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Ideas for 'Interview with Baggini and Stangroom', 'Consistency and realism (with 1972 note)' and 'Gentzen's Analysis of First-Order Proofs'

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4 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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.
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
6858 Formal logic struck me as exactly the language I wanted to think in [Williamson]
     Full Idea: As soon as I started learning formal logic, that struck me as exactly the language that I wanted to think in.
     From: Timothy Williamson (Interview with Baggini and Stangroom [2001])
     A reaction: It takes all sorts… It is interesting that formal logic might be seen as having the capacity to live up to such an aspiration. I don't think the dream of an ideal formal language is dead, though it will never encompass all of reality. Poetic truth.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
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]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
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)