Mathematical structuralism, modal nominalism, and the coherence principle
Schwartz, James S.J.
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James S.J. Schwartz Mathematical Structuralism, Modal Nominalism, and the Coherence Principle Philosophia Mathematica (2015) 23 (3): 367-385
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 (along with his position, ante rem structuralism) 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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