How to Frege a Tarski–Quine

Tarski and Quine argue that it is meaningless to quantify into quotation, the referentially opaque context par excellence. Building on Frege's thesis that ‘the introduction of a sign for identity of content necessarily produces a bifurcation in the meaning of all signs’ (Begriffsschrift, Section 8), we challenge this view. We advance a semantics for first-order languages in which every expression has a ‘bifurcated’ value—a pair consisting of the expression's ordinary referent and the expression itself. This allows treating quotation marks as a function symbol—something that is impossible to achieve within ordinary semantics. In addition to vindicating Frege's treatment of identity in Begriffsschrift, our theory of quotation solves a riddle about anaphora and gives an original account of Giorgione sentences. Building on this account, we offer a reading of quoted variables on which they retain their status as genuine variables. Finally, using this reading, we refute the Tarski–Quine orthodoxy.