9 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. |
| 3296 | Sense-data are a false objectification of what is essentially subjective [Nagel] |
| Full Idea: The private object or sense datum view is an instance of the false objectification of what is essentially subjective. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.207) |
| 3295 | Inner v outer brings astonishment that we are a particular person [Nagel] |
| Full Idea: The problem of reconciling the objective and subjective points of view takes its purest form in a sense of incredulity that one should be anyone in particular. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.206) | |
| A reaction: Nice observation. This idea has always struck me forcibly, and seems to be one of those basic intuitions which motivates philosophy, and yet the subject has almost nothing to say about it. Of course you are you, or you wouldn't be amazed by it… |
| 3293 | If you assert that we have an ego, you can still ask if that future ego will be me [Nagel] |
| Full Idea: The metaphysical ego, if it is a continuing individual with its identity over time, is just one more thing about which the same problem can be raised - will that ego still be me? | |
| From: Thomas Nagel (Subjective and Objective [1979], p.200) | |
| A reaction: You can worry too much about some philosophical questions. If it is me now, and it has continuing individual identity over time, I'm not going to lose sleep over the possibility that it might nevertheless somehow cease to be me. I'm overrated. |
| 3292 | The most difficult problem of free will is saying what the problem is [Nagel] |
| Full Idea: The most difficult problem of free will is saying what the problem is. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.198) |
| 6017 | Nomos is king [Pindar] |
| Full Idea: Nomos is king. | |
| From: Pindar (poems [c.478 BCE], S 169), quoted by Thomas Nagel - The Philosophical Culture | |
| A reaction: This seems to be the earliest recorded shot in the nomos-physis wars (the debate among sophists about moral relativism). It sounds as if it carries the full relativist burden - that all that matters is what has been locally decreed. |
| 3294 | As far as possible we should become instruments to realise what is best from an eternal point of view [Nagel] |
| Full Idea: The right thing to do is to turn oneself as far as possible into an instrument for the realisation of what is best 'sub specie aeternitatis'. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.204) |