Double vision: Two questions about the neo-Fregean program

Synthese 170 (3):443 - 456 (2009)
Abstract
Much of The Reason’s Proper Study is devoted to defending the claim that simply by stipulating an abstraction principle for the “number-of” functor, we can simultaneously fix a meaning for this functor and acquire epistemic entitlement to the stipulated principle. In this paper, I argue that the semantic and epistemological principles Hale and Wright offer in defense of this claim may be too strong for their purposes. For if these principles are correct, it is hard to see why they do not justify platonist strategies that are not in any way “neo-Fregean,” e.g. strategies that treat “the number of Fs” as a Russellian definite description rather than a singular term, or employ axioms that do not have the form of abstraction principles.
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    References found in this work BETA
    Bob Hale (2001). A Response to Potter and Smiley: Abstraction by Recarving. Proceedings of the Aristotelian Society 101 (3):339–358.
    Richard Heck (1997). Finitude and Hume's Principle. Journal of Philosophical Logic 26 (6):589-617.
    Richard Heck (2000). Cardinality, Counting, and Equinumerosity. Notre Dame Journal of Formal Logic 41 (3):187-209.

    View all 12 references

    Citations of this work BETA
    Jonathan Payne (2013). Abstraction Relations Need Not Be Reflexive. Thought: A Journal of Philosophy 2 (2):137-147.
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