PL EN


2019 | 44 (1) |
Article title

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

Content
Title variants
PL
‘Mathematics in its entirety is really geometry’. Gottlob Frege’s view of the foundations of mathematics after the fall of logicist program
Languages of publication
Abstracts
EN
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.
Year
Volume
Physical description
Dates
published
2018
References
Document Type
Publication order reference
Identifiers
URI
http://hdl.handle.net/11089/31166
YADDA identifier
bwmeta1.element.hdl_11089_31166
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