Starting with a review of the kinds of questions a foundation for mathematics should address, this paper provides a critique of set theoretical foundations, a proposal that multiple interconnected categorical foundations would be an improvement, and a way of recovering set theory within a categorical approach.
@article{PHSC_2005__9_2_5_0, author = {Neff Stout, Lawrence}, title = {Upsetting the foundations for mathematics}, journal = {Philosophia Scientiae}, pages = {5--21}, publisher = {\'Editions Kim\'e}, volume = {9}, number = {2}, year = {2005}, language = {en}, url = {http://archive.numdam.org/item/PHSC_2005__9_2_5_0/} }
Neff Stout, Lawrence. Upsetting the foundations for mathematics. Philosophia Scientiae, Aperçus philosophiques en logique et en mathématiques, Tome 9 (2005) no. 2, pp. 5-21. http://archive.numdam.org/item/PHSC_2005__9_2_5_0/
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