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Full Idea
If p follows from q, I can make an inference from q to p, deduce p from q. The nature of the inference can be gathered only from the two propositions. They are the only possible justification of the inference. 'Laws of Inference' would be superfluous.
Gist of Idea
If q implies p, that is justified by q and p, not by some 'laws' of inference
Source
Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.132)
Book Ref
Wittgenstein,Ludwig: 'Tractatus Logico-Philosophicus (Pears)', ed/tr. Pears,D. /McGuinness,B. [RKP 1961], p.39
A Reaction
That seems to imply that each inference is judged on its particulars. But logic aims to be general. There seem to be 'laws' at a more complex level in the logic.
| 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] |