Logic & Philosophy of Science


Patricia Blanchette
Department of Philosophy, University of Notre Dame

“Frege's Metatheory”

According to an increasingly-influential interpretation of Gottlob Frege's work, the Fregean conception of logic is one on which "metatheory" as a whole must be ruled unintelligible. Because Frege takes logic to be "universal," it is argued, he cannot make sense of the attempt to evaluate logical systems themselves, and hence cannot make sense of e.g. standard questions of the soundness, completeness, and consistency of logical systems. It has recently been argued that Frege's clear antipathy towards independence-proofs in geometry (as seen both in his rejection of David Hilbert's independence-proofs, and in his rejection of his own tentatively-proposed independence-proof technique of 1906) is a mark of this rejection of metatheory, and should be taken to support the "anti-metatheory" interpretation of Frege.

The central purpose of this paper is to argue that neither Frege's "universalism" with respect to logic, nor his rejection of various independence-proof techniques, gives us any reason to view his conception of logic as anti-metatheoretical. The importance of this point, as I see it, is that the sense in which Frege takes logic to be "universal" is a sense in which we all ought to agree with him, and it is crucial that we understand what is, and what is not, "ruled out" by this universalist conception.

Friday, February 11, 2000
SSPB 1208, 3 pm