"The Problem of Mathematical Objects" (Bob Hale) (1)

＠京都大学文学部。座長は Graham Priest、講演者は Bob Hale という超豪華メンバーの講演会。要旨は以下の通り（参考のために転載いたします、問題がある場合はご連絡ください）。

In seeking a foundation for mathematics, one may be looking for a single, unified set of principles―perhaps unified by their jointly constituting an acceptable axiomatization of some concept or concepts plausibly taken as fundamental―from which all, or at least a very large part of, mathematics can be derived. In this sense, some version of set theory is plausibly taken as a foundational. But one may also be interested in an epistemological foundation―roughly, an account which explains how we can know standard mathematical theories to be true, or at least justifiably believe them. If fundamental mathematical theories such as arithmetic and analysis are taken at face value, any attempt to provide such a foundation must confront the problem of mathematical objects―the problem of explaining how a belief in the existence of an infinity of natural numbers, an uncountable infinity of real numbers, etc., is to be justified. Of course, these theories may be derived within a suitable theory of sets, but then we simply replace the problem of justifying belief in numbers of various kinds with the problem―unlikely to be easier―of justifying belief in the existence of the universe of set theory. In this talk I will try to explore and defend the idea that a belief in at least some mathematical objects may be easier to justify if one thinks of them as abstracted from properties.

詳しい内容は、3/30付けの記事で紹介します。
あまり関係がないが、懇親会の際、なぜか席がHale教授とPriest教授の間でした。