6 ideas
| 13831 | Logic is based on transitions between sentences [Prawitz] |
| Full Idea: I agree entirely with Dummett that the right way to answer the question 'what is logic?' is to consider transitions between sentences. | |
| From: Dag Prawitz (Gentzen's Analysis of First-Order Proofs [1974], §04) | |
| A reaction: I always protest at this point that reliance on sentences is speciesism against animals, who are thereby debarred from reasoning. See the wonderful Idea 1875 of Chrysippus. Hacking's basic suggestion seems right. Transition between thoughts. |
| 7334 | Anti-realism needs an intuitionist logic with no law of excluded middle [Dummett, by Miller,A] |
| Full Idea: Dummett argues that antirealism implies that classical logic must be given up in favour of some form of intuitionistic logic that does not have the law of excluded middle as a theorem. | |
| From: report of Michael Dummett (works [1970]) by Alexander Miller - Philosophy of Language 9.4 | |
| A reaction: Only realists can think every proposition is either true or false, even if it is beyond the bounds of our possible knowledge (e.g. tiny details from remote history). Personally I think "Plato had brown eyes" is either true or false. |
| 13825 | Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz] |
| 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'. | |
| From: Dag Prawitz (Gentzen's Analysis of First-Order Proofs [1974], 2.2.2) | |
| 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] |
| 13823 | In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz] |
| Full Idea: In Gentzen's natural deduction, the inferences are broken down into atomic steps in such a way that each step involves only one logical constant. The steps are the introduction or elimination of the logical constants. | |
| From: Dag Prawitz (Gentzen's Analysis of First-Order Proofs [1974], 1.1) |
| 3303 | For anti-realists there are no natural distinctions between objects [Dummett, by Benardete,JA] |
| Full Idea: Dummett says that anti-realism offers us a picture of reality as an amorphous lump not yet articulated into discrete objects. | |
| From: report of Michael Dummett (works [1970]) by José A. Benardete - Metaphysics: the logical approach Ch.2 | |
| A reaction: This might be called 'weak' anti-realism, where 'strong' anti-realism is the view that reality is quite unknowable, and possibly non-existent. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |