display all the ideas for this combination of philosophers
5 ideas
| 8084 | Syllogisms are verbal fencing, not discovery [Locke] |
| Full Idea: Syllogisms are useless for discovery, and serve only for verbal fencing. | |
| From: John Locke (Essay Conc Human Understanding (2nd Ed) [1694]), quoted by Keith Devlin - Goodbye Descartes Ch.3 | |
| A reaction: This illustrates the low status of logic, and the new high status of experimental science, in Locke's time. Locke's seems to miss the point that you can infer new discoveries from old ones. |
| 12572 | Many people can reason well, yet can't make a syllogism [Locke] |
| Full Idea: There are many men that reason exceeding clear and rightly, who know not how to make a syllogism | |
| From: John Locke (Essay Conc Human Understanding (2nd Ed) [1694], 4.17.04) | |
| A reaction: On the one hand this is just Locke's scepticism about the whole business of Aristotelian logic, but on the other hand it may be a perspicuous observation that logical thought extends far beyond what was catalogued by Aristotle. |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| Full Idea: 'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference. | |
| From: Ian Hacking (What is Logic? [1979], §06.2) | |
| A reaction: That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic. |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| Full Idea: If A |- B and B |- C, then A |- C. This generalises to: If Γ|-A,Θ and Γ,A |- Θ, then Γ |- Θ. Gentzen called this 'cut'. It is the transitivity of a deduction. | |
| From: Ian Hacking (What is Logic? [1979], §06.3) | |
| A reaction: I read the generalisation as 'If A can be either a premise or a conclusion, you can bypass it'. The first version is just transitivity (which by-passes the middle step). |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| Full Idea: Only the cut rule can have a conclusion that is less complex than its premises. Hence when cut is not used, a derivation is quite literally constructive, building up from components. Any theorem obtained by cut can be obtained without it. | |
| From: Ian Hacking (What is Logic? [1979], §08) |