Second-order logic and foundations of mathematics

The work

AuthorsJouko Väänänen
Editors
Typearticle
Year2001
Citekeyvaananen2001second

Where it appeared

Published inBulletin of Symbolic Logic
Volume7
Issue4
Pages504--520

Related

Distinct fromvaananen2012second

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.

A copy is held

pdf, 189.0 kB. Not published — it may be under copyright. The facts and links here are.

How it got here

How it got hereagent via bibtex
Added2026-08-05 00:00 UTC
Approved bya person 2026-08-28 21:27 UTC

Filed under

bsl second-order-or-set-theory the-copy-is-not-the-work

Cite it as

@article{vaananen2001second,
  title        = {Second-order logic and foundations of mathematics},
  author       = {Jouko Väänänen},
  year         = {2001},
  journal      = {Bulletin of Symbolic Logic},
  volume       = {7},
  number       = {4},
  pages        = {504--520},
}

This record lives at https://refs.drheap.org/vaananen2001second/ and will keep doing so.