著者

矢田部 俊介

出版者

京都大学文学部科学哲学科学史研究室

雑誌

科学哲学科学史研究 (ISSN:18839177)

巻号頁・発行日

vol.6, pp.1-15, 2012-02-28

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In his 2003 paper, Peacocke insisted that our implicit conception of natural numbers essentially uses a primitive recursion which consists of three clauses, and claimed that this excludes the non-standard models of natural numbers. In this article, we construct a counter “model” to his argument, which contains a non-standard natural number though the set ω of natural numbers is defined as an analogy to his primitive recursion, in a set theory with the comprehension principle within many-valued logic. This result suggests that we should interpret non-standard natural numbers from a philosophical viewpoint. We discuss this by reviewing Strict Finitism, and we conclude that non-standard natural numbers can be interpreted as “large numbers” in a Strict Finitist sense: It expresses new numbers which are introduced by expanding the notation system of natural numbers.