On Gödel’s “Platonism”

Abstract

This paper concerns Gödel’s conception of the reality of mathematical objects. I distinguish three claims (i), (ii), (iii).(i) Mathematics describes a non-sensual reality, which exists independently both of the acts and [of] the dispositions of the human mind.(ii) Mathematical theories are not created by the ego out of nothing.(iii) Mathematics (or something in mathematics) is independent of the specific properties of the human being.I argue that Gödel cannot hold such the strong Platonism of (i) after 1954. His position is better described by the two weaker claims, (ii) and (iii). Claims (ii) and (iii) offer two different meanings for the idea of an ‘objectivity’ of mathematics, and philosophers can very well accept one without the other.