Frege's New Science

In this paper, we explore Fregean metatheory, what Frege called the New Science. The New Science arises in the context of Frege's debate with Hilbert over independence proofs in geometry and we begin by considering their dispute. We propose that Frege's critique rests on his view that language is a set of propositions, each immutably equipped with a truth value (as determined by the thought it expresses), so to Frege it was inconceivable that axioms could even be considered to be other than true. Because of his adherence to this view, Frege was precluded from the sort of metatheoretical considerations that were available to Hilbert; but from this, we shall argue, it does not follow that Frege was blocked frommetatheoryintoto. Indeed, FregesuggestsinDieGrundlagenderGeometrie a metatheoretical method for establishing independence proofs in the context of the New Science. Frege had reservations about the method, however, primarily because of the apparent need to stipulate the lo...

• Type: Journal
• Year: 2000
• Where: NDJFL
• Authors: Aldo Antonelli, Robert May
• Keywords: Frege, Fregean Metatheory, Independence Proofs, NDJFL 2000