Is There an Absolute Mathematical Reality?

Authors:

• Zbigniew Król

Abstract

This paper analyses mathematical Platonism in a dualistic version, reconstructible from the Gibbs lecture of Kurt Gödel, that assumes the existence of an absolute, ideal mathematical reality together with its basic object, the absolute set, construed as expressible in a single consistent theory – namely, that of proper mathematics. It argues that this position is contradicted by phenomenological data, current mathematical knowledge, and mathematical practice. Several plausible versions of phenomenological Platonism are given as alternatives to Gödel’s extreme position. From a pragmatic and phenomenological point of view, embracing the notion of absolute mathematical reality obliges one to accept a version of mathematics that is impoverished, both conceptually and in respect of its content.