more from this thinker | more from this text
Full Idea
Natural deduction systems generally depend on conditional proof, but for Frege everything is asserted unconditionally. The modern turnstile |- is allowed to have antecedents, and hence to represent inference rather than Frege's judgement sign |---.
Gist of Idea
Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents
Source
Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 03 'Axioms')
Book Ref
Potter,Michael: 'The Rise of Anaytic Philosophy 1879-1930' [Routledge 2020], p.28
A Reaction
[compressed] Shockingly, Frege's approach seems more psychological than the modern approach. I would say that the whole point of logic is that it has to be conditional, because the truth of the antecedents is irrelevant.
| 11148 | Deduction is when we suppose one thing, and another necessarily follows [Aristotle] |
| 18277 | If q implies p, that is justified by q and p, not by some 'laws' of inference [Wittgenstein] |
| 13623 | The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem' [Bostock] |
| 13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
| 22279 | Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter] |
| 10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
| 18808 | Normal deduction presupposes the Cut Law [Rumfitt] |