Bulletin of Symbolic Logic
- Bull. Symbolic Logic
- Volume 7, Number 4 (2001), 504-520.
Second-Order Logic and Foundations of Mathematics
We discuss the differences between first-order set theory and second-order logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows that if second-order logic is understood in its full semantics capable of characterizing categorically central mathematical concepts, it relies entirely on informal reasoning. On the other hand, if it is given a weak semantics, it loses its power in expressing concepts categorically. First-order set theory and second-order logic are not radically different: the latter is a major fragment of the former.
Bull. Symbolic Logic, Volume 7, Number 4 (2001), 504-520.
First available in Project Euclid: 20 June 2007
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Vaananen, Jouko. Second-Order Logic and Foundations of Mathematics. Bull. Symbolic Logic 7 (2001), no. 4, 504--520. https://projecteuclid.org/euclid.bsl/1182353825