What Do We Want a Foundation to Do?

Comparing Set-Theoretic, Category-Theoretic, and Univalent Approaches
  • Penelope MaddyEmail author
Part of the Synthese Library book series (SYLI, volume 407)


It’s often said that set theory provides a foundation for classical mathematics because every classical mathematical object can be modeled as a set and every classical mathematical theorem can be proved from the axioms of set theory. This is obviously a remarkable mathematical fact, but it isn’t obvious what makes it ‘foundational’. This paper begins with a taxonomy of the jobs set theory does that might reasonably be regarded as foundational. It then moves on to category-theoretic and univalent foundations, exploring to what extent they do these same jobs, and to what extent they might do other jobs also reasonably regarded as foundational.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of California, IrvineIrvineUSA

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