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On three arguments against categorical structuralism

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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.

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Correspondence to Makmiller Pedroso.

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Pedroso, M. On three arguments against categorical structuralism. Synthese 170, 21–31 (2009).

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