This book is concerned with `the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach through an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.

Mathematics tells us there exist infinitely many prime numbers. Nominalist philosophy, introduced by Goodman and Quine, tells us there exist no numbers at all, and so no prime numbers. Nominalists are aware that the assertion of the existence of prime numbers is warranted by the standards of mathematical science; they simply reject scientific standards of warrant.

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)

In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good argument (...) for or against platonism, but that we could never have such an argument and, indeed, that there is no fact of the matter as to whether platonism is correct. (shrink)

This is part of a three-volume collection of most of David Lewis' papers in philosophy, except for those that previously appeared in his Philosophical Papers (Oxford University Press, 1983 and 1986). They are now offered in a readily accessible form. This second volume is devoted to Lewis' work in metaphysics and epistemology. The purpose of this collection, and the volumes that precede and follow it, is to disseminate more widely the work of an eminent and influential contemporary philosopher. The volume (...) will serve as a useful work of reference for teachers and students of philosophy. (shrink)

This is a collection of twenty-five papers and reviews by the leading analytic philosopher of our time. It adds to the papers on metaphysics and epistemology to be found in his previous two-volume collection published by Oxford University Press. One previously unpublished paper—“Why Conditionalize?”—is included. Australasian philosophers may note with some pride that eleven of the pieces were first published in the Australasian Journal of Philosophy.

A transcript of three lectures, given at Princeton University in 1970, which deals with (inter alia) debates concerning proper names in the philosophy of language.

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and (...) Gödel incompleteness. I hypothesize that only computable and decidable (in Gödel’s sense) structures exist, which alleviates the cosmological measure problem and may help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems. (shrink)

First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

Vaihinger... shows that thought is primarily a biological function turned into a conscious art. It is an art of adjustment, whose chief instrument is the construction of fictions by which men may manage to live. Thought is to be tested not by correspondence to an objective reality (that fiction is neatly disposed of) nor by its mirroring in consciousness an objective external world. Thought is to be tested by its fruits. The constructions of thought are not copies of or transcripts (...) of reality; they are programs, guess-work plans; possible programs for operation. Their validity is to be measured not by verisimilitude but by value. The fruits of thought are not "true," but especially where they are false, it may be important to act as if they were true... Vaihinger's chief originality consists in his defining of fictions and his distinction of fictions from hypotheses on the one hand, and from dogmatisms on the other. An hypothesis is a tentative discovery about the universe; a fiction is a deliberate, often clearly false and internally contradictory invention of thought... Evolution is the hypothesis that man is descended from the lower animals. We assume that we can indirectly turn to the remote facts which would justify that hypothesis. But the concept of infinity in the calculus, the atom and the ether in physics, the economic man in Adam Smith, are deliberate self-contradictory fictions, and fictions at variance with all experience. But though they are not only imaginary, false to the reality they allegedly represent and logically incoherent, they nevertheless facilitate thought and proper action. They are vital lies, human conveniences. They are the faiths, the palpably false faiths, the clearly useful falsities by which we live... The discovery that fictions were fictions has led, in the past, says Vaihinger, to an abandonment of them, and a turning to other fictions believed to be truer. Pathetic and foolish adventure! What the race needs is more faith in its own effective imaginations. The myths that it has told itself, the world pictures that it has made, are not to be dismissed because they are found to be creations of the imagination. They tally with no world and they carry the canker of logical inconsistency within them. The important thing is their utility; their human scope and mortal relevance. If we ceased making fictions, we should cease altogether to be. Let us beware to plunge from fruitful fictions to less fruitful ones that masquerade as truths and are really dogmatisms. (Review of As If by Irwin Edman, Saturday Review of Literature, 10 January, 1925) This is a well-formatted version of C.K. Ogden's translation of Philosophie des Als Ob, originally published in 1925 by Kegan Paul. (shrink)

It seems obvious that I could have failed to exist. My parents could easily never have met, in which case I should never have been conceived and born. The like applies to everyone. More generally, it seems plausible that whatever exists in space and time could have failed to exist. Events could have taken an utterly different course. Our existence, like most other aspects of our lives, appears frighteningly contingent. It is therefore surprising that there is a proof of my (...) necessary existence, a proof that generalizes to everything whatsoever. I will explain the proof and discuss what to make of it. A first reaction is that a ‘proof’ of such an outrageous conclusion must contain some dreadful fallacy. Yet the proof does not collapse under scrutiny. Further reflection suggests that, suitably interpreted, it may be sound. So interpreted, the conclusion is not outrageous, although it may not be the view you first thought of. (shrink)

This disagreement extends to the fundamental details of physical and biochemical theories. On the other hand, (2) There is almostuniversal agreementthatlife did notfirstcome aboutmerely by chance. This is not to say that all scientists think that life’s existence was inevitable. The common view is that given a fuller understanding of the physical and biological conditions and processes involved, the emergence of life should be seen to be quite likely, or at least not very surprising. The view which is almost universally (...) rejected by researchers in the field is that the numerous and prima facie improbable physical and biological requirements for life all fell together just by a fluke, like so many dice tumbling out of a bag and landing all sixes. Most importantly, for the purposes of the following discussion, (3) The conviction that life did not arise largely by chance is treated as epistem- ically prior to the development of alternative theories. C 2007, Copyright the Authors Journal compilation C 2007, Blackwell Publishing, Inc. (shrink)

In this book van Fraassen develops an alternative to scientific realism by constructing and evaluating three mutually reinforcing theories.

In this book, Lawrence Sklar demonstrates the interdependence of science and philosophy by examining a number of crucial problems on the nature of space and ...

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

(1) The average Mum has 2.4 children. (2) The number of Argle’s fingers equals the number of Bargle’s toes. (3) There are two possible ways in which Joe could win this chess game. In the right contexts, and outside the philosophy room, all the above sentences may be completely uncontroversial. For instance, if we know that Joe could win either by exchanging queens and entering an endgame, or by initiating a kingside attack then, if ignorant of Quine’s work on ontology, (...) we would take (3) to be uncontroversially true. (shrink)

This is the second volume of philosophical essays by one of the most innovative and influential philosophers now writing in English. Containing thirteen papers in all, the book includes both new essays and previously published papers, some of them with extensive new postscripts reflecting Lewis's current thinking. The papers in Volume II focus on causation and several other closely related topics, including counterfactual and indicative conditionals, the direction of time, subjective and objective probability, causation, explanation, perception, free will, and rational (...) decision. Throughout, Lewis analyzes global features of the world in such a way as to show that they might turn out to supervene on the spatiotemporal arrangement of local qualities. (shrink)

Tn this paper I explore and to an extent defend HS. The main philosophical challenges to HS come from philosophical views that say that nomic concepts-laws, chance, and causation-denote features of the world that fail to supervene on non-nomic features. Lewis rejects these views and has labored mightily to construct HS accounts of nomic concepts. His account of laws is fundamental to his program, since his accounts of the other nomic notions rely on it. Recently, a number of philosophers have (...) criticized Lewis's account, and Humean accounts of laws generally, for delivering, at best, a pale imitation ofthe genuine item. These philosophers think that the notion of law needed by science requires laws-if there are any-to be fundamental features of our world that are completely distinct from and not supervenient on the particular facts that they explain. I side with Lewis against these philosophers. Here I will argue that although Lewis-laws don't fulfill all our philosophical expectations, they do play the roles that science needs laws to play. The metaphysics and epistemology of Humean laws, and more specifically, Lewis-laws, are in much better shape than the metaphysics and epistemology of the main anti-Humean alternatives. However, I do have inisgivings about Lewis's account. Both he and his critics assume that the basic properties are so individuated so that the laws are not metaphysically necessary. If this assumption is rejected, then the question of Humean supervenience lapses. I conclude with a brief discussion of this position. (shrink)

A version of relationism that takes spatiotemporal structures—spatial geometry and a standard of inertia—to supervene on the history of relations between bodies is described and defended. The account is used to explain how the relationist should construe models of Newtonian mechanics in which absolute acceleration manifestly does not supervene on the relations; Ptolemaic and Copernican models for example. The account introduces a new way in which a Lewis-style ‘best system’ might capture regularities in a broadly Humean world; a defence is (...) given against a charge of indeterminism that applies to any such approach to laws. (shrink)

Develops a structuralist understanding of mathematics, as an alternative to set- or type-theoretic foundations, that respects classical mathematical truth while ...

First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

The first volume of this series presents fifteen selected papers dealing with a variety of topics in ontology, philosophy of mind, and philosophy of language.

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.

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)