Wittgenstein and Ramsey on Identity

• Applicant: Dr. Markus Säbel
• Subject Area: Theoretical Philosophy
• Term: from 2014 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 253377321

One of the central logical doctrines of Wittgenstein's Tractatus Logico-philosophicus (1921) is the elimination of the identity sign in favour of the so-called "exclusive interpretation" of names and quantifiers. Under this interpretation, the identity sign is replaced by a symbolic convention, requiring different names to refer to different objects and (roughly) different variables to take different values. In this study I propose to examine two related aspects of this doctrine, one systematic, one historical. The first is the question of the systematic viability of Wittgenstein's proposal, which is only sketched but not worked out in the Tractatus itself. Discussion of several important aspects of the proposal has started only recently, especially in papers by Kai Wehmeier. In particular the question of how to deal with names and so-called "pseudo-propositions" like "a = a" remains open. For a solution of these problems it would be helpful to have an account of a controversy between Wittgenstein and Frank Ramsey concerning the identity relation. Ramsey had endorsed Wittgenstein's proposal in his classic paper "The Foundations of Mathematics" (1925), which attempted to rescue the logicist programme of Principia Mathematica. To this end, however, Ramsey was compelled to define a substitute for the identity relation, based on his notion of "propositional functions in extension". This proposal was criticized sharply by Wittgenstein in a letter written to Ramsey in 1927. Both kept returning to the issue of identity in their writings, Wittgenstein in Philosophical Remarks and Philosophical Grammar, Ramsey in a number of manuscripts only recently published from his Nachlass. Understanding Wittgenstein's and Ramsey's difficult arguments concerning identity, discussion of which has also started only very recently, will facilitate an understanding of Wittgenstein's proposal of an "exclusive" logic (and vice versa). Therefore, a comprehensive study of both the elimination of the identity sign and the Wittgenstein-Ramsey-controversy, based on all relevant documents (some of which are still unpublished) is an urgent desideratum of the literature on Wittgenstein and Ramsey.

• DFG Programme: Research Grants