
Indeed, the two approaches might look exactly the same.
While I suspect the same is true of the quantifiers in all (current) human languages—that is, for any quantifier of any current human language, existsF is a restriction of that quantifier—I don’t wish to assume anything about them. The ontological debates in the literature with which I am concerned have been conducted in English, and the English quantifier has led to the dismissivists’ charge.
Of course, as Meghan Sullivan pointed out, one could think there is a quantifier more fundamen- tal than the English quantifier that has in its domain simples, chairs, fusions of body parts, fusions of numbers and spacetime points and incars, and so on. I cannot make sense of a notion of fundamen- tality that would allow such things to be fundamental. One who thinks that fusions of numbers and spacetime points and incars are fundamental will have to give what most would consider shocking answers to questions about naturalness, dependence, explanation, grounding, and truthmaking. Or, she will have to say that, despite strong intuitions to the contrary, none of these notions are related to fundamentality. This will make the investigation of what is fundamental difficult to conduct.
∃2x(ϕ&ψ), for some ψ. Then the following principle: if meaning m1 is defined in terms of meaning m2, then meaning m1 is less fundamental than meaning m2. The principle plus the notion of a restricted quantifier together entail that any restricted quantifier is less fundamental than the quantifier of which it is a restriction.
But we ought to reject the principle. After all, given any quantifier, we can get what this principle considers “less restricted” quantifiers totally arbitrarily. And in many cases we have no reason to think that the less restricted quantifier is more fundamental than the quantifier we restrict to get it. Consider some quantifier ∃G that has in its domain a, b and c. Introduce a name ‘d’, that doesn’t name a or b or c. For any quantificational expression with an occurrence of ‘a’, ‘b’, or ‘c’, replacing
‘a’, ‘b’, or ‘c’ with ‘d’ yields an expression. Then introduce a quantifier ‘∃Gd’, defined as follows:
⌜∃GdxF x⌝ =df ⌜∃GxF x ∨ F d⌝
∃Gd is a restriction of ∃G according to the principle (which is odd, since ∃G’s domain is a proper subset of ∃Gd’s; one might naturally think that ∃G is a restriction of ∃Gd) in virtue of being defined in terms of ∃G; but we can just as easily define ∃G in terms of ∃Gd. We’d do so by saying: consider some quantifier ∃Gd that has in its domain a, b, c, and d. Then introduce a quantifier ‘∃G’, defined as follows:
⌜∃GxF x⌝ =df ⌜∃Gdx(F x ∧ ¬(x = d))⌝
So ∃G and ∃Gd are interdefinable. We could take either as primitive and define the other in terms of it. According to the principle, which one we choose to take as primitive would determine which one is more fundamental than the other. Note:
The notion of definition must be hyperintensional, since the principle entails that ‘being F and being G’ is less fundamental than ‘being F’, even if the two are necessarily co-extensive—for example, if F is G.
Indeed, we could even do this with the absolutely unrestricted quantifier. The new name won’t name anything, but the expressive power of the quantifier will still be greater since there is a new name associated with it.
which one we choose to take as primitive would not just determine which one we ought to think is more fundamental than the other, but which one is in fact more fundamental. This should not be. Which definitions we accept should not determine which bits of our ideology are in fact fundamental.
However we choose to define them, we end up with two quantifiers with their respective domains. It seems as if the relative fundamentality of the things in the domains of the quantifiers should be the only thing that matters to the relative fun- damentality of the quantifier meanings. But on this view, that doesn’t matter at all; the only thing that matters is the way at which we arrived at the quantifier mean- ings. And that doesn’t seem right. If one of them is in fact more fundamental than the other, then the principle tells us that there is a right way to define things; and even though both definitions are true, the principle tells us we should reject one of them. And that doesn’t seem right either.
Compare defining greenness and grueness in the following way:
⌜green⌝=df ⌜grue if first observed before January , and bleen otherwise⌝ ⌜grue⌝=df ⌜green if first observed before January , and blue otherwise⌝
Greenness and grueness are interdefinable; but greenness is more fundamental than grueness, regardless of whether anyone defines greenness in terms of grueness or vice versa. ‘Part’ and ‘proper part’ are interdefinable (one could take either part- hood or proper parthood as primitive when constructing a mereology) and ‘possible’ and ‘necessary’ are interdefinable (one could take either possibility or necessity as primitive when constructing a modal logic), but neither is more fundamental than the other. Nobody would say that choosing to define one in terms of the other is a choice about which to treat as more fundamental. The way that we arrive at a concept of a predicate has nothing to do with how relatively fundamental it is. The
Note that we’re not merely considering here the interdefinability of ‘greenness’ and ‘grueness’. I am not making a point about terms, but about their semantic content. We could treat greenness itself—the property—as primitive and define grueness in terms of it, or vice versa.
same goes with quantifiers. We need to distinguish between how we arrive at the domain of a quantifier and the domain itself. We might arrive at the domain of ∃Gd by restricting ∃G, or vice versa. That’s merely how we get to a quantifier with a certain domain. It doesn’t tell us anything about the relative fundamentality of the quantifier itself. Now for the second objection. On one way of understanding quantifier restric- tion, any restricted quantifier is still “semantically associated” with everything in the domain of the quantifier of which it is a restriction. If this way of understanding quantifier restriction is right, then if ∃F is a restriction of ∃E, it is still semantically associated with everything in the domain of ∃E. But the fundamental quantifier can’t be semantically associated with a larger domain, and so ∃F is not a restriction of ∃E. There are two ways to understand semantic association. On the first way, when
‘there is’ expresses a restricted quantifier, the semantic value of ‘there is’ is not the domain of ∃E in a context, but nevertheless the domain of ∃E is somehow still ‘in- volved’ in the sentence. This seems to be what some people who press this objection are thinking. But I don’t know what to make of it, because ‘semantic association’ and ‘involvement’ have not been defined, nor has it has it been explained how some- thing can be ‘semantically associated’ or ‘involved’ (or what have you) in a sentence without being the semantic value of any part (proper or improper) of the sentence. So I set that view of semantic association aside.
The second way of understanding semantic association is that the semantic value of ‘there is’ is always everythingE, regardless of the context. On this view, we pick out ∃F by restricting ∃E to the fundamental things, but the semantic value of ∃F in a
context is still everythingE. This way of understanding the semantics of the quanti-
I’ll discuss the semantics of restricted quantification in the next section.
Of course, we could start using ‘schmere is’ instead of ‘there is’, and stipulate that ‘schmere is’ has as its semantic value the fundamental quantifier. But proponents of the view in question would say that we can only give a semantic value for ‘schmere is’ by explaining or defining it in terms of the
fier restriction initially sounds like trouble for one who believes that the fundamental quantifier is a restriction of the English quantifier, since most of us agree that if there is a fundamental quantifier, it does not have as its semantic value everything in the domain of any non-fundamental quantifier. Otherwise there would be a quantifier more fundamental than it—the one that does not have extra things in its domain. But again, it’s important to distinguish between how we arrive at the domain of the quantifier and the domain itself. We arrive at the domain of the fundamental quantifier by restricting a quantifier semantically associated with more things—the
English quantifier. Suppose the view of quantifier restriction in question is true.
Then we can never get a quantifier that’s semantically associated with fewer things by quantifier restriction, because quantifier restriction never changes semantic asso- ciation. This is unfortunate, since people (at least, people like us) will never be able to speak the fundamental language unless we arrive at it by defining its words us- ing English words. But even if this view of quantifier restriction is true, it doesn’t show that the quantifier we arrive at by restricting the English quantifier isn’t the fundamental quantifier. We may have to pick it out and use it by restricting a quan- tifier that’s semantically associated with a larger domain and we may never be able to break that semantic association; but we understand that the semantic value of the fundamental quantifier in the fundamental language doesn’t have all those extra things in its domain. The fundamental quantifier in the fundamental language is se- mantically associated only with the things to which we restrict the English quantifier when getting at the fundamental quantifier. If quantifier restriction is to understood in any of the ways I discuss in §, then the fundamental quantifier is a restriction of the English quantifier.
English quantifier, and so it will still be semantically associated with everything in the domain of the English quantifier.
From here on, I’ll treat ‘x is semantically associated with the ys’ as meaning ‘x’s semantic value has the ys in its domain’.
In short, both objections can be met by remembering that semantic primitivity is orthogonal to fundamentality. Sometimes the meaning of the defined term is more fundamental than the meaning of the term(s) by which it is defined, and sometimes not. The method of introduction of a term should not be a factor in assessing the fundamentality of its meaning. The two objections give us no reason to think that there is something untoward if ∃F is a restriction of ∃E. In the remainder of the paper, I argue—against fellow fundamentality theorists— that the fundamental quantifier is a restriction of the ordinary English quantifier. I hope that this helps those who deny the existence of a fundamental quantifier to understand what proponents of such a quantifier are talking about. It should help the dismissivists understand what is going on in seemingly intractable ontological debates, and it should help the Quineans understand what those of us who use the phrase ‘the fundamental quantifier’ mean. Since both camps understand the English quantifier, and they understand quantifier restriction, and they understand the logical vocabulary by which I will give definitions of quantifier restriction, they ought to be able to understand what fundamentality theorists are talking about when we use ‘the fundamental quantifier’.
. The Semantics of Quantifier Restriction
.. A Brief Overview of Quantifier Restriction
Many think that we should do metaphysics with the absolutely unrestricted quantifier— the quantifier that has everything (wave the hands wildly for emphasis) in its domain.
But there are also a lot of people who think we cannot quantify over everything. Some think so because they think there is no domain of absolutely everything. Some think there is such a domain, but try as we might, we just cannot refer to it. If they’re right,
Usually because of Russellian paradoxes or indefinite extensibility.
then we’re always using a restricted quantifier, even when doing ontology; the idea that we’re always using a restricted quantifier supports my view against the charge that we shouldn’t use a restricted quantifier when doing ontology. Unfortunately, a discussion of whether there is an absolutely unrestricted quantifier would take us too far afield. One need not think there is an absolutely unrestricted quantifier in order to think that there are restricted quantifiers. And one need not think there is an absolutely unrestricted quantifier in order to do ontology.
Philosophers often introduce fictitious “disputes” in order to illustrate the ubiq- uity of quantifier restriction. Take, for example, the following conversation between
David and John during a party at John’s house. David asks, “Can I have a beer?” John responds, “Yeah, check the fridge.” David looks in the fridge and says, “There is no beer!” John replies, “False! There’s beer in the garage, and in the store down the corner, and…” David, it seems, has the right to roll his eyes at John, and proba- bly punch him (but not too hard). What explains David’s rights? It is quite obvious that when David says, “There is no beer”, he is not making the claim that there is no beer anywhere; he is just saying that there isn’t any in the fridge. The quantifica- tional phrase ‘there is’ is implicitly restricted to the domain of things in the fridge.
I take the following to be a datum: the reason John and David aren’t having a real dispute about whether or not there is beer is that one is using a restricted quantifier and the other is not. The correct analysis of quantifier restriction ought to allow us to analyze this as a case of quantifier restriction; so, for each potential analysis
I discuss in this paper, I will show how it classifies this case as a case of quantifier restriction.
There are also explicitly restricted quantifiers. For example, had David re-
But the interested reader should start with Rayo and Uzquiano () and Williamson ().
Or one is using a more restricted quantifier than the other.
I’m not using ‘explicit restriction’ the way that Neale () uses it. I am using it to refer to the
sponded, “There is no beer in the fridge”, one way of making sense of his utterance is that he is explicitly restricting the quantifier to things in the fridge. (This is per- haps easier to see if he says just, “Nothing’s cold!” when looking in the fridge for cold beer.) Whereas in the case of implicitly restricted quantifiers it seems legitimate
(though unfair) to respond as John does, in the case of an explicitly restricted quanti- fier his response makes no sense. Rather than rolling his eyes, David would respond,
“I said in the fridge”, and the punch that followed wouldn’t be for deliberately mis- interpreting the implicitly restricted quantifier, but for not listening to the explicit restriction.
In addition to knowing how we restrict a quantifier, we might wonder what the semantic values of restricted quantifiers actually are. That is the topic of the current section. Note, however, that there are two things I will not be discussing. First, I won’t discuss why conjoining quantificational phrases with restricters results in the semantic value it does; I am only interested in what the semantic value is. Second, I won’t talk about what various views of semantics (Russellian, Fregean, Chomskian, possible worlds, or the like) say about sentences or propositions containing restricted quantifiers. I am just going to talk about the various views of what semantic value the restricted quantifier contributes to the utterance, sentence, and proposition in phenomenon of uttering some bit of language which serves to restrict the quantifier, whereas in cases of implicit restriction (in my sense), context alone determines the restriction.
One might think that the most natural way of understanding “There is no beer in the fridge” is not quantifier restriction at all, but rather that the sentence ‘there is no beer’ is true relative to <α, time of utterance, the fridge>. However, if the quantifier is not restricted to things in the fridge, then even in the fridge one can quantify over things outside the fridge. So ‘there is no beer’ is false relative to <α, time of utterance, the fridge> if (i) there is beer that is not in the fridge and (ii) the quantifier is not restricted to things in the fridge.
For discussions of explicitly restricted quantification, see Cameron () and (forthcoming), Korman (), Schaffer (a), and Sider () and () .
In §& I’ll discuss three kinds of quantifier restriction and argue that the fundamental quantifier is a restricted quantifier according to every kind.
That is, I’ll be dealing with descriptive (rather than foundational) semantics.
which it occurs. There is a persistent (and perhaps growing) tendency among philosophers to think that metaphysical questions are answered by doing philosophy of language; one can reflect on the way we use language in order to determine how we should answer questions of what there is, how things persist, when some things compose another thing, and so on. In that vein, one might think that the meta-ontological questions ought to be answered the same way—by investigating the way we use language.
Thus, one might think that I am looking in the wrong place for an answer, and that my answer is false. That is, one might think that if we figure out the semantics of ontological discourse, we’ll have an answer to the meta-ontological questions. One might also think that the semantics of quantifier restriction (or certain views of the semantics of quantifier restriction) entails that my view, the view that the fundamental quantifier is a restricted quantifier, is false. In this section, I show that all the offered views of quantifier restriction are consistent with the fundamental quantifier’s being a restricted quantifier. And they are silent with respect to the meta- ontological questions.
.. A Brief Overview of the Semantics of Quantifier Restriction
Though this terrain is well-traveled, it’s still helpful to begin at the beginning. If I say, “There’s no beer” when looking into a fridge bereft of beer, you do not fault me. But of course, in some sense, there is beer; it’s just not in my fridge. So why don’t you fault me? There are different answers to this question, and they come from different views of the semantics of quantifier restriction. To explain the different views, I’ll appeal to three levels of communication: utterances, sentences, and propositions. Utterances are sounds one makes that are linguistic items (crying out in pain is not an utterance), sentences are strings of words that are grammatical and complete, and
propositions are what the (declarative) sentences express. I will call the relationship between utterances and sentences ‘tokening’ and the relationship between sentences and propositions ‘expression’. So utterances token sentences and sentences express propositions. But I want to leave open whether distinct utterances can token the same sentence (as in “John is at the barber” as said by you to two different people a couple seconds apart), some utterances can token more than one sentence (as in uttering “I am going to the store now” which, where t is the time of utterance, tokens both “I am going to the store at t” and “I am going to the store simultaneous with this utterance”), some sentence-tokens aren’t utterances (like written ones), and there are utterances that don’t token any sentence (like “Ouch.”). Similarly, I want to leave open whether distinct sentences can express the same propositions (as in
“snow is white” and “Der Schnee ist weiss”), some sentences can express more than one proposition (as some think happens in “John is tall”), some propositions aren’t expressed by any sentence (perhaps infinitary ones), and there are sentences that don’t express propositions (as in “This sentence is false” or “Colorless green ideas sleep furiously”). Utterances also express propositions, sometimes in virtue of tokening sentences that do, and sometimes without so doing (as in answering “Yes” to the question, “Are you going to Jen’s tonight?”).
There are three views of the semantics of quantifier restriction, and the only point of agreement between the various views seems to be that something is different when you say “there’s no beer” while looking in the fridge and when you say “there’s no beer” two days later while standing shocked in the grocery store—the views come
This is terribly imprecise, but to make it more so would take a lot of room. I trust that the reader is familiar with the distinction.
It’s usually understood that sentences express propositions relative to contexts. Following the usual convention, I will omit this from here on out.
Thanks to Lindsay Rettler for discussion of this point.
The latter is courtesy of Chomsky (, p).
apart when they try to say what exactly the difference is. I will argue that my proposal is compatible with all three views of the semantics of quantifier restriction. My view is that quantifier restriction occurs when the austere ontologist is doing ontology, and the views of the semantics of quantifier restriction don’t tell us anything about when quantifier restriction occurs—they just tell us what happens (semantically speaking) when it does. If any of the views of the semantics of quantifier restriction were to require an explicit linguistic utterance corresponding to the restriction, for example, or an intention to use a restricted quantifier, then my view would be in trouble, since I’m arguing that many ontologists are using a restricted quantifier without ever uttering a restricter phrase or explicitly intending to restrict the quantifier. Indeed, they do not explicitly intend to restrict the quantifier, and that’s the problem—that’s what has led to the dismissivist’s charge. Austere ontologists are using a restricted quantifier and then denying that they’re doing so!
Using the example in § will help make it clearer what’s at issue. Here’s a question we might be interested in answering: does David’s utterance of “there’s no beer” when uttered while looking into the fridge token the same sentence as he would have tokened by uttering “there’s no beer in the fridge”? This is a choice point. Those who say yes think that context supplies the missing “in the fridge” to the actual utterance, so that the actual and hypothetical utterances token the same sentence—“there’s no beer in the fridge”. This is a grammatical/syntactic theory of quantifier restriction
(in the terminology of Stanley and Szabo ()) or an explicit theory of quantifier restriction (in Neale ()). The rest think that the sentences tokened by the two
I will not possibly be able to do justice to all the work in linguistics and the philosophy of language that has been done on quantifier restriction and related topics. Those interested in a more in-depth discussion of many things I’ll gloss over should see Stanley and Szabó’s excellent () (which pro- vides a very nice overview of most of the relevant issues prior to the argument), Cooper (), von Fintel (MS), Recanati (), Reimer (), Reinhart (), Barwise and Cooper (), and Neale (, especially §.-. and Chapter ).
Of course, everyone agrees that there are different sounds made, but on this view the sentences tokened are the same.
utterances are distinct. The follow-up question, then, is whether the utterances also express different propositions; this is yet another choice point. Those who say that the two utterances express the same proposition think that the context combines with the first sentence such that it expresses the same proposition as the second sentence;
Stanley and Szabo call this a semantic theory of quantifier restriction, and Neale calls it an implicit theory. Those who say that the two utterances express different propositions have to account for the fact that we are inclined to judge them as having the same truth-conditions, or at least having some important similarity. Such people say that the two utterances “convey” or “communicate” the same proposition even though they express different propositions; this is a pragmatic theory of quantifier restriction.
So, the options divide into treating the phenomenon of quantifier restriction as syntactic, semantic, or pragmatic. I shall take each in turn.
.. Syntactic Explanation
Suppose there’s a syntactic explanation of how the quantifier occurring in “there’s no beer” is restricted to things in the fridge. This means that although one doesn’t utter “in the fridge”, the phrase “in the fridge” nevertheless occurs in the sentence tokened—it is an unpronounced predicate in the utterance. Context provides the predicate, which combines with the quantifier in such a way that the new domain delivered to the sentence is the intersection of the set of members of the domain of the quantifier and the set of things in the fridge.
The usual way to make sense of this is to say that there is an ellipsis in the syntax
Discussion of the foregoing can be found on Stanley and Szabo (, pff) and von Fintel (MS).
There are worries about whether this is a good account, since there are a lot of contexts in which it’s not clear which predicate is contributed. See Sag (, especially Chapters and ) for an extensive discussion.
of the utterance that the context fills in to arrive at the sentence. An example (of the sort that proponents of this phenomenon cite) is my utterance of what seems like,
“I went to the gym today. Alex went, too.” The syntactic explanation in this case is that my utterance is in fact, “I went to the gym today; Alex went…, too.”, and the sentence tokened by that utterance is “I went to the gym today; Alex went to the gym today, too.” This is one syntactic explanation of how I am able to convey the information that Alex went to the gym despite eliding the phrase “to the gym today”. On this view, one can token a sentence without uttering all the words of the sentence.
Not everyone agrees that there are syntactic ellipses. And it is yet a further step to think that there are syntactic ellipses in cases of quantifier restriction. Giving a syntactic ellipsis theory of quantifier restriction yields the following explanation:
When David utters what sounds like “there’s no beer” and he’s looking in the fridge, he is in fact uttering “there’s no beer…”, and, given the David-looking-in-the-fridge- for-beer context, he is tokening the sentence “there’s no beer in the fridge”. And when Erin utters “there’s no beer” while on a desert island, she utters the same thing that David utters—“there’s no beer…”—but tokens a different sentence: “there’s no beer on this island”.
On this view, David’s utterance above is “there’s no beer…”, the sentence tokened is “there’s no beer in the fridge”, and the proposition is that there’s no beer in the fridge.
I said that she utters “the same thing” as David, but it’s not clear what kind of thing it is. It can’t be a sentence, because Erin and David token different sentences. And it’s not the same utterance, since they occur in different places. Perhaps the similarity is in something like an utterance-type, or the word-types.
.. Semantic Explanation
Suppose there’s a semantic explanation of how the quantifier occurring in “there’s no beer” is restricted to things in the fridge. This means that although one doesn’t utter “in the fridge” and the phrase “in the fridge” does not occur in the sentence tokened, nevertheless context figures in such a way that the proposition has as a part a semantic value that functions as a restricter of the quantifier. Context combines with the quantifier in such a way that the new domain delivered to the proposition is the intersection of the set of members of the domain of the quantifier and the set of things in the fridge.
On the semantic explanation of quantifier restriction, when David utters “there’s no beer” while looking into the fridge, he tokens the same sentence that Erin does when she utters “there’s no beer” while stranded on a desert island. But they express different propositions, and the propositions they express are true. The sentences tokened are the same, but they express different propositions in different contexts.
Thus, the context serves to contribute some semantic content to the proposition that is not the semantic value of any individual expression—at least, not outside of the context.
In any case, the semantic theory of quantifier restriction is that in cases of quanti-
fier restriction, context combines with ‘there is’ to pick out a relevant domain that is a proper sub-domain of the quantifier, and this domain is contributed to the propo- sition. This can be done in one of two ways: either context combines with ‘there is’ in such a way that the semantic value of ‘there is’ is the aforementioned proper sub- domain, or the semantic value of ‘there is’ is constant and context then contributes a new semantic value that limits the domain to things in the fridge. Consider the
Perhaps contexts combine with individual expressions to deliver different semantic values for those expressions in different contexts.
Stanley and Szabo (, p) call the latter a “semantic parameter approach”, and they defend
aforementioned utterances: David’s of “there’s no beer” while looking into the fridge, and Erin’s of “there’s no beer” while on a desert island. On this view, they all token the same sentence but express different propositions; the context serves to either (i) add a semantic value that isn’t the semantic value of any individual expression, or
(ii) assign to “there is” a different semantic value in each context. On this view, David’s utterance is “there’s no beer”, the sentence tokened is
“there’s no beer”, and the proposition expressed is that there is no beer in the fridge.
.. Pragmatic Explanation
Suppose there’s a pragmatic explanation of how the quantifier occurring in “there’s no beer” is restricted to things in the fridge. This means that when David utters
“there’s no beer” when looking into the fridge, the sentence he tokens expresses the very same proposition as the sentence Erin tokens with an utterance of “there’s no beer” while on a desert island. The sentences they token express false propositions.
Of course, we are inclined to say that the utterances are true. Proponents of prag- matic explanations have an explanation for this: although the proposition expressed by the sentence tokened is false, our utterances are useful because they communi- cate or convey (or even express) sentences and propositions that are true. Namely, they convey the proposition expressed by the sentence “there’s no beer in the fridge” in David’s case and “there’s no beer on this island” in Erin’s case. David and Erin just elide the restricter phrase because they are still able to convey what they want without it and it’s just easier that way.
So, on this view David’s utterance is “there’s no beer”, the sentence tokened is
“there’s no beer”, and the proposition expressed by the sentence in the context is that there’s no beer. But the proposition conveyed is that there’s no beer in the fridge, and a particular version of it. There are further nuances that I gloss over, but this is enough for our purposes; I direct the interested reader to their discussion.
that’s what we ordinarily focus on when assessing whether David said something true.
.. The Semantics of Quantifier Restriction and the Fundamental Quantifier
As I said, my view is compatible with all three views of the semantics of quanti- fier restriction. My view is that anyone who thinks there is a fundamental quantifier that is not the English quantifier should think that the fundamental quantifier is a restricted quantifier, and that they should think that mereological nihilists, when ut- tering “there are no tables”, are using the fundamental quantifier by restricting their attention to things ontologists should care about—the fundamental things. Similarly, anyone who thinks there is a fundamental quantifier that is not the English quantifier should think that nominalists, when uttering “there are no numbers” and “there are no properties”, are using the fundamental quantifier by restricting their attention to the fundamental things. And so on for other with austere ontologists. van Inwagen, Quine, and most others with austere ontologies would, I’m sure, deny the latter claim–that they are using the fundamental quantifier when doing on- tology. van Inwagen, for example, claims that he doesn’t believe (i) there are, in the fundamental sense of ‘there are’, no tables, but there are, in the non-fundamental sense of ‘there are’, tables. Rather, he believes (ii) there are no tables. However, he is happy to affirm in certain contexts (like IKEA) that there are tables. So I would construe the ‘there are’ in (ii) as using the fundamental quantifier; when doing ontol- ogy, van Inwagen is restricting his attention to things ontologists should care about, which are the fundamental things. van Inwagen would deny this as well, because he thinks the English quantifier is the right one to use when doing ontology. But given that he thinks “there are tables” is true in English when in IKEA and is false
This is a similar proposal to Lewis’ (, §.) suggestion that all of us restrict our quantifiers almost all the time to the actual world without realizing it, and when asked, most of us would deny that we’re doing so.
in English when doing ontology, and given that ‘tables’ doesn’t change in meaning, there is a tension.
The tension can be brought out with the following argument. If “there are tables” is true in the context of IKEA but false in the context of doing ontology, then some word must change its meaning. It is not ‘tables’. Therefore, it must be ‘there are’— that is, the quantifier.
Thus, we ought to abandon the thought that van Inwagen is using the same quan- tifier in IKEA as he is when doing ontology. Since he is using the English quantifier in IKEA, he is not using the English quantifier when doing ontology. This generalizes to all austere ontologists; they have stopped using the English quantifier when doing ontology. Once an intelligent person says something like “there aren’t any tables or chairs or cars or houses” and proceeds to argue for it, that person has stopped us- ing the English quantifier. If one accepts that austere ontologists have stopped using the English quantifier, then one can give one of the following explanations of the semantics of their utterances.
First, syntactic ellipsis. On this view, when an austere ontologist says, “there are no tables”, what she is actually uttering is “there are no …tables”, which tokens the sentence “there are no fundamental things that are tables”. She thinks that ontology is about figuring out the fundamental features of the world, and so, when speaking to other ontologists, she implicitly restricts her quantifier to things ontologists should care about. The restriction is elided in the utterance, but context (of doing ontol- ogy) adds it to the sentence. On this view, the austere ontologist’s utterance is “there
If one wanted to say that ‘tables’ changes its meaning, then we could run the argument with ‘composites’ or ‘more things than just mereological simples’.
van Inwagen denies the first premise of this argument, because he does not accept the principle of compositionality. But those who are sanguine about the success of compositional semantics should find it compelling.
After all, she allows that the folk, and even she herself in some contexts, speak truly when saying, “there are tables”.
are no…tables”, the sentence tokened is “there are no fundamental things that are tables”, and the proposition expressed by the sentence is that there are no fundamen- tal things that are tables. Very few people are inclined to agree with the utterance, but nearly everyone agrees with the proposition that this view says it expresses. The problem is that they don’t realize that the utterance expresses the proposition it does, because they don’t realize that the austere ontologist is using a restricted quantifier.
Second, semantic theories. On this view, when an austere ontologist utters “there are no tables” when doing ontology, the sentence she tokens expresses a different proposition than when she utters it in IKEA. Context determines, in each case, a proper subdomain of the domain of the English quantifier and delivers that proper subdomain as a semantic value to the proposition expressed. On this view, the austere ontologist’s utterance is “there are no tables”, the sentence tokened is “there are no tables”, and the proposition she expresses is that there are no fundamental things that are tables. Again, very few people are inclined to agree with her utterance, but nearly everyone agrees with the proposition it expresses. The problem is the same: they don’t realize that the utterance expresses the proposition it does, because they don’t realize that she’s using a restricted quantifier.
Finally, pragmatic theories. On this view, when an austere ontologist utters “there are no tables”, she tokens the same sentence (which expresses the same proposition) that my grandmother would were she to utter “there are no tables” in the middle of an IKEA. And both of those sentences are false. But in the case of the austere on- tologist, the context (namely, doing ontology) clues us in to the fact that ontologists are interested in a more restricted domain—since she’s doing ontology, the restricted
van Inwagen agrees. But he says that the proposition he expresses in IKEA is “ontologically neutral”. He does not give a semantic theory for how this might be, and I find it suspect. If the domain of the quantifier is the same in both cases, then it seems clear that he is expressing a false proposition. If the domain of the quantifier is different in each case, then I am right—he is using a restricted quantifier when doing ontology.
Because both of them are using the English quantifier.
domain is that of the fundamental. So the austere ontologist succeeds, where my grandma does not, in conveying something true—that there are no tables that are fundamental. My grandma conveys that there are no tables in IKEA, and this is (we suppose) false. This is the reason why even those who think austere ontologists’ utterances express false propositions don’t criticize them for being totally inappro- priate, like they would my grandmother’s utterance in the middle of an IKEA.
So much for the semantics of quantifier restriction. I turn my attention now to explaining various ways of restricting the quantifier.
. Ways of Restricting Quantifiers
Most who believe that ‘existsF ’ expresses a different existential quantifier than
‘existsE’ have denied that the former is a restriction of the latter, but as far as I can tell, only Ted Sider has offered an argument. For example, Cameron:
If it could be shown that the nihilist’s sense of ‘exists’ is a restricted quan- tifier defined on the universalist’s ‘exists’ that would not be to show that the nihilist and the universalist are talking past each other; it would be to show that the universalist was right after all (, p).
And Sider:
Yet another alternative would be to claim that in the fundamental lan- guage, all quantification is restricted. But this would threaten to reintro- duce the questions of ontology. For instance, we could ask: ‘is there any context in which it would be true to say ‘there are tables and chairs’?’ It is hard to see how you could block the legitimacy of this question; and if it is phrasable in your fundamental language, it is substantive and nonverbal (, p).
But if ontological questions are framed using the fundamental quantifier and the fundamental quantifier is a restricted quantifier, then this new question that’s intro-
See Cameron (b), Fine () p, Lewis (), Sider () § and , and Turner (). Additionally, this seems the default attitude among metaphysicians in informal settings during which I have floated the idea that the fundamental quantifier is a restricted quantifier.
duced isn’t an ontological question, even though it is substantive and non-verbal. I think the fundamental quantifier is a restricted quantifier. Below I consider three ways of restricting quantification. Each has a claim on our intuitive understanding of restriction, so all of them are plausible candidates for the ways of restricting the quantifier that these ontologists have in mind when they deny that the fundamental quantifier is a restriction of the ordinary English quantifier. I shall argue that funda- mentality theorists should think that the fundamental quantifier (∃F ) is a restriction of the ordinary English quantifier (∃E).
.. Inferential Restriction
Some think that quantifiers are what they are because of the inferential roles they play. That is, quantifiers must license the inference rules of existential generaliza- tion and existential instantiation.
Existential generalization says if a is P , it is provable that something is P . Exis- tential instantiation tells us that if something is P , it is provable that a is P , where we use ‘a’ to arbitrarily name an element in the domain—whatever element it is that is P . Formally:
Existential generalization: P a ⊢ ∃xP x
Existential instantiation: If ϕ, P a ⊢ Q, and a doesn’t show up in ϕ or Q or P (x), then ϕ, ∃xP x ⊢ Q
If quantifiers are partly defined by their inferential roles, then one way to restrict a quantifier is to restrict the inferences one can make. Intuitively: ‘∃2 is a restrictionI of ∃1’ means that for any formula P open in x, it is provable from ∃2xP x that ∃1xP x,
See Lewis () and Turner () for treatments of these notions.
Thanks to Amelia Hicks and Jason Turner for comments on and discussion of this section.
and it is not provable from ∃1xP x that ∃2xP x. Formally:
∃2 is a restrictionI of ∃1=df (i) For any open formula P, ∃2xP x ⊢ ∃1xP x, and (ii) ¬(For any open formula P, ∃1xP x ⊢ ∃2xP x)
If restriction is understood as restrictionI , then we have the following explanation of the David and John case. When David says, “There’s no beer!” he means that
¬∃fridgex(Beer(x)). His quantifier licenses the inference from ∃fridgexP x to ∃ExP x; from the fact that somethingfridge is P , it is provable that somethingE is P . But his quantifier does not license the inference from ∃ExP x to ∃fridgexP x; from the fact that somethingE is P , it is not provable that somethingfridge is P , since ∃fridge is a restrictionI of ∃E. So, there isE beer, but there isfridge no beer. Since David is using
∃fridge, what he says is true, but John’s response is also true, since John is (in this case ridiculously) using ∃E. There is also the issue of practical inference. From David’s assertion that there isfridge no beer and the desire for beer, he might be justified in going in search of
beer. But if David’s assertion were to be that there isE no beer and he were to desire beer, he would not be justified in going in search of beer, since one cannot find something that does not existE.
In §. I argue that fundamentality theorists should think that ∃F is a restrictionI
of ∃E.
Compare Sider (, p).
Of course, if one defines ‘restriction’ as restrictionI , then it is trivially true that restriction is restrictionI . But then we would want to know what reasons we have for adopting restrictionD as a definition of ‘restriction’. The same goes for the other characterizations of restriction.
Where ∃fridge is ∃E restricted to the things in the fridge.
Thanks to Patrick Gamez for a suggestion along these lines.
Because: ) If there areE P s and one goes in search of P s, one has a chance of finding P s, and ) There isE beer.
Thus, ‘x is a restrictionn of y’ does not mean ‘x is a restriction of y, and restriction ought to be
.. Restriction to a Predicate
Perhaps most quantifier restriction occurs when we restrict a quantifier to a pred- icate. We ask questions of what there is that is also P , where P is filled in with some predicate; we can ask what existsE that is P . Intuitively: ‘∃2 is a restrictionP of
∃1’ means that everything1 that is P is identical to something2, nothing1 that is ¬P is identical to something2, and everything2 is identical to something1. So where ∃U is the unrestricted quantifier and R is the restricting predicate and ∃R is the restricted quan- tifier, the following are valid: ∀Rx(F x) ≡ ∀U x(Rx ⊃ F x) ; ∃Rx(F x) ≡ ∃U x(Rx∧F x)
; ∀U x(F x) ⊃ ∀Rx(F x).
Formally, we can define a quantifier ‘∃P ’ in the following way:
⌜∃P x(ϕ)⌝=df ⌜∃Ex(P x ∧ ϕ)⌝
And we can define restrictionP :
RP : ∃2 is a restrictionP of ∃1=df ∀1x(P x ≡ ∃2y(y = x)) ∧ ∀2z(∃1y(y = z))
Understanding restriction as restrictionP lets us give the following explanation of the David and John case. When David tells John, “There’s no beer!” he is restricting his quantifier to things in the fridge—present things in the fridge, probably, since beer in the fridge yesterday would not quench David’s thirst today. That is, he is saying that there isE no beer that is present and is in the fridge. Substitute ‘is present and is in the fridge’ for ‘P ’ in the above formula, and we get David’s quantifier ∃F ridge.
(∃fridge) is a restriction of John’s quantifier (∃E), so John’s assertion is provable from David’s assertion, but David’s assertion is not provable from John’s assertion.
understood as restrictionn’. Rather, it means that ‘substituting x and y for ∃1 and ∃2 in the definition of restrictionn results in a truth’.
Thanks to Meghan Sullivan for discussion.
In this case they are, in fact, both true.
In §. I argue that fundamentality theorists should think that the fundamental quantifier is a restrictionP of the English quantifier.
.. Domain Restriction
Another way of restricting a quantifier is to restrict the domain without a restrict-
ing predicate. Intuitively: ‘∃2 is a restrictionD of ∃1’ means that there is something1 that is not identical to anything2 and everything2 is identical to something1. For- mally:
RD: ∃2 is a restrictionD of ∃1=df ∃1x¬∃2y(y = x)∧∀2x∃1y(y = x)
Understanding restriction as restrictionD lets us say the following about the David and John case. ∃fridge is a restrictionD of ∃E because there are some thingsE that are not identical to anythingfridge—the beer at the liquor store down the street, my mother, the electrons in China, and Venus, for example. And there is nothing in the domain of ∃fridge that is not in the domain of ∃E. Domain restriction seems a natural view of restriction. However, there is some reason to think that quantifiers are not individuated by their domains. Consider the following case. The Illuminati meet once a month, and membership is a highly secretive affair. Moreover, the membership is constantly changing. You are the pres- ident, and the charter requires you to begin each meeting by standing up and asking, “Is everyone here?” The meeting cannot continue until everyone is there. You are clearly using a restricted quantifier, meaning to ask if everyone presently in the
One might think that for every set, there is a predicate corresponding to that set. If that is the case, then the account of restriction I am about to discuss turns out to be the same as the account in the previous subsection.
Thanks to Mike Rea for a suggestion along these lines.
The indexicals are a bit tricky since it is not obvious that indexicals are disquotable, but nothing hangs on the issue. I am using ‘there’ to refer to the same place as you (as the President) do when you use ‘here’.
Illuminati is there. And there is a certain very natural sense in which you are using the same quantifier each time. However, each time you ask the question, ‘everyone’ has a different domain. One can truthfully answer “yes” at different times when different people are at the meeting.
It seems that the reason that one can truthfully answer “yes” is that the Illuminati quantifier has the same character at all contexts of utterance, but at each context it has a different content. Since a domain is part of the content and not the character, and there is some intuitive pull to say that quantifiers with the same character are identical even if they have different content, there is some reason to resist cashing out restriction as restrictionD. Thus, while domains on first reflection seem like a natural way to individuate quantifiers, there are some problems with that account.
In any case, in §. I argue that fundamentality theorists ought to think that ∃F is a restrictionD of ∃E.
. The Fundamental Quantifier is a Restricted Quantifier
.. Inferential Restriction
Recall:
∃2 is a restrictionI of ∃1= df (i) For any open formula P, ∃2xP x ⊢ ∃1xP x, and (ii) ¬ (For any open formula P, ∃1xP x ⊢ ∃2xP x))
Intuitively: ∃2 is a restrictionI of ∃1 means that for any formula P open in x, it is
provable from ∃2xP x that ∃1xP x, and it is not provable from ∃1xP x that ∃2xP x.
If ∃F is a restrictionI of ∃E, then for any predicate P , it is provable from ‘somethingF is P ’ that ‘somethingE is P ’. This is good, because everything in the domain of ∃F is in the domain of ∃E. When speaking English, we quantify over things that seem to
Where, as usual, character is (or determines) a function from contexts to contents, and content is (or determines) a function from circumstances of evaluation to extensions.
Compare Sider (), p.
exist, and things that we have good reason to name. We also quantify over the things that our best scientific theories tell us there are. It seems reasonable to think that if scientists discovered super-duper-strings, we would not have to change our quanti-
fier from ∃E to ∃ES (where the latter has in its domain everything that ∃E has plus super-duper-strings) to talk about them. Similarly with discoveries in metaphysics. If metaphysicians were to discover an argument for a new kind of entity that most metaphysicians were to believe was cogent, we wouldn’t have to change our quanti-
fier to talk about those entities. So, it seems that the domain of the English quantifier is quite large—large enough to include everything that could count as fundamental, and more things besides. Things cannot have different properties according to which domain is being used, so (i) is true. Also, if ∃F is a restriction of ∃E, then for any predicate P , it is not provable from ‘somethingE is P ’ that ‘somethingF is P ’. Since the English quantifier has more things in its domain (like tables and such), there areE some things that have properties that don’t existF . So this inference is not licensed, and (ii) is true. All is as it should be.
Thus, the fundamentality theorist should think that ∃F is a restrictionI of ∃E.
The goal in using ∃F when doing ontology is to uncover the fundamental ontology of the world; it’s to discover the minimal ontology that we need to write the book of the world. If all we needed to do to show that somethingF is P was to show that somethingE is P , we would not be doing substantive ontology. After all, “tables are wood, therefore somethingF is wood” is not an inference we want to license. We would be in the position of the Quinean—a position we saw fit to abandon because we did not think that using ∃E to do ontology allowed us to uncover anything
This is a major difference between natural language quantifiers and the fundamental quantifier. The domains of natural language quantifiers are determined by a combination of use and naturalness, whereas the domain of the fundamental quantifier is determined purely by the fundamentality of the objects in the domain.
substantive and important about the way the world really is. And no fundamentality theorist thinks that the fundamental things don’t existE.
.. Restriction to a Predicate
First, recall:
RP : ∃2 is a restrictionP of ∃1=df ∀1x(P x ≡ ∃2y(y = x)) ∧ ∀2z(∃1y(y = z))
Intuitively: ‘∃2 is a restrictionP of ∃1’ means that everything1 that is P is identical to something2, nothing1 that is ¬P is identical to something2, and everything2 is identical to something1.
If ∃F is a restrictionP of ∃E, then there isE some predicate P such that anything in the domain of ∃E that is P is in the domain of ∃F and everything in the domain of ∃F is in the domain of ∃E. Both of these conjuncts are true. The most important step in arguing that both of these conjuncts are true is to identify the predicate in question. That’s easy; the predicate is ‘is fundamental’.
If restriction is understood as restrictionP and we agree that the predicate we ought to restrict to is ‘is fundamental’, we can even define ∃F :
⌜∃F x(ϕ)⌝=df ⌜∃Ex(x is fundamental ∧ ϕ)⌝
Thus, the fundamentality theorist should think that ∃F is a restrictionP of ∃E. The goal in using ∃F when doing ontology is to uncover the fundamental ontology—the minimal ontology needed to be the domain for the quantifier used in the best book
Of course, one could phrase it in second-order logic without identifying the predicate: ∃P (∀1x(P x ⊃ ∃P y(y = x)) ∧ ∀P z(∃1y(y = z))). But which quantifier (∃F or ∃E) is the first ex- istential quantifier? Furthermore, if one can avoid second-order logic, one should. Thankfully, we can.
I take it that the predicate ‘is fundamental’ is properly assigned to x if and only if x is in the domain of ∃E and x is fundamental.
of the world. The fundamental ontology is the things in the domain of ∃E that are fundamental.
If ∃F is not a restrictionP of ∃E, then one of the following is false: (i) everything that is in the domain of ∃E that is fundamental is also in the domain of ∃F , or (ii) everything that is in the domain of ∃F is in the domain of ∃E. If (i) is false, there areE fundamental things that are not in the domain of ∃F . That would be bad, for then the fundamental quantifier doesn’t range over all the fundamental things. If (ii) is false, then something in the domain of the fundamental quantifier is not in the domain of the English quantifier; that would also be bad, because then English speakers would have to change their quantifier when they discovered more fundamental things. So, the fundamentality theorist should think that ∃F is a restrictionP of ∃E.
.. Domain Restriction
Recall:
RD: ∃2 is a restrictionD of ∃1=df ∃1x¬∃2y(y = x)∧∀2x∃1y(y = x)
Intuitively: ‘∃2 is a restrictionD of ∃1’ means that there is something1 that is not identical to anything2 and everything2 is identical to something1.
If philosophers are using restrictionD in the claim that ∃F is not a restricted quan- tifier, then they are wrong. The reason is simple: the domain of ∃E has more things than the domain of ∃F , and there is nothing in the domain of ∃F that is not in the domain of ∃E. For example, the domain of ∃E includes tables and knees; the domain
of ∃F (probably) does not. And fundamentality theorists don’t think that we are doing substantive ontology when we argue about what things are in the domain of
∃E.
I don’t mean to settle any first-order debates about what there isE or what there isF . Presumably if one goes in for a fundamental quantifier, one thinks there is somethingE that there isn’tF ; so whatever it is, fill it in for ‘tables and knees’ above.
Of course, this does not suffice to show that ∃F is a restrictionD of ∃E, since it does not guarantee that everything in the domain of ∃F is in the domain of ∃E. The idea is that one looks first at the domain of ∃E. The members of that domain include, say a and b and c and so on. Then one looks at the English sentences containing
∃E and a and b and c and so on, and looks for which groups of sentences meet the conditions for being a fundamental description of the world. Then one picks the group that one thinks is the best fundamental description of the world. The things whose names occur in these fundamental sentences will be, say, a and e and j and so on. Those are the entities in the domain of ∃F , quantified over when one uses ‘∃F ’.
We can do interesting metaphysics using ∃F , since it is not an arbitrary restriction. It is metaphysically privileged; or, you might say, it carves nature at the joints.
Another reason to think that everything that existsF also existsE is that quantifi- cation in the English language is fluid. When we discovered that electrons existed, we did not have to start speaking a different language in order to talk about them. If we discover that photons have parts, we will not have to start speaking another lan- guage to talk about them. This gives us reason to think that the domain of the English quantifier includes a great many things—including things that we have never talked about, and things that we never will talk about. Perhaps it includes everything beings like us could talk about. But at the very least, it includes the fundamental things.
.. The Fundamental Quantifier is a Restricted Quantifier
Thus, the fundamentality theorist ought to think that ∃F is a restricted quantifier. The Quinean, however, should not. The Quinean thinks that there is only one sense of the English ‘there is’—it is the quantifier, and it is what we use to do serious
Some proposed conditions can be found in the next section.
metaphysics. We write out in English the sentences we accept, regiment them in first-order logic, and look for the values of the variables—those values are what is in our ontology.
The fundamentality theorist, however, thinks that there’s a perfectly good sense in which all the sentences one accepts can be true and yet one’s ontology doesn’t contain things over which an existential generalization on an open sentence quan- tifies. In a slogan: there’s a difference between what’s in one’s ontology and what one thinks exists. That’s precisely why she’s gone in for a fundamental quantifier.
And she accepts the slogan because she thinks many of the sentences she endorses are written in English and they contain the English quantifier. But one’s ontology only contains the things one takes to be fundamental. For example, if what you assert contains the sentence “a is a table”, an existential generalization on that open sen- tence will produce the sentence “∃Ex(Table)x”. But one’s ontology doesn’t thereby contain tables—the only things in one’s ontology are those that one thinks existF . To determine one’s ontology, says the fundamentality theorist, one should write the sentences using ∃F she accepts. But which things are those? To figure that out, one should do fundamental ontology.
One might think I have suggested changing the question from one that is abstruse
(“what is there?”) to another that is equally abstruse (“what is fundamental?”). But I have not. There are several extant notions that have been offered as relevant to
She might think there are idiomatic uses of ‘there is’, but they’re not quantificational. She would likely think that restricted quantification—like an utterance of “there is no beer”—is idiomatic. If it’s not idiomatic, it implies the non-existence of beer. It does not imply the non-existence of beer, so it must be idiomatic.
See van Inwagen () and van Inwagen () for more on this.
Because ‘exists’ picks out neither existenceE nor existenceF uniquely.
determining what is fundamental: dependence, explanation, grounding, natu- ralness, paraphrase, purity, recombination, and truthmaking. Which no- tion or notions one thinks is or are related to fundamentality will determine what one thinks the enterprise of ontology is and what one thinks the debates in ontology should be. The fundamentality theorist, then, looks for the fundamental things because she believes that the only things in one’s ontology are the things she takes to be fundamental— whatever she takes fundamentality to be. But the Quinean also has those things in his ontology. So, the fundamentality theorist’s ∃F is a restriction of the Quinean’s quantifier that the Quinean claims is the good old ∃E.
See Aristotle (), and then further discussion in Fine (a), Koslicki (), Lowe (), Rosen (forthcoming), and Schaffer (MS)
See Kraut (), Lowe (), and Schaffer (c)
See Rosen (MS), Schaffer (c), and Skiles (MSb).
Starting in Lewis (), and developed in his () and (). The project has been extended by Sider in his (). Schaffer () makes a persuasive case that we need perfectly natural prop- erties at all levels in order to do have enough relata for causal relations and in order to account for similarity and difference.
Paraphrase is the standard Quinean way of determining ontological commitment, first stated in Quine (), then developed in Quine (). See also van Inwagen (). Since paraphrases run in one direction, a natural thought is that they run from the less fundamental to the more funda- mental; we paraphrase sentences containing less fundamental terms into sentences containing more fundamental terms. The sentences we end with—those we choose not to paraphrase—contain terms we take to refer to fundamental things.
Advocated by Sider in his (MS).
The notion of recombination dates back to Hume (), and is developed in detail in Lewis () and Schaffer (a).
Various truthmaker principles are offered and critiqued in Armstrong (), Beebee and Dodd (), Mulligan et al. (b), Restall (), Rodriguez-Pereyra (), and Schaffer ().
. Toward a Stronger Conclusion
So far I’ve been content to argue for a conditional: if one thinks there’s such a thing as the fundamental quantifier, one ought to think that it’s a restriction of the ordinary English quantifier. But before I conclude, I’d like to gesture toward an argument for a stronger conclusion: that every ontologist ought to think that there’s a fundamental quantifier and that the fundamental quantifier is a restriction of the ordinary English quantifier.
The argument begins with an assumption. The assumption is that we should desire a theory T that meets the following four conditions: ) T is charitable to the folk such that, according to T , most of what the folk say is true. ) T posits an austere ontology. ) T gives us an analysis of why the folk are right when talking about tables and yet the ontology of the world is austere. ) T retains as much of
Quinean orthodoxy as allowing the truth of ()-() will allow.
A few words in support of ()-(). First, (). My grandmother is very intelligent; she was the first of her family to graduate from college, and she has a master’s degree in library science. She often talks about composite objects. The other members of my family are also quite smart. They’ve taught me how to get around in the world, and they’ve gotten around quite well in the world themselves. They all talk about composite objects, too. It would be a shame if they are systematically wrong about things they talk about all the time. Perhaps some will argue that they are; they pre- suppose absolute simultaneity and free will and the existence of mental properties and that some material objects are solid and flat. But in all of these cases, we tend to offer analyses of what they’ve been saying that make their assertions consistent with the deliverances of physics and philosophy. We tend to think that they were talking
For example, (van Inwagen, , §) offers a theory that satisfies () and (), but he says nothing about what it is about folk discourse that allows the truth of () other than that they “express propositions that are consistent with the non-existence of chairs” (p). This is not an analysis of why () is true; it is just an assertion.
about not the relation of absolute simultaneity, but a kind of simultaneity that’s con- sistent with the fundamental simultaneity relation being relative to reference frames; they weren’t expressing that everyone acts freely, but rather that everyone is respon- sible for her actions; they weren’t talking about mental properties, but rather certain aspects of physical properties; they weren’t talking about genuine solidity and flat- ness, but a property like it enough to suit their purposes. That is, we usually give a charitable semantics; only if that fails do we give an error theory. And in this case, we can give a charitable semantics, so it would be nice to do so. We ought to maintain, if we can, that what the folk say about tables and chairs is true.
Next, (). Ontologies with very few things are theoretically virtuous. One such virtue is that such ontologies are simple; simple theories are more likely to be true.
Chief among the virtues of austere ontologies are the systematic and powerful an- swers to arguments for austere ontologies: from vagueness, from overdetermina- tion, from spatio-temporal coincidence, from epistemological considerations regard- ing how we could come to know of causally inert objects, and from Okham’s Razor.
There are other ways to respond to the arguments, but they are less systematic and less powerful. Unfortunately for the austere ontologies, they seem to entail the falsity of ().
The motivation for () comes from a desire to give, whenever possible, an account of why apparent inconsistency is not real inconsistency. This motivation can be seen in Alvin Plantinga’s work on the problem of evil. It has seemed to many that the existence of God is incompatible with the existence of evil. Rather than merely affirm that God exists and that there is evil, Plantinga sought to provide a proposition that was consistent with each and, if true, made the consistency apparent. We should strive to do the same in all cases of apparent inconsistency.
See Plantinga ().
In this case, “Possibly, every essence is transworld depraved.”
Finally, (). I like Quinean meta-ontology, and so do many others. It gives us a prescription for when to saddle people with ontological commitment, it is a guide to which debates are substantive, it rules out a lot of views I don’t like, and it gives us a procedure for making precise our sentences—regiment them in first-order logic. It is misguided in the details, to be sure, but there are strong intuitions that lead us to accept it, and it would be a shame to totally discount those intuitions.
The argument for the stronger conclusion is simple. Premise: every ontologist should accept the theory that does the best with respect to ()-(). Premise: the theory I advocate in this paper—that there is a fundamental quantifier and it is a restriction of the English quantifier—is the only theory that satisfies () through (), and it doesn’t do so bad with respect to (). Conclusion: every ontologist should accept the theory advocated in this paper.
Most theories fail (), but austere ontologies survive. But most austere ontologists say that the folk speak falsely, and thus fail (). Some say they speak “correctly” or “quasi-truly”, but this is merely an error theory—the folk, on these views, speak falsely, no matter how “close” to true they get. Those who think the folk speak truly fail (), for they do not give a satisfying account of how austere ontology could be true and the folk speak truly.
My view says that the folk speak truly when they say “tables exist” because the folk are using existenceE, and tables do existE. So my view satisfies (). But my view also satisfies (), because the only things that are in the ontology of the world
Meinongianism, substitutional quantification, ontological pluralism, and the view that being is an activity.
See, e.g., Merricks (, ch). Merricks says that he, on the other hand, speaks truly when he says, “there are statues”, because he means something different than the folk.
See, e.g. Sider (). Merricks () says they say things that are “as good as true”.
The only account on offer is that of van Inwagen (, §&), and it amounts to an assertion that the folk express propositions that are consistent with the non-existence of nonliving composite material objects.
are things that existF . My view satisfies (), because it gives a reason that the folk speak truly (they use existenceE) and yet the ontology of the world doesn’t contain the things to which they ascribe existence (the ontology of the world is all and only the things that existF ). And my view satisfies () better than other accounts phrased in terms of the fundamental quantifier because, rather than simply positing such a quantifier, I give an analysis of what the fundamental quantifier is in terms that every metaphysician can understand.
Here is why one might think that the folk’s speaking truly is inconsistent with the ontology of the world’s being austere. A) If the folk speak truly, there are chairs.
B) If the ontology of the world is austere, there are no chairs. C) If the folk speak truly and the ontology of the world is austere, then there are chairs and there aren’t chairs. The consequent of (C) is a contradiction. Here is how my view makes the two consistent, or at least makes them not obviously inconsistent. A*) If the folk speak truly, there areE tables. B*) If the ontology of the world is austere, there areF no tables. C*) If the folk speak truly and the ontology of the world is austere, then
there areE tables and there aren’tF tables. The consequent of (C*) is possible. So, my view satisfies ().
And my view does reasonably well with respect to (), as the next section shows.
. The Quinean Contrast
My view does affirm three of the five Quinean theses van Inwagen lays down in his (). It affirms that (i) being is not an activity, (ii) being is the same as exis-
One might attempt to show that (A) and (B) are consistent by replacing B with B**) If the ontology of the world is austere, then tables aren’t fundamental things. Since fundamental things are the only things in the ontology of the world, there is no inconsistency between (A) and (B**). I agree that there is no tension between (A) and (B**), but I do not see how this resolves the tension between (A) and (B). I gave two ways of reading them such that they are consistent; this response merely replaces (B) with something else. And thus it does not make sense of austere ontologists’ claims that there are no chairs. The austere ontologist may or may not agree with (B**), but she will still insist on (B). On my view, she is right to so insist, because she is using existenceF .
tence, and (iii) being or existence is adequately captured by the existential quantifier of formal logic. I disagree with a certain way of thinking about the latter; some- times ‘being’ means existenceE, and sometimes ‘being’ means existenceF . If one asks whether being is existenceE or existenceF , the fundamentality theorist says that they are two distinct notions and being is ambiguous between the two. If being is the thing that objects must have in order to figure in the ontology of the world, then being is existenceF . If being is the thing that some x must have in order for the sentence “x exists” to be true, then being is existenceE. The fundamentality theorist is convinced there is not a single sense of ‘existence’.
She agrees that each sense of ‘existence’ can be captured by the existential quantifier of formal logic in that each sense of existence obeys the introduction and elimination rules of the existential quantifier of first-order logic. If it is true that “a is F ”, then it is true that “∃ExF x”. And if a names something in the fundamental language and a is
F , then it is true that “∃F xF x”. But since we speak English, regimenting our ordinary discourse into first-order logic is done using the English quantifier. It’s not clear how ordinary language maps onto the logic of the fundamental language, but certainly
“a is F ” expressed in English does not license one to infer that ∃F xF x. If someone in the context of doing ontology says “something is F ”, then she is restricting her quantifier to the fundamental, and thus her assertion is that ∃F xF x. The fundamentality theorist may depart more significantly from the Quinean with respect to the final Quinean thesis, its criterion of ontological commitment, which van Inwagen explicates as follows:
One takes sentences that the other party to the conversation accepts, and by whatever dialectical devices one can muster, one gets him to introduce more and more quantifiers and variables into those sentences…. If, at a certain point in this procedure, it emerges that the existential general- ization on a certain open sentence F can be formally deduced from the
That is, existenceE is adequately captured by ∃E and existenceF is adequately captured by ∃F .
sentences he accepts, one has shown that the sentences that he accepts, and the ways of introducing quantifiers and variables into those sentences that he has endorsed, formally commit him to there being things that sat- isfy F. (p-)
The fundamentality theorist agrees with this as stated. If existential generalizationE on a certain open sentence F can be formally deduced from the sentences one accepts, then one has shown that the sentences that he accepts formally commit him to there beingE things that satisfy F . And if existential generalizationF on a certain open sentence F can be formally deduced from the sentences one accepts, then one has shown that the sentences that he accepts formally commit him to there beingF things that satisfy F . And only existenceF suffices for ontological commitment. The fun- damentality theorist thinks most of the quantifiers that will be introduced in such a procedure are English quantifiers. And the fundamentality theorist thinks that only if the person introduces the fundamental quantifier into his discourse is he ontologi- cally committed to the things over which he quantifies.
One could perhaps be a Quinean and grant all the above about the English quan- tifier. She would do so by saying that speakers of English very often use ‘there is’ or ‘there exists’ idiomatically, and not to express existence. This, she might say, is what the fundamentality theorist is trying to describe with the invocation of existenceE— this idiomatic usage—and existenceF is just existence. Rather than think ‘existence’ often expresses existenceE, this Quinean would say that ‘existence’ is often used id- iomatically and not to express the single sense of existence.
But the Quinean is also very much interested in preventing people from dodging ontological commitment to things over which they quantify by insisting that they’re using the quantifier idiomatically so as not to express existence. Quine mandates that, in all such cases of purported idiomatic usage of apparently quantificational expressions, one paraphrase one’s sentence into a sentence that doesn’t use a quan- tificational expression. If she can’t do so, Quine insists, then she is ontologically
committed to the things over which she’s quantified. The fundamentality theorist may accept this. She may say that, for any apparent ontologically committing utterance, it must be made explicit which quantifier is being used. If the quantifier is ∃E, then no ontological commitment is incurred; but if the quantifier is ∃F , then one does incur ontological commitment. And if one utters a sentence using ∃E, one must paraphrase the sentence into a sentence using ∃F ; in this way she makes it clear what her ontological commitments are, and what there isF that provides the underlying ontology for sentences about existenceE. But she need not do this. She thinks that one can utter “there are numbers” and still be a nominalist, thinking that the sentence is using existenceE, which is not onto- logically committing; indeed, nearly every student who says, “there is an even prime” is doing this. This fundamentality theorist may think that no further story is neces- sary; the person uttering the sentence needn’t specify which sense of the quantifier she’s using, nor supply a paraphrase in terms of existenceF . Such a fundamentality theorist departs more significantly from Quineanism with respect to its criteria of ontological commitment, inasmuch as Quineanism demands a paraphrase.
. Conclusion
There is a growing movement towards construing some classic debates in ontol- ogy as meaningless, either because the answers seem obvious or the debates seem intractable. I have proposed that we reinterpret the debates over what exists as de- bates over what existsF . I have showed a relatively easy way of doing this—adopt a fundamental quantifier, ∃F , that is a restriction of the ordinary English quantifier,
∃E. Those who are giving unintuitive answers to the ontological questions are us- ing this restricted quantifier. I have argued that anyone who thinks that there is a fundamental quantifier ought to think that it is a restriction of the ordinary English quantifier. There are three ways of giving a semantics for quantifier restriction (syn-
tactic, semantic, and pragmatic), and my view is consistent with all of them. There are three ways of understanding the way we restrict quantifiers: restrictions of the inferential role (restrictionI ), restrictions to a predicate (restrictionP ), or restrictions of the domain (restrictionD). The fundamentality theorist should think that ∃F is a restriction of ∃E, whichever sense of ‘restriction’ she accepts. My hope is that fellow fundamentality theorists will see that they have been objecting to something innocu- ous. And I further hope that since the dismissivist and the Quinean can understand these characterizations (since they can understand quantifier restriction), they can understand what fundamentality theorists are talking about.
This solves the problem of debates that seem to have obvious answers and debates that seem intractable. Ontological debates that seem to have obvious answers seem so because they do have obvious answers, at least when the quantifier being used is ∃E. But as ontologists, we shouldn’t be interested in what existsE, but rather what existsF . And what things existF is an open question that should be debated. In the case of debates that seem intractable, they seem so because ontologists are using different quantifiers and are thus talking past each other. When the debate is refocused using ∃F , the intractability disappears. This helps the ontologist in her fight against the dismissivist. Both can agree that there are some ontological disputes that are not substantive. But the ontologist’s set of non-substantive disputes will be a proper subset of the dismissivist’s. When the dismissivist claims that debates like that over composition are not substantive, the ontologist can disagree. “It seems that way,” she can say, “because they’re making the same sounds when they talk about ontology and using the same sequences of letters when they write about ontology. But really they’re using different quantifiers.” And if the dismissivist claims not to understand this, the ontologist can explain it in terms of quantifier restriction.
We can ask what existsF . But that is quite a different question from what existsE.
The latter admits of obvious answers; the former does not. We can continue to do ontology, then, by arguing about what existsF .
BIBLIOGRAPHY
Aristotle. . The Complete Works of Aristotle: The Revised Oxford Translation. Princeton: Princeton University Press. Armstrong, David. . “Truthmakers for Modal Truths.” In Gonzalo Ro- dríguez Pereyra D. H. Mellor, Hallvard Lillehammer (ed.), Real Metaphysics: Es- says in Honour of D.H. Mellor, –. Routledge. Armstrong, David M. . A World of States of Affairs. Cambridge: Cambridge University Press. ——. . Truth and Truthmakers. Cambridge: Cambridge University Press. Asay, Jamin and Baron, Sam. . “Unstable Truthmaking.” Thought :–. Audi, Paul. . “A Clarification and Defense of the Notion of Grounding.” In Fabrice Correia and Benjamin Schnieder (eds.), Metaphysical Grounding: Under- standing the Structure of Reality, –. Cambridge, UK: Cambridge University Press. Barnes, Elizabeth. Forthcoming. “Ways of Truthmaking.” Proceedings of the Aris- totelian Society . Barwise, Jon and Cooper, Robin. . “Generalized Quantifiers and Natural Lan- guage.” Linguistics and Philosophy :–. Beebee, Helen and Dodd, Julian (eds.). . Truthmakers: The Contemporary Debate. Oxford: Clarendon Press. Bennett, Karen. . “Composition, Coincidence, and Metaontology.” In Chalmers et al. (). ——. a. “By Our Bootstraps.” Philosophical Perspectives :–. ——. b. “Construction Area: No Hard Hat Required.” Philosophical Studies :–. Bigelow, John. . The Reality of Numbers: A Physicalist’s Philosophy of Math- ematics. Oxford: Clarendon. Bohn, Einar. . “Composition as identity: a study in ontology and philosophical logic.” Open Access Dissertations Paper .
Bricker, Phillip. . “The Relation betwen General and Particular: Entailment vs Supervenience.” In Dean W Zimmerman (ed.), Oxford Studies in Metaphysics Volume , –. Oxford: Oxford University Press.
Cameron, Ross. a. “How to be a Truthmaker Maximalist.” Noûs :–.
——. b. “Truthmakers and Ontological Commitment: Or How to Deal with Complex Objects and Mathematical Ontology Without Getting into Trouble.” Philosophical Studies :–.
——. c. “Truthmakers, Realism and Ontology.” Royal Institute of Philosophy Supplements :–.
——. d. “Turtles All the Way Down: Regress, Priority and Fundamentality in Metaphysics.” The Philosophical Quarterly :–.
——. . “How to Have a Radically Minimal Ontology.” Philosophical Studies :–.
——. Forthcoming. “Truthmakers.” In Michael Glanzberg (ed.), The Oxford Hand- book of Truth. Oxford University Press.
Carnap, Rudolf. . “Empiricism, Semantics and Ontology.” Revue International de Philosophie :–. Reprinted in Meaning and Necessity: A Study in Seman- tics and Modal Logic. nd edn. Chicago: University of Chicago Press, .
Chalmers, David. . “Ontological Antirealism.” In David Manley David Chalmers (ed.), Metametaphysics. Oxford University Press.
Chalmers, David, Manley, David, and Wasserman, Ryan (eds.). . Metameta- physics. Oxford: Oxford University Press.
Chomsky, Noam. . Syntactic Structures. The Hague: Mouton.
Chudnoff, Elijah. MS. “Grounding and Entailment.”
Cooper, Robin. . Quantification and Syntactic Theory, volume of Synthese Language Library. Dordrecht, Holland: D. Reidel Publishing Company.
Correia, Fabrice. . Existential Dependence and Cognate Notions. Philosophia Verlag.
——. . “Ontological Dependence.” Philosophy Compass :–.
——. . “Grounding and Truth-Functions.” Logique et Analyse :–.
Cox, Damian. . “The Trouble with Truth-makers.” Pacific Philosophical Quar- terly :–.
Daly, Chris. . “Scepticism about Grounding.” In Fabrice Correia and Ben- jamin Schnieder (eds.), Metaphysical Grounding: Understanding the Structure of Reality. Cambridge University Press.
Dasgupta, Shamik. . “Individuals: An Essay in Revisionary Metaphysics.” Philosophical Studies :–.
——. MS. “The Status of Ground.” . deRosset, Louis. . “Getting Priority Straight.” Philosophical Studies :–.
——. . “Grounding Explanations.” Philosopher’s Imprint :–.
——. Forthcoming. “No Free Lunch.” In Schnieder Steinberg, Hoetlje (ed.), Dependence, Emergence, Supervenience, Basic Philosophical Concepts. Munich: Philosophia Verlag.
Descartes, Rene. . The Philosophical Writings of Descartes. Cambridge Uni- versity Press.
Fine, Kit. . “Ontological Dependence.” Proceedings of the Aristotelian Society .
——. . “The Question of Realism.” Philosopher’s Imprint .
——. . “The Question of Ontology.” In David Chalmers, David Manley, and Ryan Wasserman (eds.), Metametaphysics. Oxford University Press.
——. . “Some Puzzles of Ground.” Notre Dame Journal of Formal Logic :–.
——. a. “A Guide to Ground.” In Fabrice Correia and Benjamin Schnieder (eds.), Metaphysical Grounding: Understanding the Structure of Reality, –. Cambridge University Press.
——. b. “The Pure Logic of Ground.” The Review of Symbolic Logic :–.
Fox, John F. . “Truthmaker.” Australasian Journal of Philosophy :–.
Goggans, Phillip. . “How not to Have an Ontology of Material Objects.” Philo- sophical Studies :–.
Gorman, Michael. . “Substance and Identity-Dependence.” Philosophical Pa- pers :–.
Hawthorne, John (O’Leary-) and Cortens, Andrew. . “Towards Ontological Nihilism.” Philosophical Studies :–.
Heil, John. . From an Ontological Point of View. Oxford: Oxford University Press.
——. . The Universe as We Find It. Oxford: Oxford University Press.
Hirsch, Eli. . “Quantifier Variance and Realism.” Philosophical Issues :– .
——. . “Physical-Object Ontology, Verbal Disputes, and Common Sense.” Phi- losophy and Phenomenological Research :–.
——. . “Language, Ontology, and Structure.” Noûs :–.
Hoffman, Frank. . “Truthmaking, Recombination, and Facts Ontology.” Philo- sophical Studies :–.
Hoffman, Joshua and Rosenkrantz, Gary. . “The Independence Criterion of Substancehood.” Philosophy and Phenomenological Research :–.
——. . Substance: Its Nature and Existence. Routledge.
——. . Substance among other Categories. Cambridge University Press.
Hofweber, Thomas. . “Ambitious, yet Modest, Metaphysics.” In David Manley David Chalmers and Ryan Wasserman (eds.), Metametaphysics. Oxford University Press.
Hume, David. . An Enquiry Concerning Human Understanding. Oxford Uni- versity Press .
Jenkins, C.S. . “What is Ontological Realism?” Philosophy Compass :– .
Jenkins, C.S. . “Is Metaphysical Grounding Irreflexive?” The Monist :–.
Korman, Daniel Z. . “Unrestricted composition and restricted quantification.” Philosophical Studies –.
Koslicki, Kathrin. . The Structure of Objects. Oxford University Press.
——. . “Varieties of Ontological Dependence.” In Fabrice Correia and Ben- jamin Schnieder (eds.), Metaphysical Grounding: Understanding the Structure of Reality, –. Cambridge University Press.
——. Forthcoming. “Ontological Dependence: An Opinionated Survey.” In Ben- jamin Schnieder (ed.), Dependence. München: Philosophia Verlag.
——. Manuscript. “The Coarse-Grainedness of Grounding.”
Kraut, Robert. . “Metaphysical Explanation and the Philosophy of Mathemat- ics.” Philosophia Mathematica :–.
Kripke, Saul. . “A Puzzle About Belief.” In Avishai Margalit (ed.), Meaning and Use, –. Dordrecht: Reidel.
Leibniz, Gottfried Wilhelm. . Discourse on Metaphysics and the Monadology. Prometheus Books.
Lewis, David. . “New Work for a Theory of Universals.” Australasian Journal of Philosophy :–.
——. . “Putnam’s Paradox.” Australasian Journal of Philosophy :–.
——. . On the Plurality of Worlds. Oxford: Basil Blackwell.
——. . “Humean Supervenience Debugged.” Mind :–.
——. . “Tensed Quantifiers.” In Dean W. Zimmerman (ed.), Oxford Studies in Metaphysics, –. Oxford: Oxford University Press.
Lewis, David K. . “Truthmaking and Difference-Making.” Noûs :–.
Liggins, David. . “Truthmakers and Explanation.” In Helen Beebee and Julian Dodd (eds.), Truthmakers: The Contemporary Debate. Oxford: Clarendon.
Locke, John. . An Essay concerning Human Understanding.
Lowe, E. J. . “Ontological Dependency.” Philosophical Papers XXIII:–.
——. . The Possibility of Metaphysics. Oxford University Press.
——. . The Four-Category Ontology: a metaphysical foundation for natural science. Oxford: Clarendon Press.
——. . “Ontological Dependence.” In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/archives/spr2010/ entries/dependence-ontological/, spring edition. Last accessed on February , .
Martin, C.B. . “Substance Substantiated.” Australasian Journal of Philosophy :–.
McDaniel, Kris. . “Being and Almost Nothingness.” Noûs :–.
McFetridge, Ian. . “Truth, Correspondence, Explanation and Knowledge.” In Logical Necessity and Other Essays, –. London: Aristotelian Society.
Melia, Joseph. . “Truthmaking Without Truthmakers.” In Beebee and Dodd (), –.
Merricks, Trenton. . Objects and Persons. Oxford: Clarendon.
——. . Truth and Ontology. Oxford: Oxford University Press.
Morganti, Matteo. . “Ontological Priority, Fundamentality and Monism.” di- alectica :–.
Mulligan, Keith, Simons, Peter, and Smith, Barry. a. “Truth-Makers.” Philos- ophy and Phenomenological Research :–.
Mulligan, Kevin. . “Two Dogmas of Truth-making.” In J.M. Monnoyer (ed.), Metaphysics and Truthmakers, –. Frankfurt: Ontos Verlag.
Mulligan, Kevin, Simons, Peter, and Smith, Barry. b. “Truth-makers.” Philos- ophy and Phenomenological Research :–.
Neale, Stephen. . Descriptions. Bradford Books. MIT Press.
Nolan, Daniel. . “What’s Wrong with Infinite Regresses?” Metaphilosophy :–.
Oliver, Alex. . “The Metaphysics of Properties.” Mind :–.
Parsons, Josh. . “Truthmakers, the Past, and the Future.” In Helen Beebee and Julian Dodd (eds.), Truthmakers: The Contemporary Debate. Oxford: Clarendon.
Paul, L. A. ms. “Parthood and Individuation in a One Category Ontology.”
Pendlebury, Michael. . “Facts as Truthmakers.” The Monist :–.
Plantinga, Alvin. . The Nature of Necessity. Oxford: Oxford University Press.
Putnam, Hilary. . Ethics Without Ontology. Harvard University Press.
Quine, W. V. O. . “On What There Is.” Review of Metaphysics :–.
——. a. “On Carnap’s Views on Ontology.” Philosophical Studies :–.
——. b. “Ontology and Ideology.” Philosophical Studies :–.
——. . Word and Object. Cambridge, Mass.: MIT Press.
——. . Philosophy of Logic. Cambridge, Mass.: Harvard University Press. Second edition, .
——. . The Pursuit of Truth. Harvard University Press.
——. . “Nominalism.” In Dean W. Zimmerman (ed.), Oxford Studies in Meta- physics Volume . Oxford University Press.
Raven, Michael J. . “In Defence of Ground.” Australasian Journal of Philosophy :–.
Rayo, Agustín and Uzquiano, Gabriel (eds.). . Absolute Generality. Oxford: Oxford University Press.
Rea, Michael. . “Hylomorphism Reconditioned.” Philosophical Perspectives :–.
Recanati, François. . “Domains of Discourse.” Linguistics and Philosophy :–.
Reimer, Marga. . “Quantification and Context.” Linguistics and Philosophy :–.
Reinhart, Tanya. . “Quantifier Scope - How Labor is Divided between QR and Choice Functions.” Linguistics and Philosophy :–.
Restall, Greg. . “Truthmakers, Entailment and Necessity.” Australasian Journal of Philosophy :–.
Rhoda, Alan. . “Presentism, Truthmakers, and God.” Pacific Philosophical Quarterly :–.
Rodriguez-Pereyra, Gonzalo. . “Why Truthmakers?” In Helen Beebee and Julian Dodd (eds.), Truthmakers: The Contemporary Debate. Oxford: Clarendon Press.
——. . “Truthmakers.” Philosophy Compass :–.
Rosen, Gideon. Forthcoming. “Metaphysical Dependence: Grounding and Reduc- tion.” In Robert Hale and Aviv Hoffman (eds.), Modality: Metaphysics, Logic, and Epistemology. Oxford: Oxford University Press.
——. MS. “The Limits of Contingency.”
Ruben, David-Hillel. . Explaining Explanation. The Problems of Philosophy Their Past and Present. Routledge.
Russell, Bertrand. . The Philosophy of Logical Atomism. La Salle, Illinois: Open Court.
Sag, Ivan. . Deletion and Logical Form. Ph.D. thesis, Massachusetts Institute of Technology, http://dspace.mit.edu/handle/./. Last accessed on January , .
Schaffer, Jonathan. . “Is there a Fundamental Level?” Noûs :–.
——. . “Two Conceptions of Sparse Properties.” Pacific Philosophical Quarterly :–.
——. . “Truthmaker Commitments.” Philosophical Studies :–.
——. a. “On What Grounds What.” In David Chalmers, David Manley, and Ryan Wasserman (eds.), Metametaphysics. Oxford: Oxford University Press.
——. b. “Spacetime the One Substance.” Philosophical Studies :–.
——. a. “The Internal Relatedness of All Things.” Mind :–.
——. b. “The Least Discerning and Most Promiscuous Truthmaker.” The Philosophical Quarterly :–.
——. c. “Monism: The Priority of the Whole.” Philosophical Review :– .
——. . “Grounding, Transitivity, and Contrastivity.” In Fabrice Correia and Benjamin Schnieder (eds.), Metaphysical Grounding: Understanding the Structure of Reality, –. Cambridge University Press.
——. MS. “Grounding as the Primitive Concept of Metaphysical Structure.”
Schnieder, Benjamin. . “Truth-making without Truth-makers.” Synthese :–.
Sidelle, Alan. . “Is There a True Metaphysics of Material Objects?” Philosoph- ical Issues :–.
Sider, Theodore. . Naturalness, Intrinsicality and Duplication. Ph.D. thesis, University of Massachusetts.
——. . “Neo-Fregeanism and Quantifier Variance.” Aristotelian Society Sup- plementary Volume :–.
——. . “Ontological Realism.” In David Chalmers, David Manley, and Ryan Wasserman (eds.), Metametaphysics. Oxford: Oxford University Press.
——. . Writing the Book of the World. Oxford University Press.
——. . “Against Parthood.” In Karen Bennett and Dean W. Zimmerman (eds.), Oxford Studies in Metaphysics Volume . Oxford University Press.
Simons, Peter. . “Negatives, Numbers and Necessity: Some Worries about Arm- strong’s Version of Truthmaking.” Australasian Journal of Philosophy :– .
Skiles, Alexander. MSa. “Against Grounding Necessitarianism.”
——. MSb. “Grounding Wholes in their Parts.”
Smith, Barry and Simon, Jonathan. . “Truthmaker Explanations.” In J.M. Monnoyer (ed.), Metaphysics and Truthmakers, –. Frankfurt: Ontos Verlag.
Sosa, Ernest. . “Existential Relativity.” In Peter French and Howard K. Wettstein (eds.), Midwest Studies in Philosophy XXIII: New Directions in Phi- losophy, –. Oxford: Basil Blackwell.
Spinoza, Baruch. . The Collected Writings of Spinoza, volume , chapter Ethics. Princeton University Press.
Stanley, Jason and Szabo, Zoltan Gendler. . “On Quantifier Domain Restric- tion.” Mind and Language :–.
Thomasson, Amie L. . “Existence Questions.” Philosophical Studies :– .
——. . “Answerable and Unanswerable Questions.” In Chalmers et al. ().
Trogdon, Kelly. Forthcominga. “Grounding: Necessary or Contingent?” Pacific Philosophical Quarterly .
——. Forthcomingb. “An Introduction to Grounding.” In Alexander Steinberg Miguel Hoeltje, Benjamin Schnieder (ed.), Varieties of Dependence, Basic Philo- sophical Concepts. Philosophia Verlag.
Turner, Jason. . “Ontological Pluralism.” Journal of Philosophy .
——. . “Ontological Nihilism.” In Dean W Zimmerman and Karen Bennett (eds.), Oxford Studies in Metaphysics Volume , –. Oxford University Press. van Fraassen, Bas. . The Empirical Stance. Yale University Press. van Inwagen, Peter. . Material Beings. Ithaca, NY: Cornell University Press.
——. . “Meta-Ontology.” Erkenntnis :–.
——. . “Being, Existence, and Ontological Commitment.” In David Chalmers, David Manley, and Ryan Wasserman (eds.), Metametaphysics. Oxford: Oxford University Press. von Fintel, Kai. MS. “The Semantics and Pragmatics of Quantifier Domains.” Avail- able at: http://mit.edu/fintel/fintel--qic.pdf. Last accessed on February , .
Whitcomb, Dennis. . “Grounding and Omniscience.” In Jon Kvanvig (ed.), Oxford Studies in the Philosophy of Religion, volume . Oxford University Press.
Williams, J. R. G. . “Fundamental and Derivative Truths.” Mind :–.
Williamson, Timothy. . “Everything.” Philosophical Perspectives :–.
Wilson, Jessica. . “Fundamental Determinables.” Philosopher’s Imprint :– .
——. MS. “No Work for a Theory of Grounding.” Draft of April , .
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