Philosophy of Mathematics: Structure and Ontology - Brossura

Shapiro, Stewart

Brossura

ISBN 10: 0195139305 ISBN 13: 9780195139303

Casa editrice: Oxford University Press USA, 1997

Riassunto

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.

Su questo libro

Recensione:

Extremely interesting and deserves the attention of anyone with a serious interest in the field ... a careful study of the book will be enormously rewarding to anyone with some prior exposure to the field. (Philosophia Mathematica)

L'autore:

Stewart Shapiro is Professor of Philosophy at Ohio State University at Newark and the University of St. Andrews, Scotland.

Su questa edizione

• Editore: Oxford University Press USA
• Data di pubblicazione: 1997
• ISBN 10: 0195139305
• ISBN 13: 9780195139303
• Rilegatura: Copertina flessibile
• Numero di pagine: 296