David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Theoria 77 (4):292-311 (2011)
In his “The Foundations of Mathematics”, Ramsey attempted to marry the Tractarian idea that all logical truths are tautologies and vice versa, and the logicism of the Principia. In order to complete his project, Ramsey was forced to introduce propositional functions in extension (PFEs): given Ramsey's definitions of 1 and 2, without PFEs even the quantifier-free arithmetical truth that 1 ≠ 2 is not a tautology. However, a number of commentators have argued that the notion of PFEs is incoherent. This response was first given by Wittgenstein but has been best developed by Sullivan. While I agree with Wittgenstein and Sullivan's common conclusion, I believe that even the most compelling of Sullivan's arguments is importantly mistaken and that Wittgenstein's remarks are too opaque to be left as the end of the matter. In this article I uncover the fault in Sullivan's argument and present an alternative criticism of PFEs which is Wittgensteinian in spirit without being too mystifying.
|Keywords||Tractarian logicism Ramsey propositional functions in extension propositional functions Wittgenstein propositions Sullivan|
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References found in this work BETA
Ludwig Wittgenstein (1922). Tractatus Logico-Philosophicus. Dover Publications.
Ludwig Wittgenstein (1975). Philosophical Remarks. University of Chicago Press.
A. N. Whitehead (1926). Principia Mathematica. Mind 35 (137):130.
Frank Plumpton Ramsey & Maria Carla Galavotti (1994). Notes on Philosophy, Probability and Mathematics. Philosophical Review 103 (4):713-715.
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