Takeuti on finite and infinite sets
Gaisi Takeuti is known best as a proof theorist, but he also wrote considerably on set theory. In his proof-theoretic writings on finitism, a novel view on the difference between finite and infinite sets emerges, in the context of qualifying epsilon_0 as a finitely accessible ordinal. In this talk I want to focus on this novel view, which I will show has a background in the Japanese philosophy of the Kyoto School of the early twentieth century, with which he was acquainted through various personal connections. Takeuti identifies a set with the kind of “mind” that generates it: finite minds, infinite minds, constructive minds, etc. A consequence of this view is that the boundary between the finite and infinite is more permeable than it is on the classical view coming from Cantor.