Naturalism in the philosophy of mathematics is the view that philosophy cannot legitimately gainsay mathematics. I distinguish between reinterpretation and reconstruction naturalism: the former states that philosophy cannot legitimately sanction a reinterpretation of mathematics (i.e. an interpretation different from the standard one); the latter that philosophy cannot legitimately change standard mathematics (as opposed to its interpretation). I begin by showing that neither form of naturalism is self-refuting. I then focus on reinterpretation naturalism, which comes in two forms, and examine the (...) only available argument for it. I argue that this argument, the so-called Failure Argument, itself fails. My overall conclusion is that although there is no self-refutation argument against reinterpretation naturalism, there are as yet no good reasons to accept it. Naturalism in mathematics The consistency of mathematical naturalism The failure argument Objections to the failure argument Philosophy as the default. (shrink)

There is a recent and growing trend in philosophy that involves deferring to the claims of certain disciplines outside of philosophy, such as mathematics, the natural sciences, and linguistics. According to this trend— deferentialism , as we will call it—certain disciplines outside of philosophy make claims that have a decisive bearing on philosophical disputes, where those claims are more epistemically justified than any philosophical considerations just because those claims are made by those disciplines. Deferentialists believe that certain longstanding philosophical problems (...) can be swiftly and decisively dispatched by appeal to disciplines other than philosophy. In this paper we will argue that such an attitude of uncritical deference to any non-philosophical discipline is badly misguided. With reference to the work of John Burgess and David Lewis, we consider deference to mathematics. We show that deference to mathematics is implausible and that main arguments for it fail. With reference to the work of Michael Blome-Tillmann, we consider deference to linguistics. We show that his arguments appealing to deference to linguistics are unsuccessful. We then show that naturalism does not entail deferentialism and that naturalistic considerations even motivate some anti-deferentialist views. Finally, we set out deferentialism’s failings and present our own anti-deferentialist approach to philosophical inquiry. (shrink)

Many contemporary philosophers rate error theories poorly. We identify the arguments these philosophers invoke, and expose their deficiencies. We thereby show that the prospects for error theory have been systematically underestimated. By undermining general arguments against all error theories, we leave it open whether any more particular arguments against particular error theories are more successful. The merits of error theories need to be settled on a case-by-case basis: there is no good general argument against error theories.

Several variants of Lewis's Best System Account of Lawhood have been proposed that avoid its commitment to perfectly natural properties. There has been little discussion of the relative merits of these proposals, and little discussion of how one might extend this strategy to provide natural property-free variants of Lewis's other accounts, such as his accounts of duplication, intrinsicality, causation, counterfactuals, and reference. We undertake these projects in this paper. We begin by providing a framework for classifying and assessing the variants (...) of the Best System Account. We then evaluate these proposals, and identify the most promising candidates. We go on to develop a proposal for systematically modifying Lewis's other accounts so that they, too, avoid commitment to perfectly natural properties. We conclude by briefly considering a different route one might take to developing natural property-free versions of Lewis's other accounts, drawing on recent work by Williams. (shrink)

Do numbers exist? Do properties? Do possible worlds? Do fictional characters? Many metaphysicians spend time and effort trying to answer these and other questions about the existence of various entities. These inquiries have recently encountered opposition: a group of philosophers, drawing inspiration from Aristotle, have argued that many or all of the existence questions debated by metaphysicians can be answered trivially, and so are not worth debating. Our task is to defend existence questions from the neo-Aristotelians' attacks.

Together, these entail that for every true proposition p, there exists some thing which could not exist and p be false.

Amie Thomasson and Eli Hirsch have both attempted to deflate metaphysics, by combining Carnapian ideas with an appeal to ordinary language. My main aim in this paper is to critique such deflationary appeals to ordinary language. Focussing on Thomasson, I draw two very general conclusions. First: ordinary language is a wildly complicated phenomenon. Its implicit ontological commitments can only be tackled by invoking a context principle; but this will mean that ordinary language ontology is not a trivial enterprise. Second: ordinary (...) language often points in different directions simultaneously, so that a wide variety of existence questions cannot be deflated merely by appealing to ordinary language. (shrink)

A variety of relations widely invoked by philosophers—composition, constitution, realization, micro-basing, emergence, and many others—are species of what I call ‘building relations’. I argue that they are conceptually intertwined, articulate what it takes for a relation to count as a building relation, and argue that—contra appearances—it is an open possibility that these relations are all determinates of a common determinable, or even that there is really only one building relation.

In this important study D. M. Armstrong offers a comprehensive system of analytical metaphysics that synthesises but also develops his thinking over the last twenty years. Armstrong's analysis, which acknowledges the 'logical atomism' of Russell and Wittgenstein, makes facts the fundamental constituents of the world, examining properties, relations, numbers, classes, possibility and necessity, dispositions, causes and laws. All these, it is argued, find their place and can be understood inside a scheme of states of affairs. This is a comprehensive and (...) rigorously this-worldly account of the most general features of reality, argued from a distinctive philosophical perspective, and it will appeal to a wide readership in analytical philosophy. (shrink)

It is my aim in this paper to show that the contemporary assimilation of essence to modality is fundamentally misguided and that, as a consequence, the corresponding conception of metaphysics should be given up. It is not my view that the modal account fails to capture anything which might reasonably be called a concept of essence. My point, rather, is that the notion of essence which is of central importance to the metaphysics of identity is not to be understood in (...) modal terms or even to be regarded as extensionally equivalent to a modal notion. The one notion is, if I am right, a highly refined version of the other; it is like a sieve which performs a similar function but with a much finer mesh. (shrink)

The physicalist thesis that all entities are nothing over and above physical entities is often interpreted as appealing to a supervenience-based account of "nothing over and aboveness”, where, schematically, the A-entities are nothing over and above the B-entities if the A-entities supervene on the B-entities. The main approaches to filling in this schema correspond to different ways of characterizing the modal strength, the supervenience base, or the supervenience connection at issue. I consider each approach in turn, and argue that the (...) resulting formulation of physicalism is compatible with physicalism’s best traditional rival: a naturalist emergentism. Others have argued that supervenience-based formulations of physicalism fail. My aim here, besides addressing the full spectrum of supervenience-based approaches, is to show how certain philosophical and scientific theses concerning naturalism, properties, and laws give us new reasons to think that supervenience-based formulations of physicalism are untenable. (shrink)

It has recently been suggested that a distinctive metaphysical relation— ‘Grounding’—is ultimately at issue in contexts in which some goings-on are said to hold ‘in virtue of’’, be ‘metaphysically dependent on’, or be ‘nothing over and above’ some others. Grounding is supposed to do good work in illuminating metaphysical dependence. I argue that Grounding is also unsuited to do this work. To start, Grounding alone cannot do this work, for bare claims of Grounding leave open such basic questions as whether (...) Grounded goings-on exist, whether they are reducible to or rather distinct from Grounding goings-on, whether they are efficacious, and so on; but in the absence of answers to such basic questions, we are not in position to assess the associated claim or theses concerning metaphysical dependence. There is no avoiding appeal to the specific metaphysical relations typically at issue in investigations into dependence—for example, type or token identity, functional realization, classical mereological parthood, the set membership relation, the proper subset relation, the determinable/determinate relation, and so on—which are capable of answering these questions. But, I argue, once the specific relations are on the scene, there is no need for Grounding. (shrink)

Consider a circle and a pair of its semicircles. Which is prior, the whole or its parts? Are the semicircles dependent abstractions from their whole, or is the circle a derivative construction from its parts? Now in place of the circle consider the entire cosmos (the ultimate concrete whole), and in place of the pair of semicircles consider the myriad particles (the ultimate concrete parts). Which if either is ultimately prior, the one ultimate whole or its many ultimate parts?

According to Armstrong (amongst others) ‘any truth, should depend for its truth for something “outside” it’ where this one-way dependency is explained in terms of the asymmetric relationship that obtains between a truth and its truth-maker. But there’s no need to appeal to truth-makers to make sense of this dependency. The truth of a proposition is essentially determined by the interlocking semantic mechanism of reference and satisfaction which already ensures that the truth-value of a proposition depends on how things stand (...) outside it. By contrast, how things stand outside of a proposition is determined by other worldly mechanisms that have nothing to do with truth. (shrink)

In a series of papers, Eli Hirsch develops a deflationary account of certain ontological debates, specifically those regarding the composition and persistence of physical objects. He argues that these debates are merely verbal disputes between philosophers who fail to correctly express themselves in a common language. To establish the truth in plain English about these issues, Hirsch contends, we need only listen to the assertions of ordinary speakers and interpret them charitably. In this paper, I argue that Hirsch's conclusions rest (...) on a deficient understanding of the principle of charity. On a proper understanding of this principle, we can see that philosophical disagreement on these issues is not merely verbal. Further, it is no serious violation of charity to interpret ordinary assertions on these matters as false, for the beliefs they express can be explained as reasonable mistakes. Throughout I focus on the debate on composition; but my arguments should carry over to the debate on persistence. (shrink)

Two main claims are defended in this paper: first, that typical disputes in the literature about the ontology of physical objects are merely verbal; second, that the proper way to resolve these disputes is by appealing to common sense or ordinary language. A verbal dispute is characterized not in terms of private idiolects, but in terms of different linguistic communities representing different positions. If we imagine a community that makes Chisholm's mereological essentialist assertions, and another community that makes Lewis's four-dimensionalist (...) assertions, the members of each community speak the truth in their respective languages. This follows from an application of the principle of interpretive charity to the two communities. (shrink)

Two main claims are defended in this paper: first, that typical disputes in the literature about the ontology of physical objects are merely verbal; second, that the proper way to resolve these disputes is by appealing to common sense or ordinary language. A verbal dispute is characterized not in terms of private idiolects, but in terms of different linguistic communities representing different positions. If we imagine a community that makes Chisholm's mereological essentialist assertions, and another community that makes Lewis's four‐dimensionalist (...) assertions, the members of each community speak the truth in their respective languages. This follows from an application of the principle of interpretive charity to the two communities. (shrink)

Despite heroic efforts, philosophers have found it increasingly difficult to evade discussion of metaphysical topics. Take the philosophy of mind. Take, in particular, the mind-body problem in its latest guise: the problem of causal relevance. If mental properties are not reducible to physical properties, how can we reconcile the role such properties seem to have in producing bodily motions that constitute actions with the apparent fact that the very same motions are entirely explicable on the basis of purely physical properties (...) of purely physical events in the nervous system? Familiar approaches to the problem include appeals to “supervenient causation,” to “higher-level” laws governing putatively higher-level entities and events, and to “realizing” relations that make room in objects for overlapping properties. (shrink)

Identities formed with proper names may be contingent. this claim is made first through an example. the paper then develops a theory of the semantics of concrete things, with contingent identity as a consequence. this general theory lets concrete things be made up canonically from fundamental physical entities. it includes theories of proper names, variables, cross-world identity with respect to a sortal, and modal and dispositional properties. the theory, it is argued, is coherent and superior to its rivals, in that (...) it stems naturally from a systematic picture of the physical world. (shrink)

There is a common form of problem, to be found in many areas of philosophy, concerning the relationship between our perspective on reality and reality itself. We make statements (or form judgements) about how things are from a given standpoint or perspective. We make the statement ‘it is raining’ from the standpoint of the present time, for example, or the statement‘it is here’ from the standpoint of where we are, or the statement ‘I am glad’ from the standpoint of a (...) subject. In each of these cases, the statement has a certain ‘aspect’ or perspectival character in virtue of which its truth is capable of varying from one standpoint to another. Thus the statement ‘it is raining’ is tensed, the statement ‘it is here’ is ‘spatiocentric’ and the statement ‘I am glad’ is first-personal. The problem we then face is to determine whether this aspect is a feature of the reality which is described or merely a feature of the statement by which it is described. Is reality itself somehow tensed or spatiocentric or firstpersonal or is it merely that we describe a tenseless or spatially uncentered or impersonal reality from a tensed or spatiocentric or first-personal point of view? (shrink)

Contemporary philosophers commonly suppose that any fundamental entities there may be are maximally determinate. More generally, they commonly suppose that, whether or not there are fundamental entities, any determinable entities there may be are grounded in, hence less fundamental than, more determinate entities. So, for example, Armstrong takes the physical objects constituting the presumed fundamental base to be “determinate in all respects” (1961, 59), and Lewis takes the properties characterizing things “completely and without redundancy” to be “highly specific” (1986, 60). (...) Here I look at the usually cited reasons for these suppositions as directed against the case of determinable properties, in particular, and argue that none is compelling (Sections 1 to 3). The discussion in Section 3 moreover identifies positive reason for taking some determinable properties to be part of a fundamental (or relatively fundamental) base. I close (Section 4) by noting certain questions arising from the possibility of fundamental determinables, as directions for future research. (shrink)

Ladyman, Ross and their collaborators (Spurrett is a co-author of two chapters, Collier of one) begin their book with a ferocious attack on "analytic metaphysics", as it is currently practiced. Their opening blast claims that contemporary analytic metaphysics 'contributes nothing to human knowledge': its practitioners are 'wasting their talents', and the whole enterprise, although 'engaged in by some extremely intelligent and morally serious people, fails to qualify as part of the enlightened pursuit of objective truth, and should be discontinued' (vii). (...) They set out on a 'mission of disciplinary rescue' in the spirit of Hume and the logical positivists, in which a fair proportion of philosophy as currently practiced -- as they realize, their critique applies far beyond the boundaries of metaphysics proper -- will be consigned to the flames. (shrink)

There is a long history of worrying about whether or not metaphysics is a legitimate philosophical discipline. Traditionally such worries center around issues of meaning and epistemological concerns. Do the metaphysical questions have any meaning? Can metaphysical methodology lead to knowledge? But these questions are, in my opinion, not as serious as they have sometimes (historically) been taken to be. What is much more concerning is another set of worries about metaphysics, which I take to the greatest threat to metaphysics (...) as a philosophical discipline. These worries, in effect, hold that the questions that metaphysics tries to answer have long been answered in other parts of inquiry, ones that have much greater authority. And if they haven’t been answered yet then one should not look to philosophy for an answer. What metaphysics tries to do has been or will be done by the sciences. There is nothing left to do for philosophy, or so the worry. Let me illustrate this with two examples, one of which is our main concern here. (shrink)

draft, forthcoming Chalmers, Manley and Wasserman eds., Metametaphysics.