Bulletin of Symbolic Logic

Second-Order Logic and Foundations of Mathematics

Jouko Vaananen

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Abstract

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.

Article information

Source
Bull. Symbolic Logic, Volume 7, Number 4 (2001), 504-520.

Dates
First available in Project Euclid: 20 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1182353825

Mathematical Reviews number (MathSciNet)
MR1867954

Zentralblatt MATH identifier
1002.03013

JSTOR
links.jstor.org

Citation

Vaananen, Jouko. Second-Order Logic and Foundations of Mathematics. Bull. Symbolic Logic 7 (2001), no. 4, 504--520. https://projecteuclid.org/euclid.bsl/1182353825


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