This paper extracts some of the main theses in the philosophy of mathematics from my book, The Construction of Logical Space. I show that there are important limits to the availability of nominalistic paraphrase functions for mathematical languages, and suggest a way around the problem by developing a method for specifying nominalistic contents without corresponding nominalistic paraphrases. Although much of the material in this paper is drawn from the book — and from an earlier paper — I hope the present (...) discussion will earn its keep by motivating the ideas in a new way, and by suggesting further applications. (shrink)

Mereological realism holds that the world has a mereological structure – i.e. a distribution of mereological properties and relations. In this article, I defend Eleaticism about properties, according to which there are no causally inert non-logical properties. I then present an Eleatic argument for mereological anti-realism, which denies the existence of both mereological composites and mereological simples. After defending Eleaticism and mereological anti-realism, I argue that mereological anti-realism is preferable to mereological nihilism. I then conclude by examining the thesis that (...) composition is identity and noting its consequences for the question of mereological structure. (shrink)

Nihilism is the thesis that no composite objects exist. Some ontologists have advocated abandoning nihilism in favor of deep nihilism, the thesis that composites do not existO, where to existO is to be in the domain of the most fundamental quantifier. By shifting from an existential to an existentialO thesis, the deep nihilist seems to secure all the benefits of a composite-free ontology without running afoul of ordinary belief in the existence of composites. I argue that, while there are well-known (...) reasons for accepting nihilism, there appears to be no reason at all to accept deep nihilism. In particular, deep nihilism draws no support either from the usual arguments for nihilism or from considerations of parsimony. (shrink)

Slot theory is the view that (i) there exist such entities as argument places, or ‘slots’, in universals, and that (ii) a universal u is n-adic if and only if there are n slots in u. I argue that those who take properties and relations to be abundant, fine-grained, non-set-theoretical entities face pressure to be slot theorists. I note that slots permit a natural account of the notion of adicy. I then consider a series of ‘slot-free’ accounts of that notion (...) and argue that each of them has significant drawbacks. (shrink)

An encyclopedia entry which covers various revisionary conceptions of which macroscopic objects there are, and the puzzles and arguments that motivate these conceptions: sorites arguments, the argument from vagueness, the puzzles of material constitution, arguments against indeterminate identity, arguments from arbitrariness, debunking arguments, the overdetermination argument, and the problem of the many.

Unlike identity physicalism, ground physicalism does not achieve the physicalist dream. It faces the T-shirt problem for ground physicalism (Pautz 2014; Schaffer this volume; Rubenstein ms). In the case of insentient nature, it may be able to get by with small handful of very general ground laws to explain the emergence of nonfundamental objects and properties – for example, a few “principle of plenitude”. But I argue that for the case consciousness it will require a separate huge raft of special, (...) anomalous psychophysical ground laws. So it is just as complex and nonuniform as dualism. (shrink)

A counterpossible is a counterfactual whose antecedent is impossible. The vacuity thesis says all counterpossibles are true solely because their antecedents are impossible. Recently, some have rejected the vacuity thesis by citing purported non-vacuous counterpossibles in science. One limitation of this work, however, is that it is not grounded in experimental data. Do scientists actually reason non-vacuously about counterpossibles? If so, what is their basis for doing so? We presented biologists (N = 86) with two counterfactual formulations of a well-known (...) model in biology, the antecedents of which contain what many philosophers would characterize as a metaphysical impossibility. Participants consistently judged one counterfactual to be true, the other to be false, and they explained that they formed these judgments based on what they perceived to be the mathematical relationship between the antecedent and consequent. Moreover, we found no relationship between participants’ judgments about the (im)possibility of the antecedent and whether they judged a counterfactual to be true or false. These are the first experimental results on counterpossibles in science with which we are familiar. We present a modal semantics that can capture these judgments, and we deal with a host of potential objections that a defender of the vacuity thesis might make. (shrink)

In this paper, I develop a "safety result" for applied mathematics. I show that whenever a theory in natural science entails some non-mathematical conclusion via an application of mathematics, there is a counterpart theory that carries no commitment to mathematical objects, entails the same conclusion, and the claims of which are true if the claims of the original theory are "correct": roughly, true given the assumption that mathematical objects exist. The framework used for proving the safety result has some advantages (...) over existing nominalistic accounts of applied mathematics. It also provides a nominalistic account of pure mathematics. (shrink)

Inspired by Cantor's Theorem (CT), orthodoxy takes infinities to come in different sizes. The orthodox view has had enormous influence in mathematics, philosophy, and science. We will defend the contrary view---Countablism---according to which, necessarily, every infinite collection (set or plurality) is countable. We first argue that the potentialist or modal strategy for treating Russell's Paradox, first proposed by Parsons (2000) and developed by Linnebo (2010, 2013) and Linnebo and Shapiro (2019), should also be applied to CT, in a way that (...) vindicates Countabilism. Our discussion dovetails with recent independently developed treatments of CT in Meadows (2015), Pruss (2020), and Scambler (2021), aimed at establishing the mathematical viability, and therefore epistemic possibility, of Countabilism. Unlike these authors, our goal isn't to vindicate the mathematical underpinnings of Countabilism. Rather, we aim to argue that, given that Countabilism is mathematically viable, Countabilism should moreover be regarded as true. After clarifying the modal content of Countabilism, we canvas some of Countabilism's many positive implications, including that Countabilism provides the best account of the pervasive independence phenomena in set theory, and that Countabilism has the power to defuse several persistent puzzles and paradoxes found in physics and metaphysics. We conclude that in light of its theoretical and explanatory advantages, Countabilism is more likely true than not. (shrink)

In this paper, I argue that all expressions for abstract objects are meaningless. My argument closely follows David Lewis’ argument against the intelligibility of certain theories of possible worlds, but modifies it in order to yield a general conclusion about language pertaining to abstract objects. If my Lewisian argument is sound, not only can we not know that abstract objects exist, we cannot even refer to or think about them. However, while the Lewisian argument strongly motivates nominalism, it also undermines (...) certain nominalist theories. (shrink)

A counterpossible is a counterfactual with an impossible antecedent. Counterpossibles present a puzzle for standard theories of counterfactuals, which predict that all counterpossibles are semantically vacuous. Moreover, counterpossibles play an important role in many debates within metaphysics and epistemology, including debates over grounding, causation, modality, mathematics, science, and even God. In this article, we will explore various positions on counterpossibles as well as their potential philosophical consequences.

Plausibly, mathematical claims are true, but the fundamental furniture of the world does not include mathematical objects. This can be made sense of by providing mathematical claims with paraphrases, which make clear how the truth of such claims does not require the fundamental existence of mathematical objects. This paper explores the consequences of this type of position for explanatory structure. There is an apparently straightforward relationship between this sort of structure, and the logical sort: i.e. logically complex claims are explained (...) by logically simpler ones. For example, disjunctions are explained by their (true) disjuncts, while generalizations are explained by their (true) instances. This would seem as plausible in the case of mathematics as elsewhere. Also, it would seem to be something that the anti-realist approaches at issue would want to preserve. It will be argued, however, that these approaches cannot do this: they lead not merely to violations of the familiar principles relating logical and explanatory structure, but even to reversals of these. That is, there are cases where generalizations explain their instances, or disjunctions their disjuncts. (shrink)

Can there be an objective morality without God? Derek Parfit argues that it can and offers a theory of morality that is neither theistic nor naturalistic. This book provides a critical assessment of Parfit's metaethical theory. Jakobsen identifies some problems in Parfit’s theory – problems concerning moral normativity, the ontological status of morality, and evolutionary influence on our moral beliefs – and argues that theological resources can help solve them. By showing how Parfit’s theory may be improved by the help (...) of theology, Jakobsen demonstrates the relevance of theology in philosophical and metaethical debates and argues that Christian theism offers a better explanation of morality than what Parfit’s non-naturalism does. (shrink)

What is the relationship between objects and properties? According to a standard view, there are primitive individuals that ‘instantiate’ or ‘have’ various properties. According to a rival view, objects are mere ‘bundles’ of properties. While there are a number of reasons to be skeptical of primitive individuals, there are also a number of challenges that the bundle theorist faces. The goal of this paper is to formulate a view about the relationship between objects and properties that avoids many of the (...) problems inherent in both of these views. The view I will end up defending implies a particularly radical version of Monism, and it collapses the object-property distinction altogether. (shrink)

Some metaphysicians believe that existence debates are easily resolved by trivial inferences from Moorean premises. This paper considers how the introduction of negative Moorean facts—negative existentials that command Moorean certainty—complicates this picture. In particular, it shows how such facts, when combined with certain plausible metaontological principles, generate a puzzle that commits the proponents of this method to a contradiction.

Many favor representationalism about color experience. To a first approximation, this view holds that experiencing is like believing. In particular, like believing, experiencing is a matter of representing the world to be a certain way. Once you view color experience along these lines, you face a big question: do our color experiences represent the world as it really is? For instance, suppose you see a tomato. Representationalists claim that having an experience with this sensory character is necessarily connected with representing (...) a distinctive quality as pervading a round area out there in external space. Let us call it “sensible redness” to highlight the fact that the representation of this property is necessarily connected with the sensory character of the experience. Is this property, sensible redness, really co-instantiated with roundness out there in the space before you? (shrink)

Presenting the first comprehensive, in-depth study of hyperintensionality, this book equips readers with the basic tools needed to appreciate some of current and future debates in the philosophy of language, semantics, and metaphysics. After introducing and explaining the major approaches to hyperintensionality found in the literature, the book tackles its systematic connections to normativity and offers some contributions to the current debates. The book offers undergraduate and graduate students an essential introduction to the topic, while also helping professionals in related (...) fields get up to speed on open research-level problems. (shrink)

Easy-road mathematical fictionalists grant for the sake of argument that quantification over mathematical entities is indispensable to some of our best scientific theories and explanations. Even so they maintain we can accept those theories and explanations, without believing their mathematical components, provided we believe the concrete world is intrinsically as it needs to be for those components to be true. Those I refer to as “mathematical surrealists” by contrast appeal to facts about the intrinsic character of the concrete world, not (...) to explain why our best mathematically imbued scientific theories and explanations are acceptable in spite of having false components, but in order to replace those theories and explanations with parasitic, nominalistically acceptable alternatives. I argue that easy-road fictionalism is viable only if mathematical surrealism is and that the latter constitutes a superior nominalist strategy. Two advantages of mathematical surrealism are that it neither begs the question concerning the explanatory role of mathematics in science nor requires rejecting the cogency of inference to the best explanation. (shrink)

Metaphysics is the branch of philosophy that aims to give a theoretical account of what there is and what it is like. Social justice movements seek to bring about justice in a society by changing policy, law, practice, and culture. Evidently, these activities are very different from one another. The goal of this article is to identify some positive connections between recent work in metaphysics and social justice movements. I outline three ways in which metaphysical work on social reality can (...) make a contribution to movements seeking social justice, viz., (1) by providing basic categories and concepts useful for clarifying and defending claims made by social justice movements; (2) by offering accounts of the natures of social categories, structures, and institutions that these movements seek to change; and (3) by contributing to “unmasking” or “debunking” projects that reveal putatively natural arrange- ments to be social in nature and hence subject to moral critique, alteration, and possibly eradication. (shrink)

Fictionalists maintain that possible worlds, numbers or composite objects exist only according to theories which are useful but false. Hale, Divers and Woodward have provided arguments which threaten to show that fictionalists must be prepared to regard the theories in question as contingently, rather than necessarily, false. If warranted, this conclusion would significantly limit the appeal of the fictionalist strategy rendering it unavailable to anyone antecedently convinced that mathematics and metaphysics concern non-contingent matters. I try to show that their arguments (...) can be resisted by developing and defending a strategy suggested by Rosen, Nolan and Dorr, according to which the fiction-operator is to be analysed in terms of a counterfactual that admits of non-trival truth-values even when the antecedent is impossible. (shrink)

According to the scrutability argument against physicalism, an a priori gap between the physical and conscious experience entails a lack of necessitation and the falsity of physicalism. This paper investigates the crucial premise of the scrutability argument: the inference from an a priori gap to a lack of necessitation. This premise gets its support from modal rationalism, according to which there are important, potentially constitutive, connections between a priori justification and metaphysical modality. I argue against the strong form of modal (...) rationalism that underwrites the scrutability argument and suggest a more moderate rationalist view. I offer a novel demonstrative reply to the scrutability argument, according to which demonstratives play a vital role in the generation of meaning for our representations of conscious experience. This connection between conscious experience and demonstratives, rather than a metaphysical gap generated by the truth of dualism, is the source of the epistemic gap between consciousness and the physical. (shrink)

There’s the question of what there is, and then there’s the question of what ultimately exists. Many contend that, once we have this distinction clearly in mind, we can see that there is no sensible debate to be had about whether there are such things as properties or tables or numbers, and that the only ontological question worth debating is whether such things are ultimate (in one or another sense). I argue that this is a mistake. Taking debates about ordinary (...) objects as a case study, I show that the arguments that animate these debates bear directly on the question of which objects there are and cannot plausibly be recast as arguments about what’s ultimate. I then address the objection that, because they are easy answerable, questions about what there is cannot be a proper subject of ontological debate. (shrink)

The metaphysics of representation poses questions such as: in virtue of what does a sentence, picture, or mental state represent that the world is a certain way? In the first instance, I have focused on the semantic properties of language: for example, what is it for a name such as ‘London’ to refer to something? Interpretationism concerning what it is for linguistic expressions to have meaning, says that constitutively, semantic facts are fixed by best semantic theory. As here developed, it (...) promises to give a reductive, universal and non-revisionary account of the nature of linguistic representation. -/- Interpretationism in general, however, is threatened by severe internal tension, due to arguments for radical inscrutability. These contend that, given the interpretationist setting, there can be no fact of the matter what object an individual word refers to: for example, that there is no fact of the matter as to whether “London” refers to London or to Sydney. -/- A series of challenges emerge, forming the basis for this thesis. 1. What sort of properties is the interpretationist trying to reduce, and what kind of reductive story is she offering? 2. How are inscrutability theses best formulated? Are arguments for inscrutability effective in their own terms? What kinds of inscrutability arise? 3. Is endorsing radical inscrutability a stable position? 4. Are there theoretical virtues—such as simplicity—that can be appealed to in discrediting the rival (empirically equivalent) theories that underpin inscrutability arguments? -/- In addressing these questions, I concentrate on diagnosing the source of inscrutability, mapping the space of ways of resisting the arguments for radical inscrutability, and examining the challenges faced in developing a principled account of linguistic content that avoids radical inscrutability. -/- The effect is not to close down the original puzzles, but rather to sharpen them into a set of new and deeper challenges. (shrink)

The Significance Argument (SA) for the irreducibility of consciousness is based on a series of new puzzle-cases that I call multiple candidate cases. In these cases, there is a multiplicity of physical-functional properties or relations that are candidates to be identified with the sensible qualities and our consciousness of them, where those candidates are not significantly different. I will argue that these cases show that reductive materialists cannot accommodate the various ways in which consciousness is significant and must allow massive (...) vagueness in conscious experience. I also will argue that a nonreductive theory of the conscious-of relation can easily provide a very satisfying, unified explanation of the ways in which this relation is significant. (shrink)

“There are no gaps in logical space,” David Lewis writes, giving voice to sentiment shared by many philosophers. But different natural ways of trying to make this sentiment precise turn out to conflict with one another. One is a *pattern* idea: “Any pattern of instantiation is metaphysically possible.” Another is a *cut and paste* idea: “For any objects in any worlds, there exists a world that contains any number of duplicates of all of those objects.” We use resources from model (...) theory to show the inconsistency of certain packages of combinatorial principles and the consistency of others. (shrink)

We often speak as if there are merely possible people—for example, when we make such claims as that most possible people are never going to be born. Yet most metaphysicians deny that anything is both possibly a person and never born. Since our unreflective talk of merely possible people serves to draw non-trivial distinctions, these metaphysicians owe us some paraphrase by which we can draw those distinctions without committing ourselves to there being merely possible people. We show that such paraphrases (...) are unavailable if we limit ourselves to the expressive resources of even highly infinitary first-order modal languages. We then argue that such paraphrases are available in higher-order modal languages only given certain strong assumptions concerning the metaphysics of properties. We then consider alternative paraphrase strategies, and argue that none of them are tenable. If talk of merely possible people cannot be paraphrased, then it must be taken at face value, in which case it is necessary what individuals there are. Therefore, if it is contingent what individuals there are, then the demands of paraphrase place tight constraints on the metaphysics of properties: either (i) it is necessary what properties there are, or (ii) necessarily equivalent properties are identical, and having properties does not entail even possibly being anything at all. (shrink)

Parfit denies that the introduction of reasons into our ontology is costly for his theory. He puts forth two positions to help establish the claim: the Plural Senses View and the Argument from Empty Ontology. I argue that, first, the Plural Senses View for ‘exists’ can be expanded to allow for senses which undermine his ontological claims; second, the Argument from Empty Ontology can be debunked by Platonists. Furthermore, it is difficult to make statements about reasons true unless these statements (...) include reference to objects in reality. These arguments show the instability of Parfit’s claimed metaethical advantages over naturalism. [Open access]. (shrink)

© The Author 2017. Published by Oxford University Press on behalf of The Analysis Trust. All rights reserved. For Permissions, please email: [email protected] of the best arguments in Trenton Merricks’s book Propositions – and there are many excellent arguments to choose from – occurs near the end, where he argues that if it is primitive that propositions represent things as being various ways then we should reject the view that propositions are structured and have constituents. As Merricks shows, combining these (...) views leads to an inexplicable coincidence between what a proposition represents and its constituents. Suppose that it is a primitive and unanalysable fact that the proposition that p represents Russell as being a philosopher. Suppose also that p has Russell and the property of being a philosopher as constituents. What is the relationship between these two facts? The latter cannot explain the... (shrink)

This paper is an investigation of the general logic of "identifications", claims such as 'To be a vixen is to be a female fox', 'To be human is to be a rational animal', and 'To be just is to help one's friends and harm one's enemies', many of which are of great importance to philosophers. I advocate understanding such claims as expressing higher-order identity, and discuss a variety of different general laws which they might be thought to obey. [New version: (...) Nov. 4th, 2016]. (shrink)

It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If there were nothing otherwise “uniquely metaphysically significant” about (...) metaphysical necessity, then paradigmatic metaphysical necessities would be necessary in one sense of “necessary”, not necessary in another, and that would be it. The question of whether they were necessary simpliciter would be like the question of whether the Parallel Postulate is true simpliciter – understood as a pure mathematical conjecture, rather than as a hypothesis about physical spacetime. In a sense, the latter question has no objective answer. In this article, I argue that paradigmatic questions of modal metaphysics are like the Parallel Postulate question. I then discuss the deflationary ramifications of this argument. I conclude with an alternative conception of the space of possibility. According to this conception, there is no objective boundary between possibility and impossibility. Along the way, I sketch an analogy between modal metaphysics and set theory. (shrink)

There has been much recent interest in a distinctively metaphysical kind of determinative explanation: ground. This paper concerns various skeptical challenges to ground’s relevance to metaphysics, such as that it is an empty posit, that the work it is supposed to do is appropriated by other notions, and that it is inapt for specific issues it should serve. I argue against these challenges. My strategy is both critical and constructive. Critical because I argue that versions of these challenges raised by (...) Elizabeth Barnes, Kathrin Koslicki, Mari Mikkola, and Jessica Wilson are not persuasive. Constructive because we may nevertheless learn from them new work for ground. (shrink)

This paper examines "moderate modal skepticism", a form of skepticism about metaphysical modality defended by Peter van Inwagen in order to blunt the force of certain modal arguments in the philosophy of religion. Van Inwagen’s argument for moderate modal skepticism assumes Yablo's (1993) influential world-based epistemology of possibility. We raise two problems for this epistemology of possibility, which undermine van Inwagen's argument. We then consider how one might motivate moderate modal skepticism by relying on a different epistemology of possibility, which (...) does not face these problems: Williamson’s (2007: ch. 5) counterfactual-based epistemology. Two ways of motivating moderate modal skepticism within that framework are found unpromising. Nevertheless, we also find a way of vindicating an epistemological thesis that, while weaker than moderate modal skepticism, is strong enough to support the methodological moral van Inwagen wishes to draw. (shrink)

An epistemology of art has seemed problematic mainly because of arguments claiming that an essential element of a theory of knowledge, truth, has no place in aesthetic contexts. For, if it is objectively true that something is beautiful, it seems to follow that the predicate “is beautiful” expresses a property – a view asserted by Plato but denied by Hume and Kant. But then, if the belief that something is beautiful is not objectively true, we cannot be said to know (...) that something is beautiful and the path to an epistemology of art is effectively blocked. The article places the existence aesthetic properties in the proper context; presents a logically correct argument for the existence of such properties; identifies strategies for responding to this argument; explains why objections by Hume, Kant, and several other philosophers fail; and sketches a realization account of beauty influenced by Hogarth. (shrink)

In the ‘ordinary business of life’, everyone makes claims about what there is. For instance, we say things like: ‘There are some beautiful chairs in my favourite furniture shop’. Within the context of philosophical debate, some philosophers also make claims about what there is. For instance, some ontologists claim that there are chairs; other ontologists claim that there are no chairs. What is the relation between ontologists’ philosophical claims about what there is and ordinary claims about what there is? According (...) to Cian Dorr, ontologists’ claims and denials of existence belong to ‘a sort of professional jargon’. Dorr claims, for example, that ‘There are prime numbers between 20 and 30’ can be used superficially or used fundamentally. Ordinary uses of are superficial: we use the sentence to assert a boring, well-known truth. But in the ontology room, is used fundamentally, to assert that numbers are ‘part of the ultimate furniture of reality’: and this is a substantial metaphysical doctrine, not a boring truth. In this paper, we will show that none of Dorr’s arguments for these claims succeeds. (shrink)

It is widely assumed that sense perception cannot deliver knowledge of nonactual (metaphysical) possibilities. We are not supposed to be able to know that a proposition p is necessary or that p is possible (if p is false) by sense perception. This paper aims to establish that the role of sense perception is not so limited. It argues that we can know lots of modal facts by perception. While the most straightforward examples concern possibility and contingency, others concern necessity and (...) impossibility. The possibility of a perceptual route to some modal knowledge is not as radical as it may at first sound. On the contrary, acknowledging it has benefits. (shrink)

This article discusses two arguments in favor of perdurance. The first is Sider’s argument from vagueness, “one of the most powerful” in favor of perdurantism. I make the observation that endurantists have principled grounds to claim that the argument is unsound, at least if endurance is formulated in locative rather than mereological terms. Having made this observation, I use it to emphasize a somewhat neglected difference between endurantists and perdurantists with respect to their views on material objects. These views, in (...) the case of endurantists, lead to a further, less than conclusive but nevertheless interesting argument against endurantism—the anti-fundamentality argument—which I discuss and tentatively endorse. That argument posits that endurantists must take location to be a fundamental relation, and that this has as a consequence the metaphysical possibility of some rather unwelcome scenarios. Perdurantists may avoid this consequence by denying that location is fundamental, perhaps by embracing supersubstantivalism. (shrink)

This chapter examines the status of inference to the best explanation in naturalistic metaphysics. The methodology of inference to the best explanation in metaphysics is studied from the perspective of contemporary views on scientific explanation and explanatory inferences in the history and philosophy of science. This reveals serious shortcomings in prevalent attempts to vindicate metaphysical "explanationism" by reference to similarities between science and naturalistic metaphysics. This critique is brought out by considering a common gambit of methodological unity: (1) Both metaphysics (...) and science employ inference to the best explanation. (2) One has no reason to think that if explanationism is truth-conducive in science, it is not so in metaphysics. (3) One has a positive reason to think that if explanationism is truth-conducive in science, it is also so in metaphysics. (shrink)

When some objects are the parts of another object, they compose that object and that object is composite. This article is intended as an introduction to the central questions about composition and a highly selective overview of various answers to those questions. In §1, we review some formal features of parthood that are important for understanding the nature of composition. In §2, we consider some answers to the question: which pluralities of objects together compose something? As we will see, the (...) dominant answers are all of them and none of them. In §§3-4, we examine one of the main arguments that has driven philosophers to these extreme answers: the argument from vagueness. In §5, we turn to the question of whether composition is unique: is it sometimes the case that some things compose more than one thing? Finally, in §6, we turn from the question of which composites exist to the question of which composites exist fundamentally. (shrink)

Much recent literature in metaphysics attempts to answer the question, ‘What is metaphysics?’ In this paper I argue that many of the most influential contemporary answers to this question yield the result that feminist metaphysics is not metaphysics. I further argue this result is problematic.

Baker (Mind 114:223–238, 2005; Brit J Philos Sci 60:611–633, 2009) has recently defended what he calls the “enhanced” version of the indispensability argument for mathematical Platonism. In this paper I demonstrate that the nominalist can respond to Baker’s argument. First, I outline Baker’s argument in more detail before providing a nominalistically acceptable paraphrase of prime-number talk. Second, I argue that, for the nominalist, mathematical language is used to express physical facts about the world. In endorsing this line I follow moves (...) made by Saatsi (Brit J Philos Sci 62(1):143–154, 2011). But, unlike Saatsi, I go on to argue that the nominalist requires a paraphrase of prime-number talk, for otherwise we lack an account of what that ‘physical fact’ is in the case of mathematics that seemingly makes reference to prime numbers. (shrink)

It is a common assumption in the metaphysics of time that a commitment to presentism entails a commitment to serious presentism, the view that objects can exemplify properties or stand in relations only at times at which they exist. As a result, non-serious presentism is widely thought to be beyond the bounds for the card-carrying presentist in response to the problem of cross-temporal relations. In this paper, I challenge this general consensus by examining one common argument in favor of the (...) thesis that presentism entails serious presentism. The argument, I claim, begs the question against non-serious defenders in failing to account for their wider metaontological views concerning non-committal quantification. (shrink)

Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philosophers, and I discuss (...) potential future directions of research for each side in the debate over the existence of abstract mathematical objects. (shrink)

Nominalists are confronted with a grave difficulty: if abstract objects do not exist, what explains the success of theories that invoke them? In this paper, I make headway on this problem. I develop a formal language in which certain platonistic claims about properties and certain nominalistic claims can be expressed, develop a formal language in which only certain nominalistic claims can be expressed, describe a function mapping sentences of the first language to sentences of the second language, and prove some (...) facts about that function and facts about some sound logics for those languages. In doing so, I prove that, given some plausible metaphysical assumptions, a large class of sentences about properties of concrete objects are “safe” on nominalistic grounds. Whenever some true sentences about concrete objects and some sentences belonging to this class that are true according to platonists collectively entail a conclusion about concrete objects, some nominalistically acceptable sentences are true and entail the same conclusion. Because the proof can itself be formulated without abstract objects, it provides a nominalistic explanation of the success of theories that invoke properties of concrete objects. (shrink)

It has been suggested that intuitions supporting the nonvacuity of counterpossibles can be explained by distinguishing an epistemic and a metaphysical reading of counterfactuals. Such an explanation must answer why we tend to neglect the distinction of the two readings. By way of an answer, I offer a generalized pattern for explaining nonvacuity intuitions by a stand-and-fall relationship to certain indicative conditionals. Then, I present reasons for doubting the proposal: nonvacuists can use the epistemic reading to turn the table against (...) vacuists, telling apart significant from spurious intuitions. Moreover, our intuitions tend to survive even if we clear-headedly intend a metaphysical reading. -/- . (shrink)

In this paper, I argue that for the purposes of ordinary reasoning, sentences about properties of concrete objects can be replaced with sentences concerning how things in our universe would be related to inscriptions were there a pluriverse. Speaking loosely, pluriverses are composites of universes that collectively realize every way a universe could possibly be. As such, pluriverses exhaust all possible meanings that inscriptions could take. Moreover, because universes necessarily do not influence one another, our universe would not be any (...) different intrinsically if there were a pluriverse. These two facts enable anti-realists about abstract objects to replace, e.g. talk of anatomical features with talk of the inscriptions concerning anatomical structure that would exist were there a pluriverse. The availability of such replacements enables anti-realists to carry out essential ordinary reasoning without referring to properties, thereby making room for a consistent anti-realist worldview. The inscriptions of the would-be pluriverse are so numerous and varied that sentences about them can play the roles in ordinary reasoning served by simple sentences about properties of concrete objects. (shrink)

Classic inductive skepticism–the epistemological claim that we have no good reason to believe that the unobserved resembles the observed–is plausibly everyone’s lot, whether or not they embrace Hume’s metaphysical claim that distinct existents are “entirely loose and separate”. But contemporary advocates of a Humean metaphysic accept a metaphysical claim stronger than Hume’s own. I argue that their view plausibly gives rise to a radical inductive skepticism–according to which we are downright irrational in believing as we do about the unobserved–that we (...) don’t otherwise have reason to accept. The Metaphysical Neo-Humean is in an epistemological quagmire all her own. (shrink)

Discussion of the relevance of grounding to substantiveness, theory-choice, and “location problems” in metaphysics.

Orthodoxy has it that knowledge is absolute—that is, it cannot come in degrees. On the other hand, there seems to be strong evidence for the gradability of know-how. Ascriptions of know-how are gradable, as when we say that one knows in part how to do something, or that one knows how to do something better than somebody else. When coupled with absolutism, the gradability of ascriptions of know-how can be used to mount a powerful argument against intellectualism about know-how—the view (...) that know-how is a species of propositional knowledge. This essay defends intellectualism from the argument of gradability. It is argued that the gradability of ascriptions of know-how should be discounted as a rather superficial linguistic phenomenon, one that can be explained in a way compatible with the absoluteness of the state reported. (shrink)

It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If there were nothing otherwise “uniquely metaphysically significant” about (...) metaphysical necessity, then paradigmatic metaphysical necessities would be necessary in one sense of “necessary”, not necessary in another, and that would be it. The question of whether they were necessary simpliciter would be like the question of whether the Parallel Postulate is true simpliciter – understood as a pure mathematical conjecture, rather than as a hypothesis about physical spacetime. In a sense, the latter question has no objective answer. In this article, I argue that paradigmatic questions of modal metaphysics are like the Parallel Postulate question. I then discuss the deflationary ramifications of this argument. I conclude with an alternative conception of the space of possibility. According to this conception, there is no objective boundary between possibility and impossibility. Along the way, I sketch an analogy between modal metaphysics and set theory. (shrink)