Second-Order Logic and Foundations of Mathematics

@article{Vnnen2001SecondOrderLA,
  title={Second-Order Logic and Foundations of Mathematics},
  author={Jouko A. V{\"a}{\"a}n{\"a}nen},
  journal={Bulletin of Symbolic Logic},
  year={2001},
  volume={7},
  pages={504 - 520}
}
  • J. Väänänen
  • Published 1 December 2001
  • Philosophy
  • Bulletin of Symbolic Logic
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… 

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