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. |
| 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) |
| 12165 | Romantics say music expresses ideas, or the Will, or intuitions, or feelings [Scruton] |
| Full Idea: According to the Romantic theory music was an expression of something, of an idea (Hegel), of the Will (Schopenhauer), of 'intuitions' (Croce), or of feelings (Collingwood). | |
| From: Roger Scruton (The Nature of Musical Expression [1981], p.54) | |
| A reaction: Deryck Cooke was the culmination of music as expression of feeling, and Stravinsky was the greatest rebel against the whole idea of expression in music. You can set out to create interesting music which does or does not grab the emotions. |
| 12164 | Expressing melancholy is a good thing, but arousing it is a bad thing [Scruton] |
| Full Idea: To describe a piece of music as expressive of melancholy is to give a reason for listening to it; to describe it as arousing or evoking melancholy is to give a reason for avoiding it. | |
| From: Roger Scruton (The Nature of Musical Expression [1981], p.49) | |
| A reaction: Expressing sexual desire, while avoiding arousing it, is the nice challenge for a particular type of art. Would Scruton say that expressing joy is a good thing, but arousing it is bad? It is a nice observation, though. |
| 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? |