"Cała matematyka to właściwie geometria". Poglądy Gottloba Fregego na podstawy matematyki po upadku logicyzmu

Hybris. Internetowy Magazyn Filozoficzny 44:1 - 20 (2019)
  Copy   BIBTEX


Gottlob Frege abandoned his logicist program after Bertrand Russell had discovered that some assumptions of Frege’s system lead to contradiction (so called Russell’s paradox). Nevertheless, he proposed a new attempt for the foundations of mathematics in two last years of his life. According to this new program, the whole of mathematics is based on the geometrical source of knowledge. By the geometrical source of cognition Frege meant intuition which is the source of an infinite number of objects in arithmetic. In this article, I describe this final attempt of Frege to provide the foundations of mathematics. Furthermore, I compare Frege’s views of intuition from The Foundations of Arithmetic (and his later views) with the Kantian conception of pure intuition as the source of geometrical axioms. In the conclusion of the essay, I examine some implications for the debate between Hans Sluga and Michael Dummett concerning the realistic and idealistic interpretations of Frege’s philosophy.

Author's Profile

Krystian Bogucki
Polish Academy of Sciences


Added to PP

41 (#69,095)

6 months
11 (#61,725)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?