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.
CITATION STYLE
Maddy, P. (2019). What Do We Want a Foundation to Do?: Comparing Set-Theoretic, Category-Theoretic, and Univalent Approaches. In Synthese Library (Vol. 407, pp. 293–311). Springer Science and Business Media B.V. https://doi.org/10.1007/978-3-030-15655-8_13
Mendeley helps you to discover research relevant for your work.