Realizm w filozofii matematyki: Gödel i Ingarden

The problem of the existence of mathematical entities is the subject of many lively discussions. Realists defend the independence and autonomy of mathematical objects, while anti-realists point to their dependence and conventionality. The problem of the existence of mathematical objects is also strongly linked to the problem of mathematical cognition: do we recognize mathematical truths in special acts of intuition, as some realists claim, or do we create mathematical knowledge only by building appropriate formal systems – as some anti‑realists imagine. In this article we present the Gödel’s and Quine’s realistic stances and comment on them from the perspective of Roman Ingarden’s phenomenology. We point out the role that Gödel attributed to his mathematical intuition, and then we present the process of eidetic viewing in Ingarden’s perspective (indicating the Gödel’s and Ingarden’s common points of view). We also argue that Ingarden’s rich ontology could contribute in a significant way to the debates currently taking place in the mainstream philosophy of mathematics.