著者

三平 正明

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.36, no.2, pp.33-48, 2003-12-30 (Released:2009-05-29)

参考文献数

29

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It is a well-known story that Russell's discovery of his paradox shook the foundations of Frege's logical system for arithmetic. But there is another route to this paradox. Hilbert pointed out to Frege that he had already found other even more convincing contradictions which he communicated to Zermelo, thereby initiating Zermelo's independent discovery of Russell's paradox. In this paper, we follow this less familiar route and analyze three paradoxes, namely Hilbert's paradox, Zermelo's version of Russell's paradox and Schröder's paradox of 0 and 1. Furthermore, tradition in which these paradoxes were found is reconsidered. We examine Schröder's place in the foundational study and criticize an alleged dichotomy between the algebraic and logistic traditions.

著者

三平 正明

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.33, no.2, pp.147-161, 2000-11-25 (Released:2009-05-29)

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In his influential paper "What numbers could not be", P. Benacerraf argues that numbers could not be objects at all, and that the search for which particular objects the numbers really are is a misguided one. It is widely held that he has given a knock-down argument against a platonistic conception of arithmetic. But, in this paper, I shall try to show first that his argument fails because it depends on too strong an assumption. Second, his criticism is not applicable to the version of platonism that Frege proposed.

著者

三平 正明

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.38, no.2, pp.53-76, 2005-12-25 (Released:2009-05-29)

参考文献数

38

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Today everyone admits that Frege is one of the founders of modern logic. However, there is a wide divergence of views on whether metatheory was possible for Frege. Some insist that Frege had virtually everything that was needed to consider metasystematic questions (consistency, independence, completeness); others urge that it was impossible for Frege to raise those questions in the first place. Our aim in this paper is to reexamine the place of metatheoretical considerations in Frege's thought. We argue that usual model-theoretic techniques could not be accepted by Frege because of his distinctive "logic of judgement." But this doesn't mean that Frege was precluded from metatheory in toto. On the contrary, he planned a different kind of metatheory, namely "Neues Gebiet" resting on the permutation invariance method. We point out further two problems concerning this new conception of metatheory.

著者

三平 正明

出版者

日本イギリス哲学会

雑誌

イギリス哲学研究 (ISSN:03877450)

巻号頁・発行日

vol.33, pp.99-113, 2010-03-20 (Released:2018-03-30)

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In her influential paper ʻThe First Personʼ, Elizabeth Anscombe concludes that , despite all syntactic and semantic appearances to the contrary, the first person singular pronoun is not a referring expression. She presents three main arguments. One is the argument intended to show that any account of ʻIʼ as a device of selfreference will either be insufficient or essentially involve circularity. The other two attempt to establish directly that ʻIʼ is not a device of reference. The aim of this paper is to show that all these arguments are mistaken.We should regard ʻIʼ as a referring expression and explain its reference by the ordinary token-reflexive rule or other similar ones.

著者

三平 正明

出版者

岩波書店

雑誌

思想 (ISSN:03862755)

巻号頁・発行日

no.954, pp.123-140, 2003-10

著者

上野 修 永井 均 入不二 基義 古荘 真敬 青山 拓央 郡司 ペギオ幸夫 小山 悠 勝守 真 中野 昌宏 三平 正明 山田 友幸 重田 謙 入江 幸男

出版者

大阪大学

雑誌

基盤研究(C)

巻号頁・発行日

2007

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独在的<私>と独今的<いま>が非常によく似た仕方で現実概念の根本にあることが明らかとなった。<私>と<いま>が世界のどの個人、どの時点を開闢点とするかは偶然である。にもかかわらず、いったん開闢されるとその特異点は諸個人のうちの一人物と歴史時間の現在に位置づけられ、特異性を失う。そしてこのことがむしろ現実性の条件となっている。このような二重性は、言語の使用者がまさにその使用によって言語世界の限界内に位置づけられる、その仕方によって理解されねばならない。