Combining Texts

All the ideas for 'Sisyphus (lost)', 'Foundations of Two-Dimensional Semantics' 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 / 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)
19. Language / C. Assigning Meanings / 10. Two-Dimensional Semantics
14739 'Water' is two-dimensionally inconstant, with different intensions in different worlds [Chalmers, by Sider]
     Full Idea: For Chalmers, 'water' is two-dimensionally inconstant, in that it has different secondary intensions relative to different worlds of utterance.
     From: report of David J.Chalmers (Foundations of Two-Dimensional Semantics [2006]) by Theodore Sider - Four Dimensionalism 7.2
     A reaction: In this way 'water' is regarded as being like an indexical (such as 'I'), which has a fixed meaning component, and a second component which varies with different utterances. Maybe.