Theoria 77 (4):292-311 (2011)

Authors
Robert Trueman
University of York
Abstract
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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DOI 10.1111/j.1755-2567.2011.01105.x
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References found in this work BETA

Philosophical Remarks.Ludwig Wittgenstein - 1975 - Oxford, England: University of Chicago Press.
Principia Mathematica.A. N. Whitehead - 1926 - Mind 35 (137):130.

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Citations of this work BETA

Frank Ramsey and the Realistic Spirit.Steven Methven - 2014 - London and Basingstoke: Palgrave Macmillan.
A Dilemma for Neo-Fregeanism.Robert Trueman - 2014 - Philosophia Mathematica 22 (3):361-379.
Exclusion Problems and the Cardinality of Logical Space.Tim Button - 2017 - Journal of Philosophical Logic 46 (6):611-623.

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