Some Philosophical Consequences of Kurt Godel's Work

Abstract

This article presents Godel's defense of platonic realism taking the incompleteness theorem as a starting point. It holds a close parallelism with what we could denominate the failure of the Cartesian program. The Cartesian program failed when it wanted to show the full autonomy of reason and it had to recognize sensorial intuition as another source for objective knowledge of external objects. In the same way, Hilbert's program, as we can deduce from the incompleteness theorems, failed when it tried to show the full autonomy of formalized reason. Thus, the only resource to save the descriptive character of mathematical propositions, in Godel's view, is to postulate the intuition of abstract concepts. Godel's argument, likewise, requires that human mind be not reduced to a mere machine. This latter demand is also parallel to the defense of Cartesian dualism.