Handling mathematical objects: representations and context

Synthese 190 (17):3983-3999 (2013)
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Abstract

This article takes as a starting point the current popular anti realist position, Fictionalism, with the intent to compare it with actual mathematical practice. Fictionalism claims that mathematical statements do purport to be about mathematical objects, and that mathematical statements are not true. Considering these claims in the light of mathematical practice leads to questions about how mathematical objects are handled, and how we prove that certain statements hold. Based on a case study on Riemann’s work on complex functions, I propose that mathematicians deal with systems of representations and that truth—or what we can prove—depends on available representations in some context where the problem can be solved

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References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Platonism and anti-Platonism in mathematics.Mark Balaguer - 1998 - New York: Oxford University Press.
A subject with no object: strategies for nominalistic interpretation of mathematics.John P. Burgess & Gideon Rosen - 1997 - New York: Oxford University Press. Edited by Gideon A. Rosen.
Mathematics and Reality.Mary Leng - 2010 - Oxford: Oxford University Press.
Mathematics and reality.Mary Leng - 2010 - Bulletin of Symbolic Logic 17 (2):267-268.

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