Supervenience and necessity: A response to Balaguer

Philosophia Mathematica 8 (3):302-309 (2000)
In Platonism and Anti-Platonism in Mathematics, Mark Balaguer attempts to show that there is one and only one defensible version of platonism, one and only one defensible version of anti-platonism, and 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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DOI 10.1093/philmat/8.3.302
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