Philosophy Of Mathematics Paperback Paperback

Stewart Shapiro

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.

0195139305

9780195139303

English

Oxford University Press

1-Jan-1997

296

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

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)