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Full Idea
With Gentzen's natural deduction, we may say that the introductions represent, as it were, the 'definitions' of the logical constants. The introductions are not literally understood as 'definitions'.
Gist of Idea
Natural deduction introduction rules may represent 'definitions' of logical connectives
Source
Dag Prawitz (Gentzen's Analysis of First-Order Proofs [1974], 2.2.2)
Book Ref
'A Philosophical Companion to First-Order Logic', ed/tr. Hughes,R.I.G. [Hackett 1993], p.210
A Reaction
[Hacking, in 'What is Logic? §9' says Gentzen had the idea that his rules actually define the constants; not sure if Prawitz and Hacking are disagreeing]
| 13826 | Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz] |
| 13827 | Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz] |
| 13831 | Logic is based on transitions between sentences [Prawitz] |
| 13823 | In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz] |
| 13825 | Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz] |