First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional philosophies (...) of mathematics indicating how each is prepared to deal with the present problem. It is shown that (the standard formulations of) some views seem to deny outright that there is a relationship between mathematics and any non-mathematical reality; such philosophies are clearly unacceptable. Other views leave the relationship rather mysterious and, thus, are incomplete at best. The final, more speculative section provides the direction of a positive account. A structuralist philosophy of mathematics is outlined and it is proposed that mathematics applies to reality though the discovery of mathematical structures underlying the non-mathematical universe. (shrink)

Despite a vast philosophical literature on the epistemology of mathematics and much speculation about how, in principle, knowledge of this domain is possible, little attention has been paid to the psychological findings and theories concerning the acquisition, comprehension and use of mathematical knowledge. This contrasts sharply with recent philosophical work on language where comparable issues and problems arise. One topic that is the center of debate in the study of mathematical cognition is the question of innateness. This paper critically examines (...) the controversy. (shrink)

This book expounds a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defense of realism about the metaphysics of mathematics--the view that mathematics (...) is about things that really exist. (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)

This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject.

Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. (...) She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics. (shrink)

For some time now, academic philosophers of mathematics have concentrated on intramural debates, the most conspicuous of which has centered on Benacerraf's epistemological challenge. By the late 1980s, something of a consensus had developed on how best to respond to this challenge. But answering Benacerraf leaves untouched the more advanced epistemological question of how the axioms are justified, a question that bears on actual practice in the foundations of set theory. I suggest that the time is ripe for philosophers of (...) mathematics to turn outward, to take on a problem of real importance for mathematics itself. (shrink)

This article reviews the transition between post-Fregean anti-naturalistic epistemology and contemporary naturalistic epistemologies. It traces the revival of naturalism to Quine’s critique of the "a priori", and Kuhn’s defense of historicism, and use the arguments of Quine and Kuhn to identify a position, "traditional naturalism", that combines naturalistic themes with the claim that epistemology is a normative enterprise. Pleas for more radical versions of naturalism are articulated, and briefly confronted.

Thoughts and other mental states are defined by their role in a functional system. Since it is easier to determine when we have knowledge than when reasoning has occurred, Gilbert Harman attempts to answer the latter question by seeing what assumptions about reasoning would best account for when we have knowledge and when not. He describes induction as inference to the best explanation, or more precisely as a modification of beliefs that seeks to minimize change and maximize explanatory coherence. Originally (...) published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

No serious philosopher or student of philosophy can afford to neglect Wittgenstein's work. Professor Fogelin provides an authoritative critical evaluation of both the _Tractatus Logico-Philosophicus_ and _Philosophical Investigations_, enabling the reader to come to grips with these difficult yet key works. Fogelin explains Wittgenstein's attempt in the _Tractatus_ to combine a picture theory of propositional structure, and also explores Wittgenstein's own criticisms of the Tractarian synthesis. He gives particular attention to topics in the philosophy of language, logic, psychology and the (...) foundations of mathematics, examining Wittgenstein's work on these fields and arguing that Wittgenstein's criticisms in these areas form the basis for a radically new standpoint in philosophy. (shrink)

Preface 1 Introduction: The Persistence of the Attitudes 2 Individualism and Supervenience 3 Meaning Holism 4 Meaning and the World Order Epilogue Creation Myth Appendix Why There Still Has to be a Language of Thought Notes References Author Index.

If you wish to learn from the theoretical physicist anything about the methods which he uses, I would give you the following piece of advice: Don't listen to his words, examine his achievements. For to the discoverer in that field, the constructions of his imagination appear so necessary and so natural that he is apt to treat them not as the creations of his thoughts but as given realities.

Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defence of realism (...) about the metaphysics of mathematics--the view that mathematics is about things that really exist. Resnik's distinctive philosophy of mathematics is here presented in an accessible and systematic form: it will be of value not only to specialists in this area, but to philosophers, mathematicians, and logicians interested in the relationship between these three disciplines, or in truth, realism, and epistemology. (shrink)

pt. 1. The proposition and its sense.--pt. 2. On logic and mathematics.