Abstract

This paper has two objectives. The first is to present an interpretation of Gödel's concept of mathematical intuition and defend it against other interpretations like Charles Parsons'. The second objective is to show the necessity of realism for Gödel's mathematical intuition. The first section seeks to show what mathematical intuition is and how it works, focusing on Gödel's works and unpublished texts. Consequently, from this section, I will show that, for Gödel, the concept of mathematical intuition emerges and develops parallel to his platonistic ontological commitment. Gödel's Platonism and mathematical intuition involve not only an ontological dimension but also an epistemological dimension. In the second section, I will discuss Parsons' 1995 paper "Platonism and mathematical intuition in Kurt Gödel's thought", in which he argues for a separation between mathematical intuition and Gödel's Platonism. What I will show is that this separation is not possible in Gödel since according to the recent publications of his philosophical notebooks and works prior to 1964, mathematical intuition was already implicit and, contrary to what Parsons argues, it is not something that arises before and independently of Gödel's realism.