科学哲学

構成的数学とその動向

石原哉

2007 年 40 巻 2 号 p. 1-12
発行日: 2007/12/25
公開日: 2009/05/29

DOIhttps://doi.org/10.4216/jpssj.40.2_1

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We survey Brouwer's intuitionistic mathematics and Markov's constructive recursive mathematics by examining axioms assumed in each school and mathematical theorems derived from the axioms. It is known that Bishop's constructive mathematics is a core of the varieties of mathematics in the sense that it can be extended not only to intuitionistic mathematics and constructive recursive mathematics, but also classical mathematics. We compare a new trend of constructive mathematics, called a minimalist foundation, with Bishop's constructive mathematics.

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逆数学と超準的手法:代数学の基本定理を題材として

田中一之

2007 年 40 巻 2 号 p. 13-21
発行日: 2007/12/25
公開日: 2009/05/29

DOIhttps://doi.org/10.4216/jpssj.40.2_13

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Reverse Mathematics is an ongoing research program on foundations of mathematics, whose aim is to find out what kinds of logical or set-theoretical hypotheses are necessary and sufficient to prove a theorem of ordinary mathematics. In this paper, we show that the fundamental theorem of algebra holds within RCA₀, a weakest base theory of this program, by way of a combination of a nonstandard method and a conservation result on weak König's lemma.

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なぜ意味論は「プロセス」を含むか

表示意味論・領域理論をめぐって

岡本賢吾

2007 年 40 巻 2 号 p. 23-39
発行日: 2007/12/25
公開日: 2009/05/29

DOIhttps://doi.org/10.4216/jpssj.40.2_23

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Two remarkable results attained by Domain Theory, which serves as mathematical foundations for denotational semantics of programming languages, are explained and considered from philosophical viewpoints: 1) the analysis of recursion by the fix-point semantics and 2) the introduction of the notion of continuity and of compact elements. In particular, the author finds them conceptually illuminating in that firstly, they succeed in making explicit those unnoticed semantic elements lying behind the syntax of the languages which play essential roles in the construction and execution of recursive programs, and that secondly, they show the way to reconstruct various ordinary classical mathematical structures by virtue of complementing approximation processes to their infinite noncompact elements.

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知覚経験の対象としての性質

前田高弘

2007 年 40 巻 2 号 p. 41-56
発行日: 2007/12/25
公開日: 2009/05/29

DOIhttps://doi.org/10.4216/jpssj.40.2_41

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In this paper, I investigate the role of properties for perceptual experience via a critical examination of the view that perceptual experience has properties as its primary objects and also has those properties as the determiner of its phenomenal character. The view in question can take two forms according to whether properties are construed as universals or as tropes. So I divide the view into two types and show that each of them has its own problems. In conclusion I propose an alternative view concerning the role of properties for perceptual experience.

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エヴァンズのパラドクスと思考における固有名のはたらき

固有名の理解に関するエヴァンズ説の批判的検討

藤川直也

2007 年 40 巻 2 号 p. 57-70
発行日: 2007/12/25
公開日: 2009/05/29

DOIhttps://doi.org/10.4216/jpssj.40.2_57

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Evans' theory of proper names has paradoxical consequence; some of those who can perfectly use a proper name to refer to its referent cannot properly understand statements containing that name. In this paper, I try to avoid this counter-intuitive consequence by taking into account to what Evans fails to appreciate, i.e., contributions of social character of proper names to entertaining thought about their referents - we can use a proper name as a tool for discriminating an object. I also illustrate a type of thought component, 'proper name concept', as I call it, that Evans didn't consider of. The proper name concept is objectfile that contains 'descriptions' or 'information' of referent and is connected to the referent by social convention rather than description.

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書評

三浦俊彦他

2007 年 40 巻 2 号 p. 71-113
発行日: 2007/12/25
公開日: 2009/05/29

DOIhttps://doi.org/10.4216/jpssj.40.2_71

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