3 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. |
| 16706 | Generation is when local motions aggregate to become a single subject [Nicholas of Autrecourt] |
| Full Idea: In the case of natural things there is only local motion. When from such motion there follows an aggregation of natural bodies that are gathered to one another and acquire the nature of a single subject, this is called generation. | |
| From: Nicholas of Autrecourt (Tractatus [1335], Ch. 1) | |
| A reaction: This is explosive atomistic corpuscularianism, three centuries before its appointed date. He was duly suppressed. Can he give an account of the 'nature of a single subject' in this way? |
| 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? |