Mathematical Existence in Leibniz's Metaphysics and his Philosophy of Mathematics

2015 Fiscal Year Final Research Report

• Project/Area Number: 25770005
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Philosophy/Ethics
• Research Institution: University of Toyama
• Principal Investigator: Ikeda Shinji 富山大学, 人文学部, 准教授 (70634012)
• Project Period (FY): 2013-04-01 – 2016-03-31
• 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

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.

Free Research Field

哲学