‘Neo-logicist‘ logic is not epistemically innocent

Philosophia Mathematica 8 (2):160--189 (2000)
The neo-logicist argues tliat standard mathematics can be derived by purely logical means from abstraction principles—such as Hume's Principle— which are held to lie 'epistcmically innocent'. We show that the second-order axiom of comprehension applied to non-instantiated properties and the standard first-order existential instantiation and universal elimination principles are essential for the derivation of key results, specifically a theorem of infinity, but have not been shown to be epistemically innocent. We conclude that the epistemic innocence of mathematics has not been established by the neo-logicist.
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    Kit Fine (2005). Replies. [REVIEW] Philosophical Studies 122 (3):367 - 395.

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