9 ideas
| 12268 | Contradiction is impossible [Antisthenes (I), by Aristotle] |
| Full Idea: Antisthenes said that contradiction is impossible. | |
| From: report of Antisthenes (Ath) (fragments/reports [c.405 BCE]) by Aristotle - Topics 104b21 | |
| A reaction: Aristotle is giving an example of a 'thesis'. It should be taken seriously if a philosopher proposes it, but dismissed as rubbish if anyone else proposes it! No context is given for the remark. |
| 602 | Some fools think you cannot define anything, but only say what it is like [Antisthenes (I), by Aristotle] |
| Full Idea: There is an application of that old chestnut of the cynic Antisthenes' followers (and other buffoons of that kind). Their claim was that a definition of what something is is impossible. You cannot define silver, though you can say it is like tin. | |
| From: report of Antisthenes (Ath) (fragments/reports [c.405 BCE]) by Aristotle - Metaphysics 1043b |
| 3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
| Full Idea: Von Neumann defines each number as the set of all smaller numbers. | |
| From: report of John von Neumann (works [1935]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280 |
| 3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
| Full Idea: Von Neumann suggested that functions be pressed into service to replace sets. | |
| From: report of John von Neumann (works [1935]) by José A. Benardete - Metaphysics: the logical approach Ch.23 |
| 22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
| Full Idea: At age twenty, Von Neumann devised the formal definition of ordinal numbers that is used today: an ordinal number is the set of all smaller ordinal numbers. | |
| From: report of John von Neumann (works [1935]) by William Poundstone - Prisoner's Dilemma 02 'Sturm' | |
| A reaction: I take this to be an example of an impredicative definition (not predicating something new), because it uses 'ordinal number' in the definition of ordinal number. I'm guessing the null set gets us started. |
| 1664 | I would rather go mad than experience pleasure [Antisthenes (I)] |
| Full Idea: I would rather go mad than experience pleasure. | |
| From: Antisthenes (Ath) (fragments/reports [c.405 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 06.3 | |
| A reaction: Did he actually prefer pain? If both experiences would drive him mad, it seems like a desire for death. I cannot understand why anyone is opposed to harmless pleasures. |
| 21385 | Antisthenes said virtue is teachable and permanent, is life's goal, and is like universal wealth [Antisthenes (I), by Long] |
| Full Idea: The moral propositions of Antisthenes foreshadowed the Stoics: virtue can be taught and once acquired cannot be lost (fr.69,71); virtue is the goal of life (22); the sage is self-sufficient, since he has (by being wise) the wealth of all men (8o). | |
| From: report of Antisthenes (Ath) (fragments/reports [c.405 BCE]) by A.A. Long - Hellenistic Philosophy 1 | |
| A reaction: [He cites Caizzi for the fragments] The distinctive idea here is (I think) that once acquired virtue can never be lost. It sounds plausible, but I'm wondering why it should be true. Is it like riding a bicycle, or like learning to speak Russian? |
| 12709 | Motion is not absolute, but consists in relation [Leibniz] |
| Full Idea: In reality motion is not something absolute, but consists in relation. | |
| From: Gottfried Leibniz (On Motion [1677], A6.4.1968), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 3 | |
| A reaction: It is often thought that motion being relative was invented by Einstein, but Leibniz wholeheartedly embraced 'Galilean relativity', and refused to even consider any absolute concept of motion. Acceleration is a bit trickier than velocity. |
| 2631 | Antisthenes says there is only one god, which is nature [Antisthenes (I), by Cicero] |
| Full Idea: Antisthenes says there is only one god, which is nature. | |
| From: report of Antisthenes (Ath) (fragments/reports [c.405 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.32 |