Metaphysical explanation and the philosophy of mathematics: Reflections on Jerrold Katz's realistic rationalism

Philosophia Mathematica 9 (2):154-183 (2001)
Mathematical practice prompts theories about aprioricity, necessity, abstracta, and non-causal epistemic connections. But it is not clear what to count as the data: mathematical necessity or the appearance of mathematical necessity, abstractness or apparent abstractness, a prioricity or apparent aprioricity. Nor is it clear whether traditional metaphysical theories provide explanation or idle redescription. This paper suggests that abstract objects, rather than doing explanatory work, provide codifications of the data to be explained. It also suggests that traditional rivals—conceptualism, nominalism, realism—engage different explanatory projects, and thus are not rivals at all.
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