Zermelo s1931g

Abstract

Zermelo published three papers outlining his theory of systems of infinitely long propositions. From 1931 there is 1932a, in four pages, based on Zermelo’s presentation at the September 1931 conference in Bad Elster. From the same year comes 1932b, in two pages, which summarizes 1932a for a general audience. Finally, there is the fuller exposition of 1935. In addition, Zermelo’s Nachlass contains several related documents from the same period. Most interesting among them is handwritten s1931g, whose title is almost identical to that of 1935. One notable feature of s1931g concerns Zermelo’s notion of definiteness. That notion, familiar from 1908b and 1929a, plays no role in 1932a, 1932b, or 1935. In contrast, definiteness arises in s1931g within a context that is almost that of systems of infinitely long propositions. This suggests that definiteness never ceased to figure in Zermelo’s theorizing about mathematical systems.