Mathematical Structuralism, Modal Nominalism, and the Coherence Principle

Philosophia Mathematica 23 (3):367-385 (2015)
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Abstract

According to Stewart Shapiro's coherence principle, structures exist whenever they can be coherently described. I argue that Shapiro's attempts to justify this principle are circular, as he relies on criticisms of modal nominalism which presuppose the coherence principle. I argue further that when the coherence principle is not presupposed, his reasoning more strongly supports modal nominalism than ante rem structuralism

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J.S. Johnson-Schwartz
Wichita State University

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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.
Philosophy of mathematics: structure and ontology.Stewart Shapiro - 1997 - New York: Oxford University Press.
Mathematics and Scientific Representation.Christopher Pincock - 2012 - Oxford and New York: Oxford University Press USA.
The Pure Logic of Ground.Kit Fine - 2012 - Review of Symbolic Logic 5 (1):1-25.

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