4 ms·
TFA uses sloppy phrasing, but it's correct. The claim is not that earlier logicians such as Frege viewed logical concepts as meaningless. It's that, before Tars
by pulisse 3y ago
TFA uses sloppy phrasing, but it's correct. The claim is not that earlier logicians such as Frege viewed logical concepts as meaningless. It's that, before Tarski and Gödel, no one clearly distinguished syntax and semantics, and so earlier logicians lacked the conceptual resources to describe the difference between truth and provability, let alone investigate their relationship. (Frege only ever considers a single semantics for any formal system.)
- hackandthink 3y ago"It's that, before Tarski and Gödel, no one clearly distinguished syntax and semantics" I think this is right, but Hilbert came already close much earlier. But "Before this, logic had been strictly syntactical and proof theoretic" is at least misleading. Traditional logic was more conceptional. Frege's "formalism" was a great innovation, but he remained within the conceptual tradition (Frege-Hilbert controversy). "What Hilbert offers us, in 1899, is a systematic and powerful technique that can be used across all formalized disciplines to do just this: to prove consistency and independence. In doing so, he lays the groundwork, in concert with various of his contemporaries, for the emergence of contemporary model-theoretic techniques." https://plato.stanford.edu/entries/frege-hilbert/ https://plato.stanford.edu/entries/frege-hilbert/