display all the ideas for this combination of philosophers
3 ideas
| 22873 | Liberalism should improve the system, and not just ameliorate it [Dewey] |
| Full Idea: Liberalism must become radical in the sense that, instead of using social power to ameliorate the evil consequences of the existing system, it shall use social power to change the system. | |
| From: John Dewey (The Later Works (17 vols, ed Boydston) [1930], 11:287), quoted by David Hildebrand - Dewey 4 'Dewey' | |
| A reaction: Conservative liberals ask what people want, and try to give it to them. Radical liberals ask what people actually need, and try to make it possible. The latter is bound to be a bit paternalistic, but will probably create a better world. |
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |