David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
S. Awodey (1996). Structure in Mathematics and Logic: A Categorical Perspective. Philosophia Mathematica 4 (3):209-237.
Steve Awodey (2004). An Answer to Hellman's Question: ‘Does Category Theory Provide a Framework for Mathematical Structuralism?’. Philosophia Mathematica 12 (1):54-64.
Steve Awodey (2010). Category Theory. OUP Oxford.
J. L. Bell (1986). From Absolute to Local Mathematics. Synthese 69 (3):409 - 426.
Paul Benacerraf (1965). What Numbers Could Not Be. Philosophical Review 74 (1):47-73.
Citations of this work BETA
Jonathan Bain (2013). Category-Theoretic Structure and Radical Ontic Structural Realism. Synthese 190 (9):1621-1635.
Similar books and articles
Elaine Landry (1999). Category Theory: The Language of Mathematics. Philosophy of Science 66 (3):27.
F. A. Muller (2001). Sets, Classes, and Categories. British Journal for the Philosophy of Science 52 (3):539-573.
Geoffrey Hellman (2003). Does Category Theory Provide a Framework for Mathematical Structuralism? Philosophia Mathematica 11 (2):129-157.
Andrei Rodin (2011). Categories Without Structures. Philosophia Mathematica 19 (1):20-46.
Colin McLarty (1990). The Uses and Abuses of the History of Topos Theory. British Journal for the Philosophy of Science 41 (3):351-375.
Andrei Rodin, Toward a Hermeneutic Categorical Mathematics or Why Category Theory Does Not Support Mathematical Structuralism.
Geoffrey Hellman (2006). What is Categorical Structuralism?. In. In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. 151--161.
Øystein Linnebo & Richard Pettigrew (2011). Category Theory as an Autonomous Foundation. Philosophia Mathematica 19 (3):227-254.
M. Kary (2009). (Math, Science, ?). Axiomathes 19 (3):61-86.
Jean-Pierre Marquis (1995). Category Theory and the Foundations of Mathematics: Philosophical Excavations. Synthese 103 (3):421 - 447.
Added to index2009-01-28
Total downloads51 ( #31,425 of 1,101,125 )
Recent downloads (6 months)6 ( #44,290 of 1,101,125 )
How can I increase my downloads?