Anti-Realist Classical Logic and Realist Mathematics

Abstract

I sketch an application of a semantically anti-realist understanding of the classical sequent calculus to the topic of mathematics. The result is a semantically anti-realist defence of a kind of mathematical realism. In the paper, I begin the development of the view and compare it to orthodox positions in the philosophy of mathematics

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Greg Restall
University of Melbourne

Citations of this work

First Order Expressivist Logic.John Cantwell - 2013 - Erkenntnis 78 (6):1381-1403.
Dummett on abstract objects.George Duke - 2012 - New York: Palgrave-Macmillan.

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References found in this work

What is logic?Ian Hacking - 1979 - Journal of Philosophy 76 (6):285-319.
Multiple Conclusions.Greg Restall - 2005 - In Petr Hájek, Luis Valdés-Villanueva & Dag Westerståhl (eds.), Logic, Methodology and Philosophy of Science. College Publications.
Proofnets for S5: sequents and circuits for modal logic.Greg Restall - 2007 - In C. Dimitracopoulos, L. Newelski & D. Normann (eds.), Logic Colloquium 2005. Cambridge: Cambridge University Press. pp. 151-172.
Science Without Numbers: A Defence of Nominalism.Michael Lockwood - 1982 - Philosophical Quarterly 32 (128):281-283.
Just what is full-blooded platonism?Greg Restall - 2003 - Philosophia Mathematica 11 (1):82--91.

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