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)

The received view of computation is methodologically bifurcated: it offers different accounts of computation in the mathematical and physical cases. But little in the way of argument has been given for this approach. This article rectifies the situation by arguing that the alternative, a unified account, is untenable. Furthermore, once these issues are brought into sharper relief we can see that work remains to be done to illuminate the relationship between physical and mathematical computation.

In this paper, I defend an indexical analysis of the abstract-concrete distinction within the framework of modal realism. This analysis holds the abstract-concrete distinction to be conceptually inseparable from the distinction between the actual and the merely possible, which is assumed to be indexical in nature. The resulting view contributes to the case for modal realism by demonstrating how its distinctive resources provide a reductive analysis of the abstract-concrete distinction. This indexical analysis also provides a solution to a sceptical problem (...) regarding our concreteness, which parallels the sceptical problem that motivates indexicalism about actuality. (shrink)

Hartry Field has shown us a way to be nominalists: we must purge our scientific theories of quantification over abstracta and we must prove the appropriate conservativeness results. This is not a path for the faint hearted. Indeed, the substantial technical difficulties facing Field's project have led some to explore other, easier options. Recently, Jody Azzouni, Joseph Melia, and Stephen Yablo have argued that it is a mistake to read our ontological commitments simply from what the quantifiers of our best (...) scientific theories range over. In this paper, I argue that all three arguments fail and they fail for much the same reason; would-be nominalists are thus left facing Field's hard road. (shrink)

It is well known that Carnap, early in his philosophical career, took most of metaphysics to consist of meaningless pseudostatements. In contrast to this meaning-theoretic critique of metaphysics, we develop what we take to be Carnap’s later value-based critique. We argue that this later critique is forceful against several central contemporary metaphysical debates, its origin in the principle of tolerance notwithstanding.

There is a long tradition comparing moral knowledge to mathematical knowledge. In this paper, I discuss apparent similarities and differences between knowledge in the two areas, realistically conceived. I argue that many of these are only apparent, while others are less philosophically significant than might be thought. The picture that emerges is surprising. There are definitely differences between epistemological arguments in the two areas. However, these differences, if anything, increase the plausibility of moral realism as compared to mathematical realism. It (...) is hard to see how one might argue, on epistemological grounds, for moral antirealism while maintaining commitment to mathematical realism. But it may be possible to do the opposite. (shrink)

Drawing on the findings of neuroscience, this text proposes and defends the hypothesis that the various modalities of sensation share a generic form that the author, Austen Clark, calls feature-placing.

To Shape a New World, ShelbyTommie and TerryBrandon. Cambridge, MA: Harvard University Press, 2018. Pp. x + 449.

I develop a non-representationalist account of mathematical thought, on which the point of mathematical theorizing is to provide us with the conceptual capacity to structure and articulate information about the physical world in an epistemically useful way. On my view, accepting a mathematical theory is not a matter of having a belief about some subject matter; it is rather a matter of structuring logical space, in a sense to be made precise. This provides an elegant account of the cognitive utility (...) of mathematics. Further, it makes explicit how the brand of non-representationalism I develop is compatible with there being substantive rationality constraints on our mathematical theorizing. (shrink)

Some forms of analytic reconstructivism take natural language (and common sense at large) to be ontologically opaque: ordinary sentences must be suitably rewritten or paraphrased before questions of ontological commitment may be raised. Other forms of reconstructivism take the commitment of ordinary language at face value, but regard it as metaphysically misleading: common-sense objects exist, but they are not what we normally think they are. This paper is an attempt to clarify and critically assess some common limits of these two (...) reconstructivist strategies. (shrink)

In this paper, I develop a theory on which each of a thing’s abundant properties is immanent in that thing. On the version of the theory I will propose, universals are abundant, each instantiated universal is immanent, and each uninstantiated universal is such that it could have been instantiated, in which case it would have been immanent. After setting out the theory, I will defend it from David Lewis’s argument that such a combination of immanence and abundance is absurd. I (...) will then advocate the theory on the grounds that it accomplishes all of Lewis’s “new work” while providing a gain in parsimony and a new account of fine-grained content. I will close with a discussion of how the theory also affords a new reply to two objections to uninstantiated universals: Armstrong’s charge that they are inconsistent with naturalism, and a Benacerraf-Field-style objection about epistemic access. (shrink)

The form of nominalism known as 'mathematical fictionalism' is examined and found wanting, mainly on grounds that go back to an early antinominalist work of Rudolf Carnap that has unfortunately not been paid sufficient attention by more recent writers.

This essay explains why creationism about fictional characters is an abject failure. Creationism about fictional characters is the view that fictional objects are created by the authors of the novels in which they first appear. This essay shows that, when the details of creationism are filled in, the hypothesis becomes far more puzzling than the linguistic data it is used to explain. No matter how the creationist identifies where, when and how fictional objects are created, the proposal conflicts with other (...) strong intuitions we have about fictional characters. (shrink)

Fictionalism about fictional characters is a view according to which all claims ostensibly about fictional characters are in fact claims about the content of a story. Claims that appear to refer to or quantify over fictional objects contain an implicit prefix of the form “according to such-and-such story. In.

S. Shapiro, The Oxford handbook of philosophy of mathematics and logic Oxford and New York: Oxford University Press, 2005. xv + 833 pp. £52.00. ISBN 0-19-514...

Divine Foundationalism is the thesis that God is the source of all things (apart from God hirself). I clarify and defend the thesis, before I consider the main arguments for and against it.

In his book Philosophy of Logic, Putnam (1971) presents a short argument which reads like—and indeed, can be reconstructed as—a formal proof that a nominalistic physics is impossible. The aim of this paper is to examine Putnam’s proof and show that it is not compelling. The precise way in which the proof fails yields insight into the relation that a nominalistic physics should bear to standard physics and into Putnam’s indispensability argument.

We discuss a recent attempt by Chris Daly and Simon Langford to do away with mathematical explanations of physical phenomena. Daly and Langford suggest that mathematics merely indexes parts of the physical world, and on this understanding of the role of mathematics in science, there is no need to countenance mathematical explanation of physical facts. We argue that their strategy is at best a sketch and only looks plausible in simple cases. We also draw attention to how frequently Daly and (...) Langford find themselves in conflict with mathematical and scientific practice. (shrink)

We argue that if Stephen Yablo (2005) is right that philosophers of mathematics ought to endorse a fictionalist view of number-talk, then there is a compelling reason for deflationists about truth to endorse a fictionalist view of truth-talk. More specifically, our claim will be that, for deflationists about truth, Yablo’s argument for mathematical fictionalism can be employed and mounted as an argument for truth-theoretic fictionalism.

In this article some intriguing aspects of electromagnetic theory and its relation to mathematics and reality are discussed, in particular those related to the suppositions needed to obtain the wave equations from Maxwell equations and from there Helmholtz equation. The following questions are discussed. How is that equations obtained with so many irreal or fictitious assumptions may provide a description that is in a high degree verifiable? Must everything that is possible to deduce from a theoretical mathematical model occur in (...) the world? Does everything that takes place in the world have a mathematical description? (shrink)

Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.

There is no doughnut without a hole, the saying goes. And that’s true. If you think you can come up with an exception, it simply wouldn’t be a doughnut. Holeless doughnuts are like extensionless color, or durationless sound—nonsense. Does it follow, then, that when we buy a doughnut we really purchase two sorts of thing—the edible stuff plus the little chunk of void in the middle? Surely we cannot just take the doughnut and leave the hole at the grocery store, (...) as we cannot just eat the doughnut and save the hole for later. But then, again, surely when we eat a doughnut we do not also eat the hole. Or do we? (shrink)

In this paper, I study the kind of questions we can ask about the existence of numbers. In addition to asking whether numbers exist, and how, I argue that there is also a third relevant question: why numbers exist. In platonist and nominalist accounts this question may not make sense, but in the psychologist account I develop, it is as well-placed as the other two questions. In fact, there are two such why-questions: the causal why-question asks what causes numbers to (...) exist and the teleological why-question asks for what purpose numbers exist. I argue that in a psychologist constructivist account, in which numbers are understood to exist as referents of a particular type of culturally shared concepts, both why-questions can get plausible answers. (shrink)

If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this is also the case (...) with respect to the objects that are studied in mathematics. In addition to that, the methods of investigation of mathematics differ markedly from the methods of investigation in the natural sciences. Whereas the latter acquire general knowledge using inductive methods, mathematical knowledge appears to be acquired in a different way, namely, by deduction from basic principles. The status of mathematical knowledge also appears to differ from the status of knowledge in the natural sciences. The theories of the natural sciences appear to be less certain and more open to revision than mathematical theories. For these reasons mathematics poses problems of a quite distinctive kind for philosophy. Therefore philosophers have accorded special attention to ontological and epistemological questions concerning mathematics. (shrink)

In this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e. that mathematics cannot be naturalized. I find little reason for optimism that the argument can be effectively answered.

In this paper I argue against Divers and Miller's 'Lightness of Being' objection to Hale and Wright's neo-Fregean Platonism. According to the 'Lightness of Being' objection, the neo-Fregean Platonist makes existence too cheap: the same principles which allow her to argue that numbers exist also allow her to claim that fictional objects exist. I claim that this is no objection at all" the neo-Fregean Platonist should think that fictional characters exist. However, the pluralist approach to truth developed by WQright in (...) 'Truth and Objectivity' allows us to salvage our intuitions about the metaphysicial lightweightness of fictional characters: truth for discourse about fictional characters fails to exert 'Cognityive Command', whereas truth about arithmetic does. (shrink)

I argue that certain species of belief, such as mathematical, logical, and normative beliefs, are insulated from a form of Harman-style debunking argument whereas moral beliefs, the primary target of such arguments, are not. Harman-style arguments have been misunderstood as attempts to directly undermine our moral beliefs. They are rather best given as burden-shifting arguments, concluding that we need additional reasons to maintain our moral beliefs. If we understand them this way, then we can see why moral beliefs are vulnerable (...) to such arguments while mathematical, logical, and normative beliefs are not—the very construction of Harman-style skeptical arguments requires the truth of significant fragments of our mathematical, logical, and normative beliefs, but requires no such thing of our moral beliefs. Given this property, Harman-style skeptical arguments against logical, mathematical, and normative beliefs are self-effacing; doubting these beliefs on the basis of such arguments results in the loss of our reasons for doubt. But we can cleanly doubt the truth of morality. (shrink)

This paper formulates a general epistemological argument against what I call non-causal realism, generalizing domain specific arguments by Benacerraf, Field, and others. First I lay out the background to the argument, making a number of distinctions that are sometimes missed in discussions of epistemological arguments against realism. Then I define the target of the argument—non-causal realism—and argue that any non-causal realist theory, no matter the subject matter, cannot be given a reasonable epistemology and so should be rejected. Finally I discuss (...) and respond to several possible responses to the argument. In addition to clearing up and avoiding numerous misunderstandings of arguments of this kind that are quite common in the literature, this paper aims to present and endorse a rigorous and fully general epistemological argument against realism. (shrink)

The issues I explore in this paper are best introduced by the table with which it begins. The left-hand entry in each row gives expression to a kind objectivity; the right-hand entry affirms the existence of a special kind of object. When philosophers believe in any of the entities on the right, it is typically because they think them necessary to ground the facts on the left. By the same token, when philosophers deny any of the facts on the left, (...) it is often because they cannot bring themselves to believe in the associated kind of object on the right. My project is to explore the extent to which it is possible to have the objectivity without the objects—for example, absolute motion without substantival space, objective predication without universals, objective synonymy without propositions, and objective modality without possible worlds. Each of these combinations would have been congenial to A.N. Prior. (shrink)

Mental fictionalism is the view that, even if mental states do not exist, it is useful to talk as if they do. Mental states are useful fictions. Recent philosophy of mind has seen a growing interest in mental fictionalism. To date, much of the discussion has concerned the general features of the approach. In this paper, I develop a specific form of mental fictionalism by drawing on Kendall Walton’s work on make-believe. According to the approach I propose, talk of mental (...) states is a useful pretence for describing people and their behaviour. I try to clarify and motivate this approach by comparing it to well-known alternatives, including behaviourism, instrumentalism and eliminativism. I also consider some of the challenges that it faces. (shrink)

This paper contains a defense against anti-realism in mathematics in the light both of incompleteness and of the fact that mathematics is a ‘cultural artifact.’. Anti-realism (here) is the view that theorems, say, of aritltmetic cannot be taken at face value to express true propositions about the system of numbers but must be reconstrued to be about somctliiiig else or about nothing at all. A ‘bite-the-bullet’ aspect of the defease is that, adopting new axioms, liitherto independent, is not. a matter (...) of recognizing trutlis wliich had previoasly been unrecognized, but of extending the domain of what is true. (shrink)

A strong form of representationalism says that every conscious property of every mental state can be identified with some part of the state’s representational properties. A weaker representationalism says that some conscious property of some mental state can be identified with some part of the state’s representational properties. David Papineau has recently argued that all such theories are incorrect since they construe consciousness as consisting in “relations to propositions or other abstract objects outside space and time”, whereas consciousness is “concrete” (...) and “here and now”. Papineau defends instead a kind of “qualia theory” according to which all conscious properties are intrinsic non-relational properties of subjects. He argues that this theory bypasses the difficulties he identifies for representationalism. Similar worries about representationalism, and similar ideas to the effect that some qualia theory, adverbial theory, or sense-datum theory fares better with respect to these worries are relatively wide-spread. I argue that Papineau’s theory does not bypass the difficulties he identifies for representationalism. In fact, Papineau’s theory arguably has no advantage at all over representationalism with regard to these issues. The features that concern Papineau about representationalist views do not derive—or do not derive solely—from the representationalism of these views. They derive from a common-factorism of these views. And this common-factorism is embraced by Papineau as well as by most theories of consciousness and perception. (shrink)

A strong form of representationalism says that every conscious property of every mental state can be identified with some part of the state’s representational properties. A weaker representationalism says that some conscious property of some mental state can be identified with some part of the state’s representational properties. David Papineau has recently argued that all such theories are incorrect since they construe consciousness as consisting in “relations to propositions or other abstract objects outside space and time”, whereas consciousness is “concrete” (...) and “here and now”. Papineau defends instead a kind of “qualia theory” according to which all conscious properties are intrinsic non-relational properties of subjects. He argues that this theory bypasses the difficulties he identifies for representationalism. Similar worries about representationalism, and similar ideas to the effect that some qualia theory, adverbial theory, or sense-datum theory fares better with respect to these worries are relatively wide-spread. I argue that Papineau’s theory does not bypass the difficulties he identifies for representationalism. In fact, Papineau’s theory arguably has no advantage at all over representationalism with regard to these issues. The features that concern Papineau about representationalist views do not derive—or do not derive solely—from the representationalism of these views. They derive from a common-factorism of these views. And this common-factorism is embraced by Papineau as well as by most theories of consciousness and perception. (shrink)

There are compelling reasons to believe that musical works are abstract. However, this hypothesis conflicts with the platitude that musical works are appreciated by means of audition: the things that enter our ear canals and make our eardrums vibrate must be concrete, so how can musical works be listened to if they are abstract? This question constitutes the audibility problem. In this paper, I assess Julian Dodd’s elaborate attempt to solve it, and contend that Dodd’s attempt is unsuccessful. Then I (...) discuss what I take to be the ideal response to the audibility problem, and show that it ultimately fails. I contend, consequently, that the project of construing musical works as audible is disheartening. Accordingly, in my last section, I will argue the audibility problem may be satisfactorily resolved without ascribing audibility to musical works. (shrink)

According to a growing consensus in the secondary literature on Quine, the judgment Quine makes in favor of the nominalism outlined in “Steps Toward a Constructive Nominalism” is in tension with the naturalism he later adopts. In this paper, I show the consensus view is mistaken by showing that Quine’s judgment is rooted in a naturalistic standard of clarity. Moreover, I argue that Quine late in his career is committed to accepting one plausible reading of his judgment in 1947. In (...) making these arguments, I draw attention to a version of naturalism that misreadings of Quine have prevented philosophers from appreciating, and thereby articulate and clarify a version of naturalism I recommend philosophers investigate today. (shrink)

W.V. Quine is a well-known proponent of naturalism, the view on which reality is described only in science. He is also well-known for arguing that our current scientific theories commit us to the existence of abstract objects. It is tempting to believe that the naturalistic philosopher should think scientists outside of philosophy are in the best position to assess the merits of revising our current commitment to abstract objects. But Quine rejects this deferential view. On the reading of Quine’s philosophical (...) methodology that I defend in this paper, the naturalistic philosopher not only may assess the merits of revising the commitments of our scientific theories, but also will recommend we make such revisions if doing so simplifies and clarifies our science. To develop my reading, I will examine John Burgess and Gideon Rosen’s naturalism in ontology that includes the deferential view Quine rejects. By explaining how Quine’s naturalism differs from the anti-revisionist, deferential naturalism in philosophy of mathematics that Burgess and Rosen advance, I seek to clarify and advance contemporary debates on naturalism. (shrink)

There are many domains about which we think we are reliable. When there is prima facie reason to believe that there is no satisfying explanation of our reliability about a domain given our background views about the world, this generates a challenge to our reliability about the domain or to our background views. This is what is often called the reliability challenge for the domain. In previous work, I discussed the reliability challenges for logic and for deductive inference. I argued (...) for four main claims: First, there are reliability challenges for logic and for deduction. Second, these reliability challenges cannot be answered merely by providing an explanation of how it is that we have the logical beliefs and employ the deductive rules that we do. Third, we can explain our reliability about logic by appealing to our reliability about deduction. Fourth, there is a good prospect for providing an evolutionary explanation of the reliability of our deductive reasoning. In recent years, a number of arguments have appeared in the literature that can be applied against one or more of these four theses. In this paper, I respond to some of these arguments. In particular, I discuss arguments by Paul Horwich, Jack Woods, Dan Baras, Justin Clarke-Doane, and Hartry Field. (shrink)

Mereological nihilism is the view that all concrete objects are simple. Existence monism is the view that the only concrete object is one big simple: the world. I will argue that nihilism culminates in monism. The nihilist demands the simplest sufficient ontology, and the monist delivers it.

Las teorías que usamos para representar el mundo pueden ser extremadamente complejas. Abordan temas tales como electrones, campos cuánticos, estrellas de neutrones, materia oscura, redes neuronales, mercados económicos, la atmósfera y muchas otras entidades que suponemos existen en el universo. Al formular nuestras teorías, recurrimos a lenguajes exactos que nos permiten minimizar la vaguedad y expresarnos lo más precisa y cuantitativamente posible. Recurrimos a la matemática. Cuando formulamos nuestras teorías fácticas en lenguaje matemático, estas se refieren no solamente a objetos (...) que nosotros interpretamos como materiales, tales como partículas o personas, sino también a entidades más raras de un mundo abstracto: conjuntos, números, funciones, espacios algebraicos, variedades, topologías, y otras entidades similares. Estos objetos no son materiales en el sentido en que nosotros decimos que una manzana es material. Ellos no existen en el espacio-tiempo, no interactúan, no cambian o evolucionan. Sin embargo, allí están, profundamente arraigados en nuestras teorías más apreciadas acerca del mundo. (shrink)

Since the linguistic turn, many have taken semantics to guide ontology. Here, I argue that semantics can, at best, serve as a partial guide to ontological commitment. If semantics were to be our guide, semantic data and semantic treatments would need to be taken seriously. Through an examination of plurals and their treatments, I argue that there can be multiple, equally semantically adequate, treatments of a natural language theory. Further, such treatments can attribute different ontological commitments to a theory. Given (...) this, I argue that semantics can fail to deliver determinate ontological commitments and determinate answers to ontological questions, more generally. (shrink)