David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 170 (1):21 - 31 (2009)
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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References found in this work BETA
Penelope Maddy (1997). Naturalism in Mathematics. Oxford University Press.
Paul Benacerraf (1965). What Numbers Could Not Be. Philosophical Review 74 (1):47-73.
Steve Awodey (2010). Category Theory. OUP Oxford.
Steve Awodey (2004). An Answer to Hellman's Question: ‘Does Category Theory Provide a Framework for Mathematical Structuralism?’. Philosophia Mathematica 12 (1):54-64.
Stewart Shapiro (2005). Categories, Structures, and the Frege-Hilbert Controversy: The Status of Meta-Mathematics. Philosophia Mathematica 13 (1):61-77.
Citations of this work BETA
Jonathan Bain (2013). Category-Theoretic Structure and Radical Ontic Structural Realism. Synthese 190 (9):1621-1635.
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