Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic (...) problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians. (shrink)

With a new foreword by Dermot Moran 'the work here presented seeks to found a new science though, indeed, the whole course of philosophical development since Descartes has been preparing the way for it a science covering a new field of ...

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

Vise à découvrir comment l'intuition découle de la théorie husserlienne de l'être et le rôle qu'elle y joue. Pour situer son étude par la différence, E. Levinas commence par exposer les deux courants dominants de la philosophie allemande au tournant du siècle: le psychologisme et le naturalisme. Puis il montre comment la philosophie naturaliste est dépassée par Husserl, aboutissant à une nouvelle conception de l'être, qui fait comprendre que l'intuition n'est pas seulement un mode de connaissance parmi les autres, mais (...) le phénomène primitif qui rend possible la vérité elle-même. Le dernier chapitre montre la dimension philosophique qui s'ouvre avec une nouvelle théorie d. (shrink)

In this book, which remained unfinished at his death, Husserl attempts to forge a union between phenomenology and existentialism.

This book analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis--the success of mathematical physics ...

In this book Robert Tragesser sets out to determine the conditions under which a realist ontology of mathematics and logic might be justified, taking as his starting point Husserl's treatment of these metaphysical problems. He does not aim primarily at an exposition of Husserl's phenomenology, although many of the central claims of phenomenology are clarified here. Rather he exploits its ideas and methods to show how they can contribute to answering Michael Dummet's question 'Realism or Anti-Realism?'. In doing so he (...) makes a challenging and provocative contribution to the debate. (shrink)

Edmund Husserl is the founder of phenomenology and the Logical Investigations is his most famous work. It had a decisive impact on twentieth century philosophy and is one of few works to have influenced both continental and analytic philosophy. This is the first time both volumes have been available in paperback. They include a new introduction by Dermot Moran, placing the Investigations in historical context and bringing out their contemporary philosophical importance. These editions include a new preface by Sir Michael (...) Dummett. (shrink)

This is a book that no one but Weyl could have written--and, indeed, no one has written anything quite like it since.

CHAPTER I THE EMERGENCE AND DEVELOPMENT OF HUSSERL'S 'PHILOSOPHY OF ARITHMETIC'. HISTORICAL BACKGROUND: WEIERSTRASS AND THE ARITHMETIZATION OF ANALYSIS In ...