大家

その分野の一線で活躍する大家がふとしたきっかけで書くインフォーマルな論文は、たいがい読んでいて面白い。

• Saharon Shelah, "The Future of Set Theory", in H. Judah (ed.), Set Theory of the Reals, Bar-Ilan University, 1993, pp. 1-12.

を読む。印象的な箇所を抜き出しておこう。

My feeling, in an overstated form, is that beauty is for eternity, while philosophical value follows fashion. (p.2)

My feeling is that ZFC exhausts our intuition except for things like consisteny statements, so a proof means a proof in ZFC. (p.3)

Intuition tells me that the power set and replacement axioms hold, as well as choice (except in artificial universes), whereas it does not tell me much on the existstence of inaccessibles. (p.5)

I am in my heart a card-carrying Platonist seeing before my eyes the universe of sets, but I cannot discard the independence phenomena. (p.6)