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- Title
Hintikka on the Foundations of Mathematics: IF Logic and Uniformity Concepts.
- Authors
Bazzoni, André
- Abstract
The initial goal of the present paper is to reveal a mistake committed by Hintikka in a recent paper on the foundations of mathematics. His claim that independence-friendly logic (IFL) is the real logic of mathematics is supported in that article by an argument relying on uniformity concepts taken from real analysis. I show that the central point of his argument is a simple logical mistake. Second and more generally, I conclude, based on the previous remarks and on another standard fact of IFL, that first-order logic (FOL) can adequately express uniformity concepts in real analysis, whereas IFL (understood as a non-trivial extension of FOL) cannot. This not only radically contradicts Hintikka's particular claim in that article, but also undermines his whole enterprise of founding mathematics on his logic system.
- Subjects
FOUNDATIONS of mathematical analysis; ARGUMENT; UNIFORMITY of nature; FIRST-order logic; REAL analysis (Mathematics)
- Publication
Journal of Philosophical Logic, 2015, Vol 44, Issue 5, p507
- ISSN
0022-3611
- Publication type
Article
- DOI
10.1007/s10992-014-9340-8