Frege: Identity

Frege claims that sentences of the form ‘A’ are equivalent to sentences of the form ‘it is true that A’ (The Equivalence Thesis). Frege also says that there are fictional names that fail to refer, and that sentences featuring fictional names fail to refer as a result. The thoughts such sentences express, Frege says, are also fictional, and neither true nor false. Michael Dummett argues that these claims are inconsistent. But his argument requires clarification, since there are two ways The (...) Equivalence Thesis has been formulated, according as the thesis equates the senses or the referents of the relevant sentences. -/- I have two aims in this paper. The first is to demonstrate that a sameness of sense thesis is inconsistent with Frege’s other theses. The second is to argue that a sameness of reference thesis is consistent with them. Thus, all else being equal, Frege ought to endorse a sameness of reference, rather than a sameness of sense thesis. (shrink)

The aim of this paper is to present a constructive solution to Frege's puzzle (largely limited to the mathematical context) based on type theory. Two ways in which an equality statement may be said to have cognitive significance are distinguished. One concerns the mode of presentation of the equality, the other its mode of proof. Frege's distinction between sense and reference, which emphasizes the former aspect, cannot adequately explain the cognitive significance of equality statements unless a clear identity criterion for (...) senses is provided. It is argued that providing a solution based on proofs is more satisfactory from the standpoint of constructive semantics. (shrink)

Many philosophers have argued or taken for granted that Frege's puzzle has little or nothing to do with identity statements. I show that this is wrong, arguing that the puzzle can only be motivated relative to a thinker's beliefs about the identity or distinctness of the relevant object. The result is important, as it suggests that the puzzle can be solved, not by a semantic theory of names or referring expressions as such, but simply by a theory of identity statements. (...) To show this, I sketch a framework for developing solutions of this sort. I also consider how this result could be implemented by two influential solutions to Frege's puzzle, Perry's referential-reflexivism and Fine's semantic relationism. (shrink)

The paper argues, as against Thau and Caplan, that the traditional interpretation that Frege abandoned his earlier views about identity and identity--statements is correct.