1992 Fiscal Year Final Research Report Summary
Historical Developments and Contemporary Tasks of the Philosophy of Logic and Mathematics in Analytic Philosophy
| Project/Area Number |
03301001
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
Philosophy
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| Research Institution | Hokkaido University |
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Principal Investigator |
YAMADA Tomoyuki Hokkaido University Faculty of Letters Associate Professor, 文学部, 助教授 (40166723)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAGAWA Hajime Hokkaido University Faculty of Letters Instructor, 文学部, 助手 (40237227)
NAKATOGAWA Koji Hokkaido University Faculty of Letters Associate Professor, 文学部, 助教授 (20237316)
KANEKO Hiroshi Senshu University Faculty of Letters Lecturer, 文学部, 講師 (60191988)
ITO Kunitake Kyoto University Faculty of Letters Associate Professor, 文学部, 助教授 (90144302)
IIDA Takashi Chiba University, Faculty of Letters Professor, 文学部, 教授 (10117327)
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| Project Period (FY) |
1991 – 1992
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| Keywords | infinity / self-reference paradox / set theory / intuitionism / theory of meaning / model theory / pragmatism / situation theory |
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| Research Abstract |
This year did we try to make much more study of each of our tasks and to give a synthetic view of our whole task. Concretely, concerning the historical development of the philosophy of logic and mathematics,did we study (1)Frege's conception of generality by looking at his text, (2)Poincare's constructive view of mathematics by reconstruct his argument with Russell and Zermelo, (3)Wittgenstein's criticism to intuitionistic philosophy and (4)Ramsey's theory of truth and belief by pondering his pragmatism. And concerning the contemporary tasks of the philosophy of logic, did we study (5)the radical criticism from the situation theory to the classical theory of truth and semantics, (6)an adaptation of situation theory to the semantics of Japanese and (7)an essential question 'what is a logical constant' by surveying recent researches on this matter. And concerning the contemporary tasks of the philosophy of mathematics, did we study, especially about groundings of set theory, (8)D.Lewis' mereological reconstruction of set theory, (9) M.Dummett's criticism to set theory from his class-monistic point of view. And we made a survey of (10)new developments of the intuitionistic type theory. We, therefore, have gained a new vision of the part which set theory plays in the philosophy of mathematics both in the historical context and in contemporary arguments. And so we have examined constructive views, e.g. intuitionism, both for the philosophy of mathematics and for the philosophy of logic. And we have clarified philosophical tasks which overlap computer science and other empirical sciences.
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