| Project/Area Number |
25770005
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Philosophy/Ethics
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| Research Institution | University of Toyama |
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Principal Investigator |
Ikeda Shinji 富山大学, 人文学部, 准教授 (70634012)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | ライプニッツ / 数理哲学史 / 抽象 / モナドロジー / 原子論 / 数学的存在 / 延長 / 連続体 / 初期近代ヨーロッパ / 形而上学 / 普遍数学 / 普遍論争 / 数学 / 実体的紐帯 / 虚量 / デカルト |
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| Outline of Final Research Achievements |
In our research project, we have considered the problem of the metaphysical status of mathematical existence, by seeing the interrelation between Leibniz's metaphysics and mathematics; and we have unified his argument on this problem from his theory of abstraction. Through our analysis of his struggle against atomism, we have clarified the formation of his theory of substance which is based on the simple substances called 'Monads'. And through his critics on Cartesian notion of extension and Empiricists theory of abstraction, we have clarified his theory of abstraction which is based on his theory of substance. Finally, by considering the problem of the situation of Monad in the continuum (extended body), we have found a reason why he required the concept of actual extension which founds the true continuum.
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