Since Benacerraf’s “Mathematical Truth” a number of epistemological challenges have been launched against mathematical platonism. I first argue that these challenges fail because they unduely assimilate mathematics to empirical science. Then I develop an improved challenge which is immune to this criticism. Very roughly, what I demand is an account of how people’s mathematical beliefs are responsive to the truth of these beliefs. Finally I argue that if we employ a semantic truth-predicate rather than just a deflationary one, there surprisingly (...) turns out to be logical space for a response to the improved challenge where no such space appeared to exist. (shrink)

Descartes has often been called the 'father of modern philosophy'. His attempts to find foundations for knowledge, and to reconcile the existence of the soul with the emerging science of his time, are among the most influential and widely studied in the history of philosophy. This is a classic and challenging introduction to Descartes by one of the most distinguished modern philosophers. Bernard Williams not only analyzes Descartes' project of founding knowledge on certainty, but uncovers the philosophical motives for his (...) search. With acute insight, he demonstrates how Descartes' _Meditations _are not merely a description but the very enactment of philosophical thought and discovery. Williams covers all of the key areas of Descartes' thought, including God, the will, the possibility of knowledge, and the mind and its place in nature. He also makes profound contributions to the theory of knowledge, metaphysics and philosophy generally. With a new foreword by John Cottingham. (shrink)

In Writing the Book of the World, Ted Sider argues that David Lewis’s distinction between those predicates which are ‘perfectly natural’ and those which are not can be extended so that it applies to words of all semantic types. Just as there are perfectly natural predicates, there may be perfectly natural connectives, operators, singular terms and so on. According to Sider, one of our goals as metaphysicians should be to identify the perfectly natural words. Sider claims that there is a (...) perfectly natural first-order quantifier. I argue that this claim is not justified. Quine has shown that we can dispense with first-order quantifiers, by using a family of ‘predicate functors’ instead. I argue that we have no reason to think that it is the first-order quantifiers, rather than Quine’s predicate functors, which are perfectly natural. The discussion of quantification is used to provide some motivation for a general scepticism about Sider’s project. Shamik Dasgupta’s ‘generalism’ and Jason Turner’s critique of ‘ontological nihilism’ are also discussed. (shrink)

This is a symposium on my book, Writing the Book of the World, containing a precis from me, criticisms from Dorr, Fine, and Hirsch, and replies by me.

This paper is a response to Theodore Sider's book, Writing the Book of the World. It raises some puzzles about Sider's favoured methodology for finding out about naturalness (or 'structure').

Four- Dimensionalism defends the thesis that the material world is composed of temporal as well as spatial parts. This defense includes a novel account of persistence over time, new arguments in favour of the four-dimensional ontology, and responses to the challenges four- dimensionalism faces." "Theodore Sider pays particular attention to the philosophy of time, including a strong series of arguments against presentism, the thesis that only the present is real. Arguments offered in favour of four- dimensionalism include novel arguments based (...) on time travel, the debate between spacetime substantivalists and relationalists, and vagueness. Also included is a comprehensive discussion of the paradoxes of coinciding material objects, and a novel resolution of those paradoxes based on temporal counterpart theory. In conclusion Sider replies to prominent objections to four- dimensionalism, including discussion of the problem of the rotating homogenous disk. (shrink)

In order to perfectly describe the world, it is not enough to speak truly. One must also use the right concepts - including the right logical concepts. One must use concepts that "carve at the joints", that give the world's "structure". There is an objectively correct way to "write the book of the world". Much of metaphysics, as traditionally conceived, is about the fundamental nature of reality; in the present terms, this is about the world's structure. Metametaphysics - inquiry into (...) the status of metaphysical questions - turns on structure. The question of whether ontological, causal, or modal questions are "substantive" is in large part a question of whether the world has ontological, causal, and modal structure - whether quantifiers, causal relations, and modal operators carve at the joints. (shrink)

I believe that Tom is the proud father of a baby boy. Why do I think his child is a boy? A natural answer might be that I remember that his name is ‘Owen’ which is usually a boy’s name. Here I’ve given information that might be part of a causal explanation of my believing that Tom’s baby is a boy. I do have such a memory and it is largely what sustains my conviction. But I haven’t given you just (...) any causally relevant information, I’ve given my grounds for my belief. I’ve given reasons that might justify me in supposing that Tom’s baby is a boy. Less naturally, the question might be taken as a request for a broader causal explanation of my holding this belief. Appropriate answers might cite all manner of facts concerning the evolution of the human race, why I chose to pursue philosophy and hence came to know Tom, the mechanisms of email transmission, the firing of various neurons, the circumstances of concept formation as a result of which I’m able to grasp the thought that Tom’s baby is a boy, and so on. It is an interesting question what distinguishes the narrower set of answers that I first suggested. I won’t pursue that here. I assume you have a good enough sense of the distinction I’m drawing. We might call the narrower set of answers justifying reasons, the kind of reasons I might cite in justifying my belief. Answers of the first sort are clearly relevant to epistemological evaluation. In assessing whether you know p or are rational in believing it to the degree you do, I will naturally want to consider what reasons you have for your belief. In deliberating myself about whether to believe p, in seeking an answer to the question of whether p, I will naturally consider what reasons or grounds I have to suppose that p. But what I want to focus on here is how explanations of the broader sort bear on such questions as whether to believe p. From a third-person perspective we can ask, ‘In assessing the epistemic status of S’s belief that p, what is the relevance of causal information that lies outside of the realm of justifying reasons?’ From the first-person standpoint we can ask ‘In seeking to answer whether p, how should such causal information affect my deliberations?’ At first it might seem that such broader causal information could have little relevance if any. Like any belief my belief that p can be traced back to innumerable causes from far and wide.. (shrink)

Modern empiricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truth which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall argue, are ill founded. One effect of abandoning them is, as (...) we shall see, a blurring of the supposed boundary between speculative metaphysics and natural science. Another effect is a shift toward pragmatism. (shrink)

At least since [Frege, 1960] and [Geach, 1965], there has been some consensus about the relation between negation, the speech act of denial, and the attitude of rejection: a denial, the consensus has had it, is the assertion of a negation, and a rejection is a belief in a negation. Recently, though, there have been notable deviations from this orthodox view. Rejectivists have maintained that negation is to be explained in terms of denial or rejection, rather than vice versa. Some (...) other theorists have maintained that negation is a separate phenomenon from denial, and that neither is to be explained in terms of the other. In this paper, I present and consider these heterodox theories of the relation between negation, denial, and rejection. (shrink)

We think of logic as objective. We also think that we are reliable about logic. These views jointly generate a puzzle: How is it that we are reliable about logic? How is it that our logical beliefs match an objective domain of logical fact? This is an instance of a more general challenge to explain our reliability about a priori domains. In this paper, I argue that the nature of this challenge has not been properly understood. I explicate the challenge (...) both in general and for the particular case of logic. I also argue that two seemingly attractive responses – appealing to a faculty of rational insight or to the nature of concept possession – are incapable of answering the challenge. (shrink)

A sense of unity -- Basic objects : a reply to Xu -- Objectivity without objects -- The vagueness of identity -- Quantifier variance and realism -- Against revisionary ontology -- Comments on Theodore Sider's four dimensionalism -- Sosa's existential relativism -- Physical-object ontology, verbal disputes, and common sense -- Ontological arguments : interpretive charity and quantifier variance -- Language, ontology, and structure -- Ontology and alternative languages.

v. 1. Nominalism and realism.--v. 2. A theory of universals.

Nozick analyzes fundamental issues, such as the identity of the self, knowledge and skepticism, free will, the foundations of ethics, and the meaning of life.

Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured previous (...) discussions of these projects, and presents clear, concise accounts of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed. (shrink)

The central question in this book is why it seems reasonable for the words of our language to divide up the world in ordinary ways rather than other imaginable ways. Hirsch calls this the division problem. His book aims to bring this problem into sharp focus, to distinguish it from various related problems, and to consider the best prospects for solving it. In exploring various possible responses to the division problem, Hirsch examines series of "division principles" which purport to express (...) rational constraints on how our words ought to classify and individuate. The ensuing discussion deals with a wide range of metaphysical and epistemological topics, including projectibility and similarity, alternative analyses of natural properties and things, the inscrutability of reference, and the relevance of such pragmatic notions as salience and economy. The final chapters of the book develop what Hirsch contends is the most promising response to the division problem: a theory in which constraints on classification and individuation are seen to derive from the necessary structure of "fine-grained" propositions and the necessary dependence of some concepts on others. (shrink)

Metaethical—or, more generally, metanormative— realism faces a serious epistemological challenge. Realists owe us—very roughly speaking—an account of how it is that we can have epistemic access to the normative truths about which they are realists. This much is, it seems, uncontroversial among metaethicists, myself included. But this is as far as the agreement goes, for it is not clear—nor uncontroversial—how best to understand the challenge, what the best realist way of coping with it is, and how successful this attempt is. (...) In this paper I try, first, to present the challenge in its strongest version, and second, to show how realists—indeed, robust realists—can cope with it. The strongest version of the challenge is, I argue, that of explaining the correlation between our normative beliefs and the independent normative truths. And I suggest an evolutionary explanation as a way of solving it. (shrink)

This is one of the seminal articles of the pragmatist tradition where C.S. Peirce sets out his doctrine of doubt and belief --and their relationship to inquiry and clarity of our concepts. Originally published in the Popular Science Monthly; and widely available in reprints and collections of Peirce's writings.

Theodore Sider has given us a terrific book, bursting at the seams with new arguments and new takes on old arguments. Whether or not one is convinced by his conclusions, the thoroughness, lucidity, fair-mindedness—and the sheer exuberance—of his discussions make Four Dimensionalism a major contribution to contemporary metaphysics.

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)

Recently a number of works in meta-ontology have used a variant of J.H. Harris's collapse argument in the philosophy of logic as an argument against Eli Hirsch's quantifier variance. There have been several responses to the argument in the literature, but none of them have identified the central failing of the argument, viz., the argument has two readings: one on which it is sound but doesn't refute quantifier variance and another on which it is unsound. The central lesson I draw (...) is that arguments against quantifier variance must pay strict attention to issues of translation and interpretation. The paper also has a substantial appendix in which I prove the equivalence of plural mereological nihilism and standard first-order atomistic mereology; results of this kind are often appealed to in the literature on quantifier variance but without many details on the nature or proof of the result. (shrink)

A response is given here to Benacerraf's 1973 argument that mathematical platonism is incompatible with a naturalistic epistemology. Unlike almost all previous platonist responses to Benacerraf, the response given here is positive rather than negative; that is, rather than trying to find a problem with Benacerraf's argument, I accept his challenge and meet it head on by constructing an epistemology of abstract (i.e., aspatial and atemporal) mathematical objects. Thus, I show that spatio-temporal creatures like ourselves can attain knowledge about mathematical (...) objects by simply explaininghow they can do this. My argument is based upon the adoption of a particular version of platonism — full-blooded platonism — which asserts that any mathematical object which possiblycould exist actuallydoes exist. (shrink)

Debunking arguments are arguments that aim to undermine some range of beliefs by showing that those beliefs are not appropriately connected to their subject matter. Arguments of this sort rear their heads in a wide variety of domains, threatening beliefs about morality, mathematics, logic, color, and the existence of God. Perceptual beliefs about ordinary objects, however, are widely thought to be invulnerable to such arguments. I will show that this is a mistake. I articulate a debunking argument that purports to (...) undermine our most basic perceptual beliefs. I then challenge a number of responses to the argument, including the “permissivist” response that there are a plenitude of objects before us, virtually guaranteeing the accuracy of our object beliefs. (shrink)

Precis of my book by this title, for a symposium.

To appear in David Chalmers, Ryan Wasserman and David Manley, eds., Metametaphysics (OUP, 2009).

In the middle of the twentieth century a dispute erupted between the chief architect of Logical Empiricism, Rudolf Carnap, and Logical Empiricism’s chief reformer, Willard van Orman Quine -- who was attempting to save what he took to be its main insights by recasting them in a more acceptable form. Though both eschewed metaphysics of the traditional apriori sort, and both were intent on making the investigation of science the center of philosophy, they disagreed about how to do so. Part (...) of the disagreement involved the nature of ontological disputes. The central documents in the debate are: (i) Quine’s 1948 article, “On What There Is,” which tells us how to discern ontological.. (shrink)

Kant's question 'How are synthetic judgments a priori possible?' pre- cipitated the Critique of Pure Reason. Question and answer notwith- standing, Mill and others persisted in doubting that such judgments were possible at all. At length some of Kant's own clearest purported.