6 ideas
| 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. |
| 2596 | Maybe mind and body are parallel, like two good clocks [Leibniz] |
| Full Idea: Two clocks in perfect agreement must be by natural influence, or the control of a craftsman, or their perfect construction at the beginning. Only the third way (of "preestablished harmony" by God) is possible. | |
| From: Gottfried Leibniz (The Nature and Communication of Substance [1690], p.121) | |
| A reaction: Presumably 'natural influence' would cover the possibility that (unnoticed by you, apparently) one clock is attached to the other clock at the relevant points. If they are unconnected, presumably they are quite unaware of one another's existence. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 2595 | If the universe is a perfect agreement of uncommunicating substances, there must be a common source [Leibniz] |
| Full Idea: The perfect agreement of so many substances which have no communication whatever with each other can only come from a common source. | |
| From: Gottfried Leibniz (The Nature and Communication of Substance [1690], p.120) |