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    Mathematical structuralism, modal nominalism, and the coherence principle

    Date
    2015-10
    Author
    Schwartz, James S.J.
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    Citation
    James S.J. Schwartz Mathematical Structuralism, Modal Nominalism, and the Coherence Principle Philosophia Mathematica (2015) 23 (3): 367-385
    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 (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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    URI
    http://dx.doi.org/10.1093/philmat/nkv013
    http://hdl.handle.net/10057/11583
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