Graduate studies at Western
Manuscrito 31 (1) (2008)
|Abstract||Current versions of nominalism in the philosophy of mathematics face a significant problem to understand mathematical knowledge. They are unable to characterize mathematical knowledge as knowledge of the objects mathematical theories are taken to be about. Oswaldo Chateaubriand’s insightful reformulation of Platonism (Chateaubriand 2005) avoids this problem by advancing a broader conception of knowledge as justified truth beyond a reasonable doubt, and by introducing a suitable characterization of logical form in which the relevant mathematical facts play an important role in the truth of the corresponding mathematical propositions. In this paper, I contrast Chateaubriand’s proposal with an agnostic form of nominalism that is able to accommodate mathematical knowledge without the commitment to mathematical facts.|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Jean-Pierre Marquis (1999). Mathematical Engineering and Mathematical Change. International Studies in the Philosophy of Science 13 (3):245 – 259.
Michael Potter (2007). What is the Problem of Mathematical Knowledge? In Michael Potter, Mary Leng & Alexander Paseau (eds.), Mathematical Knowledge.
Audrey Yap (2009). Logical Structuralism and Benacerraf's Problem. Synthese 171 (1):157 - 173.
Edwin Coleman (2009). The Surveyability of Long Proofs. Foundations of Science 14 (1-2):27-43.
Mary Leng (2010). Mathematics and Reality. OUP Oxford.
Anthony Peressini (1999). Confirming Mathematical Theories: An Ontologically Agnostic Stance. Synthese 118 (2):257-277.
Charles Sayward (2005). A Wittgensteinian Philosophy of Mathematics. Logic and Logical Philosophy 15 (2):55-69.
Mary Leng, Alexander Paseau & Michael D. Potter (eds.) (2007). Mathematical Knowledge. Oxford University Press.
Janet Folina (1994). Poincaré's Conception of the Objectivity of Mathematics. Philosophia Mathematica 2 (3):202-227.
Added to index2009-02-09
Total downloads111 ( #6,385 of 740,467 )
Recent downloads (6 months)1 ( #61,957 of 740,467 )
How can I increase my downloads?