On Certain Aspects of Mathematical Objectivity

Abstract

Physics, biology, chemistry, astronomy, psychology, sociology, history, and similar sciences that deal with empirical facts can describe the reality they investigate in varying levels of detail and provide specific statements and results about it. However, the question of describing mathematical objectivity appears to be more challenging than describing the objectivity addressed in the aforementioned sciences. This difficulty likely stems from the immaterial nature of mathematical objects, as well as their physical and temporal indeterminacy.
In this text, we will revisit one of Cantor’s attempts to describe mathematical reality, select a few comments of that description, and analyse them. Additionally, we will compare Cantor’s approach with some contemporary representations of mathematical Platonism that incorporate significant empiricist elements. Finally, we will propose what we believe to be a promising approach to understanding mathematical reality, one that we think offers a promising support for Platonism in mathematics.