Kagaku tetsugaku
Online ISSN : 1883-6461
Print ISSN : 0289-3428
ISSN-L : 0289-3428
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Displaying 1-6 of 6 articles from this issue
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  • [title in Japanese]
    [in Japanese]
    2007 Volume 40 Issue 2 Pages 1-12
    Published: December 25, 2007
    Released on J-STAGE: May 29, 2009
    DOIhttps://doi.org/10.4216/jpssj.40.2_1
    JOURNAL FREE ACCESS
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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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  • [title in Japanese]
    [in Japanese]
    2007 Volume 40 Issue 2 Pages 13-21
    Published: December 25, 2007
    Released on J-STAGE: May 29, 2009
    DOIhttps://doi.org/10.4216/jpssj.40.2_13
    JOURNAL FREE ACCESS
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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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  • [title in Japanese]
    [in Japanese]
    2007 Volume 40 Issue 2 Pages 23-39
    Published: December 25, 2007
    Released on J-STAGE: May 29, 2009
    DOIhttps://doi.org/10.4216/jpssj.40.2_23
    JOURNAL FREE ACCESS
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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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  • [title in Japanese]
    [in Japanese]
    2007 Volume 40 Issue 2 Pages 41-56
    Published: December 25, 2007
    Released on J-STAGE: May 29, 2009
    DOIhttps://doi.org/10.4216/jpssj.40.2_41
    JOURNAL FREE ACCESS
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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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  • [title in Japanese]
    [in Japanese]
    2007 Volume 40 Issue 2 Pages 57-70
    Published: December 25, 2007
    Released on J-STAGE: May 29, 2009
    DOIhttps://doi.org/10.4216/jpssj.40.2_57
    JOURNAL FREE ACCESS
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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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  • [title in Japanese]
    [in Japanese]
    2007 Volume 40 Issue 2 Pages 71-113
    Published: December 25, 2007
    Released on J-STAGE: May 29, 2009
    DOIhttps://doi.org/10.4216/jpssj.40.2_71
    JOURNAL FREE ACCESS
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