A matemática das Philosophische Bemerkungen: Wittgenstein no contexto da Grundlagenkrise

Abstract

This thesis provides a reading and interpretation of Wittgenstein’s writings on mathematics at the beginning of his “middle period” (more precisely, at the “mathematical chapters” of Philosophische Bemerkungen), placing these writings in the context of two crises. The first, internal to his thought, consists of inconsistencies regarding what the Tractatus prescribed as the result of the application of logic and the effective logical analysis of certain domains of reality, which characterized, in Wittgenstein’s view, a crisis in the foundations of logic. On the other hand, controversies about the foundations of mathematics were intensified throughout the 1920s, and debates between three schools who attempted to impose their way not only of conceiving mathematics, but also of doing it, became increasingly frequent. This crisis, also called Grundlagenkrise der Mathematik, is an important historical and conceptual background for these early writings immediately after Wittgenstein’s return to philosophy in 1929. If in the Tractatus Wittgenstein had positioned himself only with regard to Frege’s and Russell’s logicism, in these writtings he tries in his own way to contrast his thought with the prevailing trends of his time: the intuicionism of Brouwer and Weyl, Hilbert’s formalism and, finally, Ramsey’s renewed logicism. This thesis develops, in its concluding Chapter, a reflection on Wittgenstein’s posture with respect to these three classical schools and with respect to the problems faced by them.