Graduate studies at Western
Philosophia Mathematica 20 (1):111-113 (2012)
|Abstract||Linnebo and Pettigrew's critique in this journal of categorical foundations well emphasizes that the particulars of various categorical foundations matter, and that mathematical practice must be a major consideration. But several categorists named by the authors as proposing categorical foundations do not propose foundations, notably Awodey, and the article's description of current textbook practice seems inaccurate. They say that categorical foundations have justificatory autonomy if and only if mathematics can be justified simply by its practice. Do they seriously believe philosophers may be able to justify some currently unpractised mathematics better than current practice justifies itself?|
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
|Through your library||Configure|
Similar books and articles
Colin McLarty (2005). Learning From Questions on Categorical Foundations. Philosophia Mathematica 13 (1):44-60.
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.
S. Awodey (1996). Structure in Mathematics and Logic: A Categorical Perspective. Philosophia Mathematica 4 (3):209-237.
F. William Lawvere (2003). Foundations and Applications: Axiomatization and Education. Bulletin of Symbolic Logic 9 (2):213-224.
Frank Plumpton Ramsey (1960). The Foundations of Mathematics and Other Logical Essays. Paterson, N.J.,Littlefield, Adams.
Anthony Birch (2007). Waismann's Critique of Wittgenstein. Analysis and Metaphysics 6 (2007):263-272.
Jean-Pierre Marquis (2012). Categorical Foundations of Mathematics. The Review of Symbolic Logic.
Jean Paul Van Bendegem (1989). Foundations of Mathematics or Mathematical Practice: Is One Forced to Choose? Philosophica 43.
Kazem Sadegh-Zadeh (1982). Foundations of Clinical Praxiology Part II: Categorical and Conjectural Diagnoses. Theoretical Medicine and Bioethics 3 (1):101-114.
Colin McLarty (2008). Review of S. Duffy, Virtual Mathematics: The Logic of Difference. [REVIEW] Australasian Journal of Philosophy 86 (2):332-336.
Ian J. Dove (2009). Towards a Theory of Mathematical Argument. Foundations of Science 14 (1-2):136-152.
Robert Schroer (2010). Is There More Than One Categorical Property? Philosophical Quarterly 60 (241):831-850.
Added to index2012-01-14
Total downloads35 ( #39,349 of 740,298 )
Recent downloads (6 months)2 ( #37,455 of 740,298 )
How can I increase my downloads?