著者
斉藤 健
出版者
北海道大学哲学会 = The Philosophical Society of Hokkaido University
雑誌
哲学 (ISSN:02872560)
巻号頁・発行日
vol.40, pp.45-63, 2004-07-18

The aim of this paper is to examine Shapiro's structuralism in philosophy of mathematics and to show several difficulties in his structuralism. He adopts ante rem structuralism which is based upon his realism. After delineating his arguments I will point out some advantages of his structuralism, which become apparent when it is compared especially with a traditional type of mathematical Platonism. Then I will show, by using examples taken from mathematics, that there are some ambiguities in his uses of the basic notions, such as structure, system, exemplification and place. Finally I criticize his axiomatic theory of structure mainly because it relies upon too many undefined terms, and show that in his ontological views there is an underlying discrepancy between his ante rem structuralism and his set-theoretic approach to structures.

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『数学の哲学におけるシャピロの構造主義』

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http://t.co/q4ghXOfF シャピロの構造主義について批判的に論じた論文もあるな。。
「構造とは、ある体系の抽象的形式で[…]諸対象がその体系における他の諸対象にいかに関係するかに関して影響を与えない諸特徴を一切無視する[…]。そして構造はそれが含む数学的諸対象に先立つ。構造と体系の関係はタイプとトークンの関係に例えられる」http://t.co/p0Mj0zqz

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