| 13824 | Proof theory began with Frege's definition of derivability [Frege, by Prawitz] |
| Full Idea: Frege's formal definition of derivability is perhaps the first investigation in general proof theory. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Dag Prawitz - Gentzen's Analysis of First-Order Proofs 2 n2 | |
| A reaction: In 'On General Proof Theory §1' Prawitz says "proof theory originated with Hilbert" in 1900. Presumably Frege offered a theory, and then Hilbert saw it as a general project. |
| 15089 | Logical proof just explicates complicated tautologies [Wittgenstein] |
| Full Idea: Proof in logic is merely a mechanical expedient to facilitate recognition of tautologies in complicated cases. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.1262) |
| 13801 | An 'informal proof' is in no particular system, and uses obvious steps and some ordinary English [Bostock] |
| Full Idea: An 'informal proof' is not in any particular proof system. One may use any rule of proof that is 'sufficiently obvious', and there is quite a lot of ordinary English in the proof, explaining what is going on at each step. | |
| From: David Bostock (Intermediate Logic [1997], 8.1) |
| 15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess] |
| Full Idea: There are atomic formulas, and formulas built from the connectives, and that is all. We show that all formulas have some property, first for the atomics, then the others. This proof is 'induction on complexity'; we also use 'recursion on complexity'. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.4) | |
| A reaction: That is: 'induction on complexity' builds a proof from atomics, via connectives; 'recursion on complexity' breaks down to the atomics, also via the connectives. You prove something by showing it is rooted in simple truths. |