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. |
| 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) |
| 6019 | If someone squashed a horse to make a dog, something new would now exist [Mnesarchus] |
| Full Idea: If, for the sake of argument, someone were to mould a horse, squash it, then make a dog, it would be reasonable for us on seeing this to say that this previously did not exist but now does exist. | |
| From: Mnesarchus (fragments/reports [c.120 BCE]), quoted by John Stobaeus - Anthology 179.11 | |
| A reaction: Locke would say it is new, because the substance is the same, but a new life now exists. A sword could cease to exist and become a new ploughshare, I would think. Apply this to the Ship of Theseus. Is form more important than substance? |
| 23633 | Many truths seem obvious, and point to universal agreement - which is what we find [Reid] |
| Full Idea: There are many truths so obvious to the human faculties, that it should be expected that men should universally agree in them. And this is actually found to be the case with regard to many truths, against which we find no dissent. | |
| From: Thomas Reid (Essays on Intellectual Powers 1: Preliminary [1785], 2) | |
| A reaction: He says that a few sceptical philosophers may disagree. This is a nice statement of his creed of common sense. I agree with him, and Aristotle observes the same fact. |
| 23630 | Only philosophers treat ideas as objects [Reid] |
| Full Idea: The vulgar allow that an 'idea' implies a mind that thinks, an act of mind which we call thinking, and an object about which we think. But the philosopher conceives a fourth - the idea, which is the immediate object. …I believe this to be a mere fiction. | |
| From: Thomas Reid (Essays on Intellectual Powers 1: Preliminary [1785], 1) | |
| A reaction: Another example, to add to Yablo's list, of abstract objects invented by philosophers to fill holes in their theories. This one is illuminating, because we all say 'I've got an idea'. Cf discussions of the redundancy of truth. Cf propositions. |
| 23629 | The ambiguity of words impedes the advancement of knowledge [Reid] |
| Full Idea: There is no greater impediment to the advancement of knowledge than the ambiguity of words. | |
| From: Thomas Reid (Essays on Intellectual Powers 1: Preliminary [1785], 1) | |
| A reaction: He means that ambiguity leads to long pointless disagreements. |
| 23632 | Similar effects come from similar causes, and causes are only what are sufficient for the effects [Reid] |
| Full Idea: A first principle is that similar effects proceed from the same or similar causes; that we ought to admit of no other causes …but such as are sufficient to account for the effects. | |
| From: Thomas Reid (Essays on Intellectual Powers 1: Preliminary [1785], 2) | |
| A reaction: He treats these as a priori axioms of natural philosophy. In evolution similar causes seem to produce startlingly divergent effects, such as the mating needs of male birds. |