Philosophy of Mathematics 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024


Philosophy of Mathematics

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Stewart Shapiro 作者
Oxford University Press, USA
译者
2000-9-28 出版日期
296 页数
USD 50.00 价格
Paperback
丛书系列
9780195139303 图书编码

Philosophy of Mathematics 在线电子书 图书标签: 数学  哲学  f数哲  MathematicalLogic  Math  0001  00   


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发表于2024-06-29


Philosophy of Mathematics 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

Philosophy of Mathematics 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

Philosophy of Mathematics 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024



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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.

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