Frege on Identity

Frege’s most celebrated paper “On Sense and Reference” begins with a puzzle. The sentences “a=a” and “a=b” superficially strike the reader as being different kinds of claims. Among other things, “a=a” seems to be trivially true, even self-evident. On the other hand, “a=b” is an informative sentence. It is of a kind important to many episodes in the history of science. Deeper reflection, however, reveals that the situation is more complicated. Both sentences express identity or sameness relations. If we think that sameness is a relation between an object and itself, both sentences have the same content. So the puzzle is to explain identity in a way that accounts for the difference between these two sentences. At the beginning of “On Sense and Reference,” as the fictional philosopher McWood notes, Frege suggests two possible accounts of identity. The first possibility is that sameness is a relation between objects. Frege’s second suggestion is that identity sentences express a relation between the names (or signs) of objects. This second suggestion is the view that Frege claims to have endorsed in his earlier book the Begriffsschrift. McWood notes that Frege does not actually tell us which of these models he has chosen. She also notes that the two models have the same truth conditions, so some of the All references and translations are from “On Sense and Nominatum” by Gottlob Frege. Trans. Herbert Feigl, reprinted in A.P. Martinich, The Philosophy of Language, p. 186198. I have substituted the word ‘reference’ for Feigl’s ‘nominatum’ according to customary practice.