Zermelo 1932b

pp. 550-555

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

Abstract

What is a "mathematical proposition", a "mathematical proof", a "mathematical theory", a "mathematical discipline"? A general theory of propositional systems as it underlies all mathematical disciplines is the subject of the following considerations outlined briefly here. A mathematical "proposition" makes sense and has a meaning only within a mathematical system, a theory or a (comprehensive) discipline as, e.g., "Euclidean geometry" or the "arithmetic of real numbers". But what are the characteristic features, what are the general basic laws of logic common to all "mathematical systems"?