著者

岡本 賢吾

出版者

日本科学哲学会

雑誌

科学哲学 (ISSN:02893428)

巻号頁・発行日

vol.34, no.1, pp.7-19, 2001

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Frege's well-known thesis that arithmetic is reducible to logic leaves unexplained what is the gain of the reduction and what he means by logic in principle. First, the author contends that the real interest of the reduction consists in a form of conceptual reduction: it frees us from the ordinary naive conception of numbers as forming extremely peculiar genus and replaces it with a very general and basic conception of them. Second, it is pointed out that Frege's concept of logic involves two elements. One is based on the iteratability of the operation of abstraction and naturally leads him to accept a sort of denumerably higher order logical language. The other is based on the so-called comprehension principle. Each of the two elements could be said to be logical in some sense but they are inconsistent with each other. Still, we can learn much from his attempt to search for as extensive and global a conception of logic as possible.