On three arguments against categorical structuralism |
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Authors: | Makmiller Pedroso |
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Affiliation: | (1) Department of Philosophy, University of Calgary, 1231 Social Sciences Calgary, Alberta, Canada, T2N 1N4 |
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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. |
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Keywords: | Set theory Category theory Foundation of mathematics Categorical structuralism |
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