Philosophical Foundation of the «transfinite» in G. Cantor and the Question of Infinity

Abstract

The «transfinite» of Cantor is an important mathematical as well as philosophical contribution to the question of infinity. Beyond the relevance that the transfinite of Cantor has in the field of mathematics, here is an attempt to analyse the philosophical dimension that Cantor himself gives to his «transfinite», relating the same with the historical-philosophical debates about the possibility and reality of the traditionally called «actual» infinity. In this sense, on the base of the thematic writings and correspondence of Cantor is shown his interest to defend not only the possibility but also the reality of the «transfinite» or of the «actual» infinity both in the cognitive dimension as in the material reality.