9 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. |
| 3570 | Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M] |
| Full Idea: Nozick suggests that knowledge is just belief which 'tracks the truth' (hence leaving out justification). | |
| From: report of Robert Nozick (Philosophical Explanations [1981]) by Michael Williams - Problems of Knowledge Ch. 2 |
| 2748 | A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J] |
| Full Idea: Nozick says Gettier cases aren't knowledge because the proposition would be believed even if false. Proper justification must be more sensitive to the truth ("track the truth"). | |
| From: report of Robert Nozick (Philosophical Explanations [1981], 3.1) by Jonathan Dancy - Intro to Contemporary Epistemology 3.1 | |
| A reaction: This is a bad idea. I see a genuine tree in my garden and believe it is there, so I know it. That I might have believed it if I was in virtually reality, or observing a mirror, won't alter that. |
| 411 | If we succeed in speaking the truth, we cannot know we have done it [Xenophanes] |
| Full Idea: No man has seen certain truth, and no man will ever know about the gods and other things I mentioned; for if he succeeds in saying what is fully true, he himself is unaware of it; opinion is fixed by fate on all things. | |
| From: Xenophanes (fragments/reports [c.530 BCE], B34), quoted by Sextus Empiricus - Against the Professors (six books) 7.49.4 |
| 412 | If God had not created honey, men would say figs are sweeter [Xenophanes] |
| Full Idea: If God had not created yellow honey, men would say that figs were sweeter. | |
| From: Xenophanes (fragments/reports [c.530 BCE], B38), quoted by Herodian - On Peculiar Speech 41.5 |
| 1640 | The basic Eleatic belief was that all things are one [Xenophanes, by Plato] |
| Full Idea: The Eleatic tribe, which had its beginnings from Xenophanes and still earlier, proceed on the grounds that all things so-called are one. | |
| From: report of Xenophanes (fragments/reports [c.530 BCE]) by Plato - The Sophist 242d |
| 3055 | Xenophanes said the essence of God was spherical and utterly inhuman [Xenophanes, by Diog. Laertius] |
| Full Idea: Xenophanes taught that the essence of God was of a spherical form, in no respect resembling man. | |
| From: report of Xenophanes (fragments/reports [c.530 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.2.3 |
| 408 | Ethiopian gods have black hair, and Thracian gods have red hair [Xenophanes] |
| Full Idea: Ethiopians have gods with snub noses and black hair, Thracians have gods with grey eyes and red hair. | |
| From: Xenophanes (fragments/reports [c.530 BCE], B16), quoted by Clement - Miscellanies 7.22.1 |
| 407 | Mortals believe gods are born, and have voices and clothes just like mortals [Xenophanes] |
| Full Idea: Mortals believe the gods to be created by birth, and to have raiment, voice and body like mortals'. | |
| From: Xenophanes (fragments/reports [c.530 BCE], B14), quoted by Clement - Miscellanies 5.109.2 |