Zermelo s1931d

pp. 500-501

in: Ernst Zermelo, Set theory, miscellanea / Mengenlehre, varia, Berlin, Springer, 2010

Abstract

Dear Mr. Gödel!I'd like to thank you for your friendly letter. I am able to gain a better understanding from it about what you really want to say than before from your paper and your lecture. Your "finitistic restriction" (as I call it) on the formation of types is thus only meant to apply to the provable propositions of your "PM-system", and not to its propositions in general. At the same time, you allow for new propositions of the system to be freely formed in accordance with Cantor's diagonal procedure. Of course, you then obtain an uncountable system of possible propositions only a countable partial set of which would be "provable", and there would certainly have to exist "undecidable" propositions. That these "undecidable" propositions still become "decidable" in a "higher system" you freely admit.