This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers.

This is the first systematic survey of modern nominalistic reconstructions of mathematics, and for this reason alone it should be read by everyone interested in the philosophy of mathematics and, more generally, in questions concerning abstract entities. In the bulk of the book, the authors sketch a common formal framework for nominalistic reconstructions, outline three major strategies such reconstructions can follow, and locate proposals in the literature with respect to these strategies. The discussion is presented with admirable precision and clarity, (...) and should be accessible even to readers with only minimal background in logic and mathematics. There will be many who will turn directly to these pages and use them as a brief manual on the state of the art of nominalism in mathematics. But the most intriguing parts of this elegant book—at least in my view—are the introduction and the conclusion, where the authors examine the significance of reconstructive nominalism. (shrink)

[Robert Stalnaker] Saul Kripke made a convincing case that there are necessary truths that are knowable only a posteriori as well as contingent truths that are knowable a priori. A number of philosophers have used a two-dimensional model semantic apparatus to represent and clarify the phenomena that Kripke pointed to. According to this analysis, statements have truth-conditions in two different ways depending on whether one considers a possible world 'as actual' or 'as counterfactual' in determining the truth-value of the statement (...) relative to that possible world. There are no necessary a posteriori or contingent a priori propositions: rather, contingent a priori and necessary a posteriori statements are statements that are necessary when evaluated one way, and contingent when evaluated the other way. This paper distinguishes two ways that the two-dimensional framework can be interpreted, and argues that one of them gives the better account of what it means to 'consider a world as actual', but that it provides no support for any notion of purely conceptual a priori truth. /// [Thomas Baldwin] Two-dimensional possible world semantic theory suggests that Kripke's examples of the necessary a posteriori and contingent a priori should be handled by interpreting names as implicitly indexical. Like Stalnaker, I reject this account of names and accept that Kripke's examples have to be accommodated within a metasemantic theory. But whereas Stalnaker maintains that a metasemantic approach undermines the conception of a priori truth, I argue that it offers the opportunity to develop a conception of the a priori aspect of stipulations, conceived as linguistic performances. The resulting position accommodates Kripke's examples in a way which is both intrinsically plausible and fits with Kripke's actual discussion of them. (shrink)

[Robert Stalnaker] Saul Kripke made a convincing case that there are necessary truths that are knowable only a posteriori as well as contingent truths that are knowable a priori. A number of philosophers have used a two-dimensional model semantic apparatus to represent and clarify the phenomena that Kripke pointed to. According to this analysis, statements have truth-conditions in two different ways depending on whether one considers a possible world 'as actual' or 'as counterfactual' in determining the truth-value of the statement (...) relative to that possible world. There are no necessary a posteriori or contingent a priori propositions: rather, contingent a priori and necessary a posteriori statements are statements that are necessary when evaluated one way, and contingent when evaluated the other way. This paper distinguishes two ways that the two-dimensional framework can be interpreted, and argues that one of them gives the better account of what it means to 'consider a world as actual', but that it provides no support for any notion of purely conceptual a priori truth. /// [Thomas Baldwin] Two-dimensional possible world semantic theory suggests that Kripke's examples of the necessary a posteriori and contingent a priori should be handled by interpreting names as implicitly indexical. Like Stalnaker, I reject this account of names and accept that Kripke's examples have to be accommodated within a metasemantic theory. But whereas Stalnaker maintains that a metasemantic approach undermines the conception of a priori truth, I argue that it offers the opportunity to develop a conception of the a priori aspect of stipulations, conceived as linguistic performances. The resulting position accommodates Kripke's examples in a way which is both intrinsically plausible and fits with Kripke's actual discussion of them. (shrink)

Mathematical realism is the doctrine that mathematical objects really exist, that mathematical statements are either determinately true or determinately false, and that the accepted mathematical axioms are predominantly true. A realist understanding of set theory has it that when the sentences of the language of set theory are understood in their standard meaning, each sentence has a determinate truth value, so that there is a fact of the matter whether the cardinality of the continuum is א2 or whether there are (...) measurable cardinals, whether or not those facts are knowable by us. (shrink)

This paper criticizes George Boolos's famous use of plural quantification to argue that monadic second-order logic is pure logic. I deny that plural quantification qualifies as pure logic and express serious misgivings about its alleged ontological innocence. My argument is based on an examination of what is involved in our understanding of the impredicative plural comprehension schema.

What is truth. Paul Horwich advocates the controversial theory of minimalism, that is that the nature of truth is entirely captured in the trivial fact that each proposition specifies its own condition for being true, and that truth is therefore an entirely mundane and unpuzzling concept. The first edition of Truth, published in 1980, established itself as the best account of minimalism and as an excellent introduction to the debate for students. For this new edition, Horwich has refined and developed (...) his treatment of the subject in the light of subsequent discussions, while preserving the distinctive format that made the earlier edition so successful. (shrink)

Since Edmund L. Gettier reminded us recently of a certain important inadequacy of the traditional analysis of "S knows that p," several attempts have been made to correct that analysis. In this paper I shall offer still another analysis (or a sketch of an analysis) of "S knows that p," one which will avert Gettier's problem. My concern will be with knowledge of empirical propositions only, since I think that the traditional analysis is adequate for knowledge of nonempirical truths.

Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...

Paul Horwich gives the definitive exposition of a prominent philosophical theory about truth, `minimalism'. His theory has attracted much attention since the first edition of Truth in 1990; he has now developed, refined, and updated his treatment of the subject, while preserving the distinctive format of the book. This revised edition appears simultaneously with a new companion volume, Meaning; the two books demystify central philosophical issues, and will be essential reading for all who work on the philosophy of language.

Mathematical realism is the doctrine that mathematical objects really exist, that mathematical statements are either determinately true or determinately false, and that the accepted mathematical axioms are predominantly true. A realist understanding of set theory has it that when the sentences of the language of set theory are understood in their standard meaning, each sentence has a determinate truth value, so that there is a fact of the matter whether the cardinality of the continuum is א2 or whether there are (...) measurable cardinals, whether or not those facts are knowable by us. (shrink)