抄録
This paper considers the early philosophy of mathematics of Tanabe
Hajime (1885-1962). Tanabe began his philosophical studies with an interest
in the foundation of mathematics. He obtained a Ph.D. in 1918 and published
his dissertation titled An Inquiry into the Philosophy of Mathematics (1925).
Although this fact is well known in general, there is very little research on
his early philosophy of mathematics and thus the contents and importance of this work have not been fully appreciated. This paper examines Tanabe’s
early works on mathematics from the perspective of Nishida Kitarō, who
was Tanabe’s Ph.D. supervisor. Tanabe was specially interested in Nishida’s
concepts of “intuition” and “reflection”, and established the foundation of
mathematics through his theory of genetic cognition, that was organized
logically according to mathematical rationality. Section one situates and
introduces Tanabe’s early philosophy. Section two provides an overview of
the problem of genetic cognition and the generation of numbers. Section
three examines how Tanabe establishes the foundation for natural numbers
and then considers the significance of Tanabe’s philosophy from the
perspective of intuition and reflection. Section four focuses on Tanabe’s
theory of real numbers in his text “Continuous, Differential and Infinite”
(1916). Here, I argue that the transcendental meaning of irrational numbers
could be understood as “intuition”.
https://ror.org/02kpeqv85 
