If There Were No Numbers, What Would You Think?

Thought: A Journal of Philosophy 3 (4):283-287 (2014)
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Abstract
Hartry Field has argued that mathematical realism is epistemologically problematic, because the realist is unable to explain the supposed reliability of our mathematical beliefs. In some of his discussions of this point, Field backs up his argument by saying that our purely mathematical beliefs do not ‘counterfactually depend on the facts’. I argue that counterfactual dependence is irrelevant in this context; it does nothing to bolster Field's argument
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