A Dilemma for Neo-Fregeanism

Philosophia Mathematica 22 (3):361-379 (2014)

Robert Trueman
University of York
Neo-Fregeans need their stipulation of Hume's Principle — $NxFx=NxGx \leftrightarrow \exists R (Fx \,1\hbox {-}1_R\, Gx)$ — to do two things. First, it must implicitly define the term-forming operator ‘Nx…x…’, and second it must guarantee that Hume's Principle as a whole is true. I distinguish two senses in which the neo-Fregeans might ‘stipulate’ Hume's Principle, and argue that while one sort of stipulation fixes a meaning for ‘Nx…x…’ and the other guarantees the truth of Hume's Principle, neither does both
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DOI 10.1093/philmat/nku012
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Speaking with Shadows: A Study of Neo-Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.

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Citations of this work BETA

Abstractionism and Mathematical Singular Reference.Bahram Assadian - forthcoming - Philosophia Mathematica:nkz003.
A Vindication of Logicism.Peter Roeper - 2016 - Philosophia Mathematica 24 (3):360-378.

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