12 ideas
| 13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
| Full Idea: Von Neumann's decision was to start with the ordinals and to treat cardinals as a special sort of ordinal. | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by William D. Hart - The Evolution of Logic 3 | |
| A reaction: [see Hart 73-74 for an explication of this] |
| 12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
| Full Idea: In Von Neumann's definition an ordinal is a transitive set in which all of the elements are transitive. | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Alain Badiou - Briefings on Existence 11 |
| 18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
| Full Idea: For Von Neumann the successor of n is n U {n} (rather than Zermelo's successor, which is {n}). | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n8 |
| 18180 | Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann] |
| Full Idea: Von Neumann's version of the natural numbers is in fact preferred because it carries over directly to the transfinite ordinals. | |
| From: comment on John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n9 |
| 15925 | Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine] |
| Full Idea: Each Von Neumann ordinal number is the set of its predecessors. ...He had shown how to introduce ordinal numbers as sets, making it possible to use them without leaving the domain of sets. | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Shaughan Lavine - Understanding the Infinite V.3 |
| 3986 | The 'intentional stance' is a way of interpreting an entity by assuming it is rational and self-aware [Dennett] |
| Full Idea: The 'intentional stance' is the tactic of interpreting an entity by adopting the presupposition that it is an approximation of the ideal of an optimally designed (i.e. rational) self-regarding agent. | |
| From: Daniel C. Dennett (Daniel Dennett on himself [1994], p.239) | |
| A reaction: This is Dennett's 'instrumentalism', a descendant of behaviourism, which strikes me as a pragmatist's evasion of the ontological problems of mind which should interest philosophers |
| 3987 | Like the 'centre of gravity', desires and beliefs are abstract concepts with no actual existence [Dennett] |
| Full Idea: Like such abstracta as centres of gravity and parallelograms of force, the beliefs and desires posited by the highest intentional stance have no independent and concrete existence. | |
| From: Daniel C. Dennett (Daniel Dennett on himself [1994], p.239) | |
| A reaction: I don't see why we shouldn't one day have a physical account of the distinctive brain events involved in a belief or a desire |
| 3984 | The nature of content is entirely based on its functional role [Dennett] |
| Full Idea: All attributions of content are founded on an appreciation of the functional roles of the items in question. | |
| From: Daniel C. Dennett (Daniel Dennett on himself [1994], p.239) | |
| A reaction: This seems wrong to me. How can anything's nature be its function? It must have intrinsic characteristics in order to have the function. This is an evasion. |
| 3983 | Learning is evolution in the brain [Dennett] |
| Full Idea: Learning is evolution in the brain. | |
| From: Daniel C. Dennett (Daniel Dennett on himself [1994], p.238) | |
| A reaction: This is a rather non-conscious, associationist view, connected to Dawkins' idea of 'memes'. It seems at least partially correct. |
| 3985 | Biology is a type of engineering, not a search for laws of nature [Dennett] |
| Full Idea: Biology is not a science like physics, in which one should strive to find 'laws of nature', but a species of engineering. | |
| From: Daniel C. Dennett (Daniel Dennett on himself [1994], p.239) | |
| A reaction: Yes. This is also true of chemistry, which has always struck me as minitiarised car mechanics. |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |