Frege's /Begriffsschrift/ Theory of Identity Revisited (joint work with Ulrich Pardey, Bochum)

Presented by: Kai Wehmeier UC Irvine

In section 8 of /Begriffsschrift/, Frege explains that an identity statement of the form 'a=b' says of the names a and b that they co-refer. Thus identity, in /Begriffsschrift/, is a relation between names rather than between the objects they designate. Since the beginning of serious Frege scholarship, virtually every commentator who has addressed the /Begriffsschrift/ conception of identity at all, including Alonzo Church, Michael Dummett, and Richard Heck, has claimed it to be formally defective, the principal point of criticism being that it cannot make sense of bound variables occurring on either side of the identity sign. We show that these commentators are mistaken. In fact, Frege's co-reference conception of identity is fully compatible with standard quantification theory. Time permitting, we will mention some respects in which this result has consequences for systematic debates regarding the nature of the identity relation.