On three arguments against categorical structuralism

Synthese 170 (1):21 - 31 (2009)
Abstract
Some mathematicians and philosophers contend that set theory plays a foundational role in mathematics. However, the development of category theory during the second half of the twentieth century has encouraged the view that this theory can provide a structuralist alternative to set-theoretical foundations. Against this tendency, criticisms have been made that category theory depends on set-theoretical notions and, because of this, category theory fails to show that set-theoretical foundations are dispensable. The goal of this paper is to show that these criticisms are misguided by arguing that category theory is entirely autonomous from set theory.
Keywords Set theory  Category theory  Foundation of mathematics  Categorical structuralism
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DOI 10.1007/s11229-008-9346-2
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Naturalism in Mathematics.Penelope Maddy - 1997 - Oxford University Press.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Category Theory.Steve Awodey - 2010 - Oxford University Press.

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