Putting Davidson’s Semantics to Work to Solve Frege’s Paradox on Concept and Object

In T. Achourioti, H. Galinon, J. Martínez Fernández & K. Fujimoto (eds.), Unifying the Philosophy of Truth. Dordrecht: Imprint: Springer (2015)
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Abstract

What Frege’s paradox on concept and object (FP) consists in and the manner in which Frege coped with it (the ladder strategy) are briefly reviewed (§ 1). An idea for solving FP inspired by Husserl’s semantics is presented; it results in failure, for it leads to a version of Russell’s paradox, the usual solution of which implies something like a resurgence of FP (§ 2). A generalized version of Frege’s paradox (GFP) and an idea for solving it inspired by Davidson’s semantics are presented; three theorems about recursive definability of truth are put forward and used to determine whether this idea can be successfully applied to certain putative forms of the Language of Science (§ 3). Proofs of these three theorems, in particular of the third, which answers a question that does not seem to have drawn logicians’ attention, are then given (§ 4). Finally, it turns out that there is a tension between the proposed solution of GFP and the idea of Language of Science assumed so far in this paper, and a way of solving it is proposed (§ 5).

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Philippe De Rouilhan
Centre National de la Recherche Scientifique

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