8 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. |
| 13827 | Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz] |
| Full Idea: Defining logical consequence in the way Tarski does is a rather meagre result, treating an argument as a black box, observing input and output, while disregarding inner structure. We should define logical consequence on the basis of valid arguments. | |
| From: Dag Prawitz (On the General Idea of Proof Theory [1974], §2) |
| 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) |
| 13826 | Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz] |
| Full Idea: In model theory, which has dominated the last decades, one concentrates on logically valid sentences, and what follows logically from what, but one disregards questions concerning how we know these things. | |
| From: Dag Prawitz (On the General Idea of Proof Theory [1974], §1) |
| 19729 | 'Modal epistemology' demands a connection between the belief and facts in possible worlds [Black,T] |
| Full Idea: In 'modal epistemologies' a belief counts as knowledge only if there is a modal connection - a connection not only to the actual world, but also to other non-actual possible worlds - between the belief and the facts of the matter. | |
| From: Tim Black (Modal and Anti-Luck Epistemology [2011], 1) | |
| A reaction: [Pritchard 2005 seems to be a source for this] This sounds to me a bit like Nozick's tracking or sensitivity theory. Nozick is, I suppose, diachronic (time must pass, for the tracking), where this theory is synchronic. |
| 19728 | Gettier and lottery cases seem to involve luck, meaning bad connection of beliefs to facts [Black,T] |
| Full Idea: The protagonists in Gettier cases and in lottery cases fail to have knowledge because their beliefs are true simply as a matter of luck, where this means that their beliefs themselves are not appropriately connected to the facts. | |
| From: Tim Black (Modal and Anti-Luck Epistemology [2011], 1) | |
| A reaction: The lottery problem is you correctly believe 'my ticket won't win the lottery' even though you don't seem to actually know it won't. Is the Gettier problem simply the problem of lucky knowledge? 'Luck' is a rather vague concept. |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles. | |
| From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro' | |
| A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture? |