Is There an Absolute Mathematical Reality?
- Zbigniew Król
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.
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- Trepczyński Marcin Marcin Trepczyński (eds.): Philosophical Approaches to the Foundations of Logic and Mathematics. In Honor of Stanisław Krajewski, Poznan Studies in the Philosophy of the Sciences and the Humanities, vol. 114, 2021, Brill, 310 p., ISBN 978-90-04-44594-9. DOI:10.1163/9789004445956 Opening in a new tab
- DOI:10.1163/9789004445956_4 Opening in a new tab
- https://doi.org/10.1163/9789004445956_4 Opening in a new tab
- (en) English
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- = 75.0, 10-05-2021, MonographChapterAuthor
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