7 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. |
| 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. |
| 8090 | Since the language of thought is the same for all, it must be something like logical form [Fodor, by Devlin] |
| Full Idea: Fodor and Jackendorff argue that since the internal language of thought, or conceptual structure, has to be more or less the same for all people, of whatever language, it will surely be something like logical form. | |
| From: report of Jerry A. Fodor (The Language of Thought [1975]) by Keith Devlin - Goodbye Descartes Ch.8 | |
| A reaction: The discovery (by, e.g., Frege and Russell) that there is something called 'logical form', which we can track down and represent in precise and fairly unambiguous symbolism, may be one of the greatest of all human discoveries. Perhaps. |
| 11143 | If concept-learning is hypothesis-testing, that needs innate concepts to get started [Fodor, by Margolis/Laurence] |
| Full Idea: Fodor argues that virtually all lexical concepts are innate, because most models of learning treat concept-learning as hypothesis testing, but that invariably employs the very concept to be learned. | |
| From: report of Jerry A. Fodor (The Language of Thought [1975]) by E Margolis/S Laurence - Concepts 3.3 | |
| A reaction: The obvious response is to reject the theory which gave rise to this difficulty. I take concept formation to be a fairly mechanical and barely conscious response to environment, not a process of fully rational and conscious hypothesising. |