TY - JOUR
N2 - The problem of the existence of mathematical entities is the subject of lively discussions. Realists defend the independence and autonomy of mathematical objects, while antirealists 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 K. Gödel’s and W.V. 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 intuition in Ingarden’s perspective (indicating 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.
L1 - http://journals.pan.pl/Content/118074/PDF/2020-04-PFIL-15-Skowron.pdf
L2 - http://journals.pan.pl/Content/118074
PY - 2020
IS - No 4
EP - 223-248
KW - eidetic intuition
KW - K. Gödel
KW - ideal qualities
KW - ideas
KW - R. Ingarden
KW - mathematical intuition
A1 - Skowron, Bartłomiej
A1 - Wójtowicz, Krzysztof
PB - Komitet Nauk Filozoficznych PAN
PB - Wydział Filozofii Uniwersytetu Warszawskiego
SP - 223-248
T1 - Realism in the philosophy of mathematics: Gödel and Ingarden
DA - 2021.02.25
UR - http://journals.pan.pl/dlibra/publication/edition/118074
DOI - 10.24425/pfns.2020.135072
ER -