Frege's Theorem in Plural Logic


We note that a plural version of logicism about arithmetic is suggested by the standard reading of Hume's Principle in terms of `the number of Fs/Gs'. We lay out the resources needed to prove a version of Frege's principle in plural, rather than second-order, logic. We sketch a proof of the theorem and comment philosophically on the result, which sits well with a metaphysics of natural numbers as plural properties.



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Simon Hewitt
University of Leeds

Citations of this work

Tuples all the Way Down?Simon Thomas Hewitt - 2018 - Thought: A Journal of Philosophy 7 (3):161-169.

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References found in this work

New work for a theory of universals.David K. Lewis - 1983 - Australasian Journal of Philosophy 61 (4):343-377.
New Work For a Theory of Universals.David Lewis - 1997 - In David Hugh Mellor & Alex Oliver (eds.), Properties. New York: Oxford University Press.
Frege's conception of numbers as objects.Crispin Wright - 1983 - [Aberdeen]: Aberdeen University Press.
Frege meets dedekind: A neologicist treatment of real analysis.Stewart Shapiro - 2000 - Notre Dame Journal of Formal Logic 41 (4):335--364.

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