Zermelo s1921

pp. 302-307

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

Abstract

The question of greatest urgency confronting nineteenth- and early twentieth- century mathematicians was arguably that of the status of the infinite within mathematics. Zermelo's s1921, comprising five multi-part philosophical "theses", should be understood in that spirit. Despite its brevity, s1921 is somewhat repetitive. It seems that Zermelo had no intention of publishing it even as part of some longer piece. Instead, s1921 likely functioned as a personal manifesto; clearly, Zermelo sees himself as breaking new ground here. If conceived in July 1921, in fact, s1921 would contain the earliest intimation of the theory of systems of infinitely long propositions described in 1932a, 1932b, and 1935; but serious questions regarding the dating of s1921 have been raised (see Ebbinghaus 2007b, 205). In any case, talk of theses implies supplementary elaboration, and 1932a, 1932b, and 1935 will provide it.