10 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 |
| 10121 | Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal] |
| Full Idea: Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth. | |
| From: Blaise Pascal (works [1660]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: [Quoted in Auden and Kronenberger's Book of Aphorisms] Presumably we would now say that contradiction is a purely formal, syntactic notion, and not a semantic one. If you hit a contradiction, something has certainly gone wrong. |
| 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. |
| 6375 | The taste of chocolate is a 'finer-grained' sensation than the taste of sweetness [Polger] |
| Full Idea: The taste of chocolate is presumably a 'finer-grained' sensation than the taste of sweetness. | |
| From: Thomas W. Polger (Natural Minds [2004], Ch.1.4) | |
| A reaction: An interesting distinction when it comes to what they are like, and whether two very different brains can realise them. Sweetness might be the same for most creatures, but the tast of chocolate subtly different. |
| 6381 | The mind and the self are one, and the mind-self is a biological phenomenon [Polger] |
| Full Idea: We should return to the old idea that the mind and the self are one and combine it with the new idea that the mind-self is a biological phenomenon. | |
| From: Thomas W. Polger (Natural Minds [2004], §8.3) | |
| A reaction: This doesn't make allowance for the fact that some parts of my mind seem like irritating visitors, and other parts seem like the home-owner. Personally I take the self to be the brain's central controller, or the centre (forum) of brain integration. |
| 6378 | Teleological functions explain why a trait exists; causal-role functions say what it does [Polger] |
| Full Idea: Teleological functions help explain why a trait has come to exist; causal-role functions tell what a trait does or is apt to do. | |
| From: Thomas W. Polger (Natural Minds [2004], §5.4) | |
| A reaction: The teleological view has the merit of nesting nicely with the theory of evolution, and with Aristotelian virtue ethics (which I like). Causal-role functionalism focuses better on what is actually happening inside the head. |
| 6380 | Identity theory says consciousness is an abstraction: a state, event, process or property [Polger] |
| Full Idea: Identity theories locate consciousness at a certain order of abstraction, typically among neurophysiological states, events, processes, or properties. | |
| From: Thomas W. Polger (Natural Minds [2004], Ch.7.6) | |
| A reaction: I increasingly think that processes are the answer. My new analogy for the mind is a waterfall: its physical ontology is simple, it only exists because there is a sustained process, and it is far too complex to predict individual droplet outcomes. |
| 6379 | A mummified heart has the teleological function of circulating blood [Polger] |
| Full Idea: A preserved heart in a jar of formaldehyde has the teleological function of circulating blood. | |
| From: Thomas W. Polger (Natural Minds [2004], §5.4) | |
| A reaction: A nice illustration. |
| 6377 | Teleological notions of function say what a thing is supposed to do [Polger] |
| Full Idea: Teleological notions of function specify not just what a thing happens to do, but what it is supposed to do. | |
| From: Thomas W. Polger (Natural Minds [2004], Ch.5.3) | |
| A reaction: This is the basis of a distinct theory of the mind. It seems to be akin to the 'dispositions' of behaviourism, so that the mind becomes once more a theoretical and abstract entity, rather than a thing of occurrent events and processes. |