著者
照井 一成
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.49-64, 2003-12-30 (Released:2009-05-29)
参考文献数
13

It is observed by Grishin that inconsistency of naive set theory can be avoided by restricting the logical law of contraction, as it is contraction that enables us to derive logical inconsistency from set-theoretic paradoxes such as Russell's paradox.In this paper, we examine Grishin's contraction-free naive set theory to better understand Russell's paradox and the naive comprehension principle from a purely formal standpoint. We study both static-propositional and dynamic-procedural aspects of naive comprehension and argue that it could lead to an ideal formalization of (part of) mathematics, where both propositional knowledge (theorems) and procedural knowledge (algorithms) reside in harmony.

言及状況

外部データベース (DOI)

はてなブックマーク (1 users, 1 posts)

Twitter (3 users, 3 posts, 0 favorites)

素朴集合論とコントラクション https://t.co/UpEgEbnBVB
@y_bonten確かに非古典論理上の無制限な包括原理による集合論(https://t.co/JP7EZNP1Wt等)じゃなく、Zermelo's axiom of comprehensionと異なる制限付き包括原理での普遍集合をもつ集合論も「素朴集合論」と呼んでいるようですね

収集済み URL リスト