We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.

I argue that one’s views about which “metaphysical laws” obtain—including laws about what is identical with what, about what is reducible to what, and about what grounds what—can be used to deflect or neutralize the threat posed by a debunking explanation. I use a well-known debunking argument in the metaphysics of material objects as a case study. Then, after defending the proposed strategy from the charge of question-begging, I close by showing how the proposed strategy can be used by certain (...) moral realists to resist the evolutionary debunking arguments. (shrink)

Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...) work in numerical cognition and ontogenetic studies. (shrink)

There is an old meta-philosophical worry: very roughly, metaphysical theories have no observational consequences and so the study of metaphysics has no value. The worry has been around in some form since the rise of logical positivism in the early twentieth century but has seen a bit of a renaissance recently. In this paper, I provide an apology for metaphysics in the face of this kind of concern. The core of the argument is this: pure mathematics detaches from science in (...) much the same manner as metaphysics and yet it is valuable nonetheless. The source of value enjoyed by pure mathematics extends to metaphysics as well. Accordingly, if one denies that metaphysics has value, then one is forced to deny that pure mathematics has value. The argument places an added burden on the sceptic of metaphysics. If one truly believes that metaphysics is worthless (as some philosophers do), then one must give up on pure mathematics as well. (shrink)

I argue in this paper that the debate over composition is factually empty; in other words, I argue that there’s no fact of the matter whether there are any composite objects like tables and rocks and cats. Moreover, at the end of the paper, I explain how my argument is suggestive of a much more general conclusion, namely, that there’s no fact of the matter whether there are any material objects at all. Roughly speaking, the paper proceeds by arguing that (...) if there were a fact of the matter about whether composite objects exist, then it would be either a necessary fact or a contingent fact, and both of these alternatives are implausible. (shrink)

In this paper, I outline and defend a novel approach to alethic pluralism, the thesis that truth has more than one metaphysical nature: where truth is, in part, explained by reference, it is relational in character and can be regarded as consisting in correspondence; but where instead truth does not depend upon reference it is not relational and involves only coherence. In the process, I articulate a clear sense in which truth may or may not depend upon reference: this involves (...) distinguishing semantic denotation from pragmatic speaker reference and claiming that there may or may not exist a metasemantic connection between these two notions. Finally, I argue that reference is not in general inscrutable—that this metasemantic connection does exist in the case of our ordinary discourse about present macroscopic concrete objects—but that it is in pure mathematics, where reference cannot be secured, and which therefore plays no role in accounting for truth. In this manner, alethic pluralism is upheld. (shrink)

Beginning with Aristotle, philosophers have taken artifacts to be ontologically deficient. This paper proposes a theory of artifacts, according to which artifacts are ontologically on a par with other material objects. I formulate a nonreductive theory that regards artifacts as constituted by - but not identical to - aggregates of particles. After setting out the theory, I rebut a number of arguments that disparage the ontological status of artifacts.

Metaphysics has enjoyed a vigorous revival in the last few decades. Even so, there has been little ontological interest in the things that we interact with everyday—trees, tables, other people.1 It is not that metaphysicians ignore ordinary things altogether. Indeed, they are happy to say that sentences like ‘The daffodils are out early this year’ or ‘My computer crashed again’ are true. But they take the truth of such sentences not to require that a full description of reality mention daffodils (...) or computers. Many metaphysicians now interpret the apparent variety of things in the world as variety only of concepts applied to things that are basically of the same sort—for example, sums of particles or of temporal parts of particles. (shrink)

Some have it that wholes are, somehow, identical to their parts. This doctrine is as alluring as it is puzzling. But in this paper, I show that the doctrine is inconsistent with two widely accepted theses. Something has to go.

Can Quine’s criterion for ontological commitment be comparatively applied across different logics? If so, how? Cross-logical evaluations of discourses are central to contemporary philosophy of mathematics and metaphysics. The focus here is on the influential and important arguments of George Boolos and David Lewis that second-order logic and plural quantification don’t incur additional ontological commitments over and above those incurred by first-order quantifiers. These arguments are challenged by the exhibition of a technical tool—the truncation-model construction of notational equivalents—that compares the (...) ontological role and increased expressive strength of non-first-order ideology to first-order ideology. (shrink)

Why is it that whenever a structural property is instantiated, its constituent properties are instantiated as well, by proper parts of the original object? By developing a suggestion from Lewis :25–46, 1986), Hawley :117–133, 2010) rises to this explanatory challenge by taking structural properties to be mereologically composed by their constituents, and by taking composition to be analogous to identity. However, setting up a plausible framework for composition and CAI claims about properties, I will argue that structural properties are not (...) identical to their constituents, at least not in any sense robust enough to warrant an Hawley-style argument—and perhaps not identical to them in any sense whatsoever. More generally, core principles of extensional mereology are in danger when applied to structural properties, which may force an extensionalist to either reconsider the application altogether, or reconsider mereological monism, thus granting the mereology of structural properties a peculiarly non-extensional status. Finally, although this debate has been traditionally framed as a debate about universals, an appeal to structural tropes can reconcile, at least to some extent, the mereology of structural properties with Lewisian extensional mereology— CAI included. (shrink)

According to contemporary ‘process ontology’, organisms are best conceptualised as spatio-temporally extended entities whose mereological composition is fundamentally contingent and whose essence consists in changeability. In contrast to the Aristotelian precepts of classical ‘substance ontology’, from the four-dimensional perspective of this framework, the identity of an organism is grounded not in certain collections of privileged properties, or features which it could not fail to possess, but in the succession of diachronic relations by which it persists, or ‘perdures’ as one entity (...) over time. In this paper, I offer a novel defence of substance ontology by arguing that the coherency and plausibility of the radical reconceptualisation of organisms proffered by process ontology ultimately depends upon its making use of the ‘substantial’ principles it purports to replace. (shrink)

As there is currently a neo-Aristotelian revival currently taking place within contemporary metaphysics and dispositions, or causal powers are now being routinely utilised in theories of causality and modality, more attention is beginning to be paid to a central Aristotelian concern: the metaphysics of substantial unity, and the doctrine of hylomorphism. In this paper, I distinguish two strands of hylomorphism present in the contemporary literature and argue that not only does each engender unique conceptual difficulties, but neither adequately captures the (...) metaphysics of Aristotelian hylomorphism. Thus both strands of contemporary hylomorphism, I argue, fundamentally misunderstand what substantial unity amounts to in the hylomorphic framework – namely, the metaphysical inseparability of matter and form. (shrink)

Truthmaker theorists often express their core commitment by saying that truth is grounded in being, and grounding theorists often take truthmaking to be a paradigm case of grounding. But I will argue that truthmaking is not a case of grounding. What is crucial for understanding truthmaking is not grounding but rather meaning (in a broad sense including reference). Truth is still constrained by how things are, so even if (so‐called) truthmakers don't play a role in grounding truths, the methodological program (...) of truthmaker theory survives. Here I lay out my understanding of truth and truthmaking, and distinguish two conceptions of grounding. I argue that truthmaking is not plausibly seen as a case of grounding on either conception. I argue further that treating truthmaking as grounding threatens to violate a plausible irreflexivity principle, and makes trouble for the view that grounding is transitive. I then suggest that there is no genuine relation of truthmaking (which there would have to be if it were a true case of grounding). Finally, I show how the core insights of truthmaker theory are preserved by the understanding of truthmaking that I favor. (shrink)

In the analysis of Anaxagoras’ physics in view of the relation between his teachings on multitude and heterogeneity, two central questions emerge: 1) How can the structure of the universe considered purely mereo-topologically help us explain that at the first cosmic stage no qualitative difference is manifest in spite of the fact that the entire qualitative heterogeneity is supposedly already present there? 2) How can heterogeneity become manifest at the second stage, resulting from the noûs intervention, if according to fragment (...) B 6 such a possibility requires the existence of “the smallest”, while according to the general principle stated in fragment B 3 there is not “the smallest” but always only “a smaller”? This paper showcases the perplexity of these two questions but deals only with the former. The answer follows from Anaxagoras’ being a thoroughgoing infinitist in the way in which no Greek physicist was: the principle of space isotropy operative in geometry is extended to physics as well. So any two parts of the original mixture are similar to each other not only in view of the smaller-larger relation but also because each contains everything that the other one contains. This in effect means that at the stage of maximal possible heterogeneity each part of any part contains infinitely many heterogeneous parts of any kind whatsoever. So, neither can there be homogeneous parts in view of any qualitative property, nor can there be predominance in quantity of parts of any kind that would make some property manifest. (shrink)

Ontic Structural Realism is a version of realism about science according to which by positing the existence of structures, understood as basic components of reality, one can resolve central difficulties faced by standard versions of scientific realism. Structures are invoked to respond to two important challenges: one posed by the pessimist meta-induction and the other by the underdetermination of metaphysics by physics, which arises in non-relativistic quantum mechanics. We argue that difficulties in the proper understanding of what a structure is (...) undermines the realist component of the view. Given the difficulties, either realism should be dropped or additional metaphysical components not fully endorsed by science should be incorporated. (shrink)

In this paper I propose a defense of a posteriori materialism.Problems with a posteriori identity materialism are identified,and a materialism based on composition, not identity, is proposed.The main task for such a proposal is to account for the relationbetween physical and phenomenal properties. Composition does notseem to be fit as a relation between properties, but I offer apeculiar way to understand property-composition, based on somerecent ideas in the literature on ontology. Finally, I propose amaterialist model for the mind-body relation that (...) is able to resistthe attack from conceivability arguments. (shrink)

This paper is an investigation in the use of truthmaker theory for exploring the relation of logic to world, and as a tool for metaphysics. A variant of truthmaker theory, which we call the simple theory, is defined and defended against objections. It is characterized formally, and its central features are derived. As part of this project, we give a formal metaphysics based on nondeterministic necessitation relations among possible entities. In what is called the fundamental theorem of truthmaking, it is (...) shown that, as long as a logic is sound and complete, its inferential structure will be isomorphic to the necessitation structure of our metaphysics. We thus arrive at a purely structural logic–world relationship which can be used for metaphysical investigations. Other products of our investigation are a sound and complete semantics for first-order logic with identity and a solution to a result of Restall which has threatened to make truthmaker theory trivial. (shrink)

It is argued here that it is part of our concept of a ‘person’ that persons should be, by its nature, able to endure in time. In no conception of persons as ‘perduring’ entities with different temporal parts for different times, or as sequences of stages in the relation of ‘being a survival of ’ between them, it is possible to make sense of some of our normative intuitions about persons. It is argued also that the traditional psychological theory of (...) personal identity is untenable. Psychological continuity appears to be neither sufficient nor necessary for personal identity. A reasonable conception of persons seems to be either a form of ‘animalism’ where persons are biological organisms, or a theory in which persons are primitive substances, with primitive conditions of identity. (shrink)

un estado de cosas es una estructura no-mereológica compuesta por universales, objetos y tiempos. En principio, un estado de cosas no está fundado en sus componentes, pues tales componentes podrían existir, pero no el estado de cosas que componen. La introducción de otras relaciones de 'instanciación' no mejoran la situación, si tales relaciones son universales. Un estado de cosas, sin embargo, sí está fundado en un universal, uno o varios objetos, un tiempo y un tropo que, esencialmente, es la instanciación (...) de tal universal en tal objeto, o en tales objetos, en tal tiempo. Si los estados de cosas están fundados en sus constituyentes, entonces hay una razón para admitir tropos. Finalmente, se discuten varias razones por los que los estados de cosas deben estar fundados. a state of affairs is a non-mereological structure composed by universals, objects and times. In principle, a state of affairs is not grounded in its components, for those components could exist, but not the state of affairs that they compose. The introduction of other relations of 'instantiation' doesn't improve the situation, if those relations are universal. A state of affairs, though, is grounded on a universal, object or objects, time and a trope that, essentially, is the instantiation of that universal in that object, or in those objects, in that time. If states of affairs are grounded in their constituents, then there is reason to admit tropes. Finally, several reasons by which states of affairs should be grounded are discussed. (shrink)

A ‘state of affairs’ is understood here as any kind of concrete entity that can play the role of truthmaker. Different ontologies propose different structures of entities to work as ‘states of affairs’ in this sense. Defenders of universals will propose for the role non- mereological structures of universals, objects and times. Defenders of tropes will propose tropes, either with or without universals and objects. Resemblance nominalists will propose primitive ontological facts of resemblance between objects in time. In any of (...) these cases, times are an essential component of a state of affairs. Any ontology of states of affairs, then, should clarify what times are in order to clarify what states of affairs are. An examination of the dominant reductivist conceptions of times shows that these connections have not yet been thought through carefully. In any of the dominant reductivist conceptions, times are entities that either include or describe everything that happens simultaneously at a given instant. Even in some cases they include the description of everything that happens at any time. If one introduce times taken as they are in any of these reductivist conceptions, it will be essential to a state of affairs everything that happens simultaneously with it, or even everything that happens at any time. Under some assumptions the internal relation of every state of affairs with every other state of affairs expands to the internal relation of everything with everything. This is an unhappy theoretical situation that calls for a more careful consideration of some central tenets in our ontology of time. (shrink)

Special Issue: The Material Bases of Cognition Guest Editors: Fred Adams · Kenneth Aizawa -/- Compositional Explanatory Relations and Mechanistic Reduction K.L. Theurer 287 -/- Constitution, and Multiple Constitution, in the Sciences: Using the Neuron to Construct a Starting Framework C. Gillett 309 -/- The Mark of the Cognitive F. Adams · R. Garrison 339 -/- Dynamics and Cognition L.A. Shapiro 353 -/- Causal Parity and Externalisms: Extensions in Life and Mind P. Huneman 377 -/- Did I Do That? Brain–Computer (...) Interfacing and the Sense of Agency P. Haselager 405 . (shrink)

Canonical defenders of the principle of sufficient reason (PSR), such as Leibniz and Spinoza, are metaphysical foundationalists of one stripe or another. This is curious since the PSR—which says that everything has a ground, cause, or explanation—in effect, denies fundamental entities. In this paper, I explore the apparent inconsistency between metaphysical foundationalism and approaches to metaphysical system building that are driven by a commitment to the PSR. I do so by analyzing how Indian Buddhist philosophers arrive at foundationalist and anti-foundationalist (...) positions motivated by implicit commitments to different versions of the PSR. I begin by introducing the Buddhist principle of dependent origination (pratītyasamutpāda) as a proto-PSR that is restricted to causal explanation. Next, I show how Vasubandhu’s Sautrāntika Abhidharma metaphysics is shaped by a qualified commitment to both causal and metaphysical grounding versions of the PSR. I then reveal how Nāgārjuna’s Madhyamaka metaphysics is driven by an unrestricted and exceptionless commitment to causal and metaphysical grounding versions of the PSR. Finally, I consider how Nāgārjuna’s account may put him in a unique position to respond to a common contemporary objection to the PSR from necessitarianism. I conclude by addressing a competing interpretation on which Nāgārjuna is best understood as an anti-rationalist rather than an uber-rationalist, as I characterize him. (shrink)

The revival of analytic metaphysics in the latter half of the twentieth century is typically understood as a consequence of the critiques of logical positivism, Quine’s naturalization of ontology, Kripke’s Naming and Necessity, clarifications of modal notions in logic, and the theoretical exploitation of possible worlds. However, this explanation overlooks the work of metaphysicians at the height of positivism and linguisticism that affected metaphysics of the late twentieth century. Donald C. Williams is one such philosopher. In this paper I explain (...) how Williams’s fundamental ontology and philosophy of time influenced in part the early formation of David Lewis’s metaphysics. Thus, Williams played an important role in the revival of analytic metaphysics. (shrink)

An introduction to composition, persistence, and identity.

This paper responds to John Burgess's ‘Mathematics and _Bleak House_’. While Burgess's rejection of hermeneutic fictionalism is accepted, it is argued that his two main attacks on revolutionary fictionalism fail to meet their target. Firstly, ‘philosophical modesty’ should not prevent philosophers from questioning the truth of claims made within successful practices, provided that the utility of those practices as they stand can be explained. Secondly, Carnapian scepticism concerning the meaningfulness of _metaphysical_ existence claims has no force against a _naturalized_ version (...) of fictionalism, according to which our ordinary standards of scientific evidence may show that we have no reason to believe the mathematical existence claims made within the context of our mathematical and scientific theories. (shrink)

Are there any things that are such that any things whatsoever are among them. I argue that there are not. My thesis follows from these three premises: (1) There are two or more things; (2) for any things, there is a unique thing that corresponds to those things; (3) for any two or more things, there are fewer of them than there are pluralities of them.

This volume covers a wide range of topics in the most recent debates in the philosophy of mathematics, and is dedicated to how semantic, epistemological, ontological and logical issues interact in the attempt to give a satisfactory picture of mathematical knowledge. The essays collected here explore the semantic and epistemic problems raised by different kinds of mathematical objects, by their characterization in terms of axiomatic theories, and by the objectivity of both pure and applied mathematics. They investigate controversial aspects of (...) contemporary theories such as neo-logicist abstractionism, structuralism, or multiversism about sets, by discussing different conceptions of mathematical realism and rival relativistic views on the mathematical universe. They consider fundamental philosophical notions such as set, cardinal number, truth, ground, finiteness and infinity, examining how their informal conceptions can best be captured in formal theories. The philosophy of mathematics is an extremely lively field of inquiry, with extensive reaches in disciplines such as logic and philosophy of logic, semantics, ontology, epistemology, cognitive sciences, as well as history and philosophy of mathematics and science. By bringing together well-known scholars and younger researchers, the essays in this collection – prompted by the meetings of the Italian Network for the Philosophy of Mathematics (FilMat) – show how much valuable research is currently being pursued in this area, and how many roads ahead are still open for promising solutions to long-standing philosophical concerns. Promoted by the Italian Network for the Philosophy of Mathematics – FilMat. (shrink)

In this article ideas from Kit Fine’s theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generis mathematical structures can be viewed as generic systems of mathematical objects, where mathematical objects are conceived of as arbitrary objects in Fine’s sense.

Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While STT, understood as (...) a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

Alessandro Torza argues that Ted Sider’s Lewisian argument against vague existence is insufficient to rule out the possibility of what he calls ‘super-vague existence’, that is the idea that existence is higher-order vague, for all orders. In this chapter it is argued that the possibility of super-vague existence is ineffective against the conclusion of Sider’s argument since super-vague existence cannot be consistently claimed to be a kind of linguistic vagueness. Torza’s idea of super-vague existence seems to be better suited to (...) model vague existence under the assumption that vague existence is instead a form of ontic indeterminacy, contra what Ted Sider and David Lewis assume. (shrink)

The details of St. Thomas Aquinas’s anthropological view are subject to debate. Some philosophers believe he held that human persons survive their deaths. Other philosophers think he held that human persons cease to exist at their death, but come back into being at the general resurrection. In this paper, I defend the latter view against one of the most significant objections it faces, namely, that it entails that God punishes and rewards separated souls for the sins or merits of something (...) else: the (non-existent) persons to whom those souls once belonged. The objector takes this entailment to be problematic. I argue that it fits in well with St. Thomas’s views about punishment and about persons. (shrink)

This is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...) and neighbouring fields, including those of mathematics, psychology, literature and film, and neuroscience. (shrink)

In a series of publications, Eli Hirsch has presented a sustained defense of common-sense ontology. Hirsch's argument relies crucially on a meta-ontological position sometimes known as ‘superficialism’. Hirsch's argument from superficialism to common-sense ontology is typically resisted on the grounds that superficialism is implausible. In this paper, I present an alternative argument for common-sense ontology, one that relies on (what I argue is) a much more plausible meta-ontological position, which I call ‘constructivism’. Note well: I will not quite argue that (...) constructivism is true; merely that it is significantly more plausible than superficialism, and consequently affords a safer route to common-sense ontology. Thus my main goal in the paper is not quite to establish common-sense ontology, nor for that matter to refute Hirsch's argument for it. My goal is, in a way, more expressive than argumentative: I wish to articulate a novel meta-ontological position, one that I take to be in no way obviously less plausible than already familiar positions, and to point out that the position probably leads to common-sense ontology. I open, in section 1, with a discussion of Hirsch's argument and the main objection to it. I then develop, in section 2, a sketch of the alternative meta-ontology I have in mind. I close, in section 3, with the argument that this alternative meta-ontology, too, leads to common-sense ontology. (shrink)

Van Inwagen proposes that besides simples only living organisms exist as composite objects. This paper suggests expanding van Inwagen’s ontology by also accepting composite objects in the case that physical bonding occurs (plus some extra conditions). Such objects are not living organ-isms but rather physical bodies. They include (approximately) the complete realm of inanimate ordinary objects, like rocks and tables, as well as inanimate scientific objects, like atoms and mol-ecules, the latter filling the ontological gap between simples and organisms in (...) van Inwagen’s origi-nal picture. We thus propose a compositional pluralism claiming that composition arises if and on-ly if bonding or life occurs. (shrink)

Recently, I’ve championed the doctrine that fundamentally different sorts of things exist in fundamentally different ways.1 On this view, what it is for an entity to be can differ across ontological categories.2 Although historically this doctrine was very popular, and several important challenges to this doctrine have been dealt with, I suspect that contemporary metaphysicians will continue to treat this view with suspicion until it is made clearer when one is warranted in positing different modes of existence.3 I address this (...) concern here. The question of when to posit ways of being is closely related to a more general question: when should one think that some philosophically interesting expression is analogous? Accordingly, my strategy here is as follows. First, I briefly explain my interpretation of ontological pluralism, the doctrine that there are ways of being.4 Second, I introduce the notion of an analogous term, and show how, on most ways of implementing ontological pluralism, “existence” is analogous. Third, I discuss two sufficient conditions for when one is warranted in claiming that a philosophically interesting term is analogous. Fourth, I present a series of ontological schemes, each of which satisfies at least one of the sufficient conditions. The upshot is this: if you are attracted to one of these ontologies, you have reason to believe in ways of being. The careful reader will have noted the apparent modesty of my conclusion. Unfortunately, I do not believe that one could ever be rationally required to believe in ways of being. Still, in general a metaphysic is a live option to the extent that it is shown to be rationally permissible to believe. Since the apparent consensus among contemporary analytic metaphysicians is that believing that things can exist in different ways is silly or confused, establishing the rational permissibility of belief in ways of being is a non-trivial task. Let us begin. (shrink)

Dispositional monists believe that all properties are essentially causal. Recently, an overdetermination argument has been proposed by Trenton Merricks to support nihilism about ordinary objects. I argue that this argument can be extended to target both nihilism about ordinary objects and nihilism about physical particles when dispositional monism is assumed. It implies that a philosopher who both endorses dispositional monism and takes seriously the overdetermination argument should not believe in the existence of physical particles. I end up by discussing possible (...) objections. I suggest, then, that if we live in a world that is inhabited by causal properties but not by chairs and tables, then we also live in a world without electrons and quarks, a world of dispositional properties, that is, a world of causal fields. (shrink)

I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. -/- It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but (...) on the logical conception of set which motivates naive set theory. The accepted solution is to replace this with the iterative conception of set. -/- I show that this picture is doubly mistaken. After a close examination of the paradoxes in chapters 2--3, I argue in chapters 4 and 5 that it is possible to rescue naive set theory by restricting quantification over sets and that the resulting restrictivist set theory is expressible. In chapters 6 and 7, I argue that it is the iterative conception of set and the thesis of absolutism that should be rejected. (shrink)

John MacFarlane explores how we might make sense of the idea that truth is relative. He provides new, satisfying accounts of parts of our thought and talk that have resisted traditional methods of analysis, including what we mean when we talk about what is tasty, what we know, what will happen, what might be the case, and what we ought to do.

Contemporary philosophy’s three main naturalisms are methodological, ontological and epistemological. Methodological naturalism states that the only authoritative standards are those of science. Ontological and epistemological naturalism respectively state that all entities and all valid methods of inquiry are in some sense natural. In philosophy of mathematics of the past few decades methodological naturalism has received the lion’s share of the attention, so we concentrate on this. Ontological and epistemological naturalism in the philosophy of mathematics are discussed more briefly in section (...) 6. (shrink)

On a view implicitly endorsed by many, a concept is epistemically better than another if and because it does a better job at ‘carving at the joints', or if the property corresponding to it is ‘more natural' than the one corresponding to another. This chapter offers an argument against this seemingly plausible thought, starting from three key observations about the way we use and evaluate concepts from en epistemic perspective: that we look for concepts that play a role in explanations (...) of things that cry out for explanation; that we evaluate not only ‘empirical' concepts, but also mathematical and perhaps moral concepts from an epistemic perspective; and that there is much more complexity to the concept/property relation than the natural thought seems to presuppose. These observations, it is argued, rule out giving a theory of conceptual evaluation that is a corollary of a metaphysical ranking of the relevant properties. -/- conceptual ethics, explanation, naturalness, epistemic value, concept/property, semantic internalism. (shrink)

The Special Composition Question asks under what conditions a plurality of objects form another, composite object. We propose a condition grounded in our scientific knowledge of physical reality, the essence of which is that objects form a composite object when and only when they are in a bound state – whence our Bound State Proposal. We provide a variety of reasons in favour of a mereological theory that accommodates our Proposal. We consider but reject another proposal, which is quantum-physical in (...) nature: the Entanglement Proposal. We close by responding to Teller’s ‘Suit Objection’. (shrink)