David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
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.
Peter M. Sullivan (1992). The Functional Model of Sentential Complexity. Journal of Philosophical Logic 21 (1):91 - 108.
Citations of this work BETA
No citations found.
Similar books and articles
George Bealer (1989). On the Identification of Properties and Propositional Functions. Linguistics and Philosophy 12 (1):1 - 14.
Peter M. Sullivan (2005). What is Squiggle? Ramsey on Wittgenstein's Theory of Judgement. In Hallvard Lillehammer & D. H. Mellor (eds.), Ramsey's Legacy. Oxford University Press 53--71.
Richard L. Cartwright (2005). Remarks on Propositional Functions. Mind 114 (456):915-927.
William Demopoulos (2013). Logicism and its Philosophical Legacy. Cambridge University Press.
Crispin Wright (1980). Wittgenstein on the Foundations of Mathematics. Harvard University Press.
Kevin C. Klement (2004). Putting Form Before Function: Logical Grammar in Frege, Russell, and Wittgenstein. Philosophers' Imprint 4 (2):1-47.
Gert Jan Lokhorst (1988). Ontology, Semantics and Philosophy of Mind in Wittgenstein's Tractatus: A Formal Reconstruction. [REVIEW] Erkenntnis 29 (1):35 - 75.
Ernst Zimmermann (2002). A Predicate Logical Extension of a Subintuitionistic Propositional Logic. Studia Logica 72 (3):401-410.
William Demopoulos (2003). On the Rational Reconstruction of Our Theoretical Knowledge. British Journal for the Philosophy of Science 54 (3):371-403.
Alex Grzankowski (2012). Not All Attitudes Are Propositional. European Journal of Philosophy (3):374-391.
Alfred North Whitehead & Bertrand Russell (1962). Principia Mathematica, to *56. Cambridge University Press.
José Antonio Lopez Cerezo (1994). La naturaleza de la ciencia en el Tractatus. Theoria 9 (1):75-88.
Daesuk Han (2011). Wittgenstein and the Real Numbers. History and Philosophy of Logic 31 (3):219-245.
Peter Roeper & Hugues Leblanc (1999). Absolute Probability Functions for Intuitionistic Propositional Logic. Journal of Philosophical Logic 28 (3):223-234.
Added to index2011-06-30
Total downloads56 ( #76,384 of 1,906,955 )
Recent downloads (6 months)17 ( #38,460 of 1,906,955 )
How can I increase my downloads?