 Despite the clear failure of communication between Hilbert and Frege, their debate brings to light a number of important issues, not least of which are (i) the role of schematically-understood sentences in providing implicit definitions, which Frege articulates more clearly on Hilbert’s behalf than Hilbert had yet done, and (ii) the extent to which the logical relations are to be treated as “formal”. On this last issue, the difference between Frege and Hilbert is instructive. Long before the debate with Hilbert, Frege already held that logical rigor requires the use of formal systems of deduction, “formal” in the sense that all thoughts are expressed via precisely-determined sentences, and that all inference-rules and axioms are presented syntactically (see, e.g., Frege 1879). Most important for our purposes is the fact that Frege’s formal systems are entirely modern in the sense that the derivability in such a system of a sentence from a set of sentences turns just on the syntactic form of those sentences. The famous conceptual analyses on which much of Frege’s work turns are all provided prior to proof; it is on the basis of conceptual analyses that one arrives at the appropriate sentences to treat within the formal system, but the analyses themselves play no role within the proofs proper. Hence when it comes to the positive work of demonstrating that a given sentence is derivable from a set of sentences, Frege is just like Hilbert: meanings don’t matter. Indeed, at the time of their correspondence, Frege’s work was considerably more “formal” than Hilbert’s, since Hilbert at this time was not using an explicit syntactically-defined system of deduction.