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Philosophia Mathematica 2000 8(3):302-309; doi:10.1093/philmat/8.3.302
© 2000 by Oxford University Press
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© Oxford University Press

Supervenience and Necessity: A Response to Balaguer{dagger}

J. M. DIETERLE*

*Department of History and Philosophy, Eastern Michigan Unversity, Ypsilanti, Michigan 48197 U. S. A. his_dieterle@online.emich.edu

In Platonism and Anti-Platonism in Mathematics, Mark Balaguer attempts to show that there is (1) one and only one defensible version of platonism, (2) one and only one defensible version of anti-platonism, and (3) no fact of the matter as to which is true. His arguments depend essentially on the notion of supervenience, yet he rejects metaphysical necessity. I argue that he cannot use logical, conceptual, or nomological necessity to explicate supervenience. Balaguer must either give up the arguments that make use of supervenience or accept metaphysical necessity. I also consider and reject a possible response to my arguments.


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