Double vision: two questions about the neo-Fregean program
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.
KeywordsNeo-Fregean Neologicism Hume’s principle Implicit definition Singular term
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- Boolos G. (1987). The consistency of Frege’s Foundations of arithmetic. In: Thomson J.J. (eds) On being and saying: Essays in honor of Richard Cartwright. Cambridge, MIT Press, pp. 3–20Google Scholar
- Chierchia G., McConnell-Ginet S. (1996). Meaning and grammar. Cambridge, MIT Press, pp. 425–430.Google Scholar
- Frege G. (1964). The basic laws of arithmetic, trans. Montgomery Furth. Berkeley, University of California PressGoogle Scholar
- Heck, R. (2000). Cardinality, counting, and equinumerosity. Notre Dame Journal of Formal Logic, 41.Google Scholar
- King J. (2001). Complex demonstratives: A quantificational account. Cambridge, MIT Press, pp. 10–11Google Scholar
- Kripke S. (1980). Naming and necessity. Cambridge, Harvard University PressGoogle Scholar
- Neale S. (1990). Descriptions. Cambridge, MIT PressGoogle Scholar
- Quine W.V. (1969). Ontological relativity and other essays. New York, Columbia University PressGoogle Scholar
- Shapiro S., Weir A. (2000). ‘Neo-Logicist’ logic is not epistemically innocent. Philosophia Mathematica 3, 160–189Google Scholar
- Wright C. (1983). Frege’s Conception of numbers as objects. Aberdeen, Aberdeen University PressGoogle Scholar