4 ideas
| 9548 | A mathematical object exists if there is no contradiction in its definition [Waterfield] |
| Full Idea: A mathematical object exists provided there is no contradiction implied in its definition. | |
| From: Robin Waterfield (Introduction to 'Hippias Minor' [1987], p.44), quoted by Charles Chihara - A Structural Account of Mathematics 1.4 | |
| A reaction: A rather bizarre criterion for existence. Not one, for example, that you would consider applying to the existence of physical objects! But then Poincaré is the father of 'conventionalism', rather than being a platonist. |
| 16285 | A possible world can be seen as a complete and consistent novel [Jeffrey] |
| Full Idea: A novel describes a possible world in as much detail as is possible without exceeding the resources of the agent's language. But if talk of possible worlds seems dangerously metaphysical, focus on the novels themselves, when complete and consistent. | |
| From: Richard Jeffrey (The Logic of Decision [1965], 12.8), quoted by David Lewis - On the Plurality of Worlds | |
| A reaction: Lewis seems to cite this remark from Jeffrey as the source of the idea that ersatz linguistic worlds are like novels. Why won't a novel with one tiny inconsistency count as a possible world? People seem to live in it. |
| 19155 | Instead of gambling, Jeffrey made the objects of Bayesian preference to be propositions [Jeffrey, by Davidson] |
| Full Idea: Jeffrey produced a version of Bayesianism that made no direct use of gambling (as Ramsey had), but treats the objects of preference ...as propositions. | |
| From: report of Richard Jeffrey (The Logic of Decision [1965]) by Donald Davidson - Truth and Predication 3 | |
| A reaction: I'm guessing that Jeffreys launched modern Bayesian theory with this idea. It suggest that one can consider degrees of truth, rather than mere winning or losing. |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| Full Idea: Hermarchus said that animal killing is justified by considerations of human safety and nourishment and by animals' inability to form contractual relations of justice with us. | |
| From: report of Hermarchus (fragments/reports [c.270 BCE]) by David A. Sedley - Hermarchus | |
| A reaction: Could the last argument be used to justify torturing animals? Or could we eat a human who was too brain-damaged to form contracts? |