# 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} }

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… Expand

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