5 ideas
| 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. |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
| From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |
| 22817 | Citizenship involves a group of mutually supporting rights, which create community and equality [Miller,D] |
| Full Idea: The idea of citizenship is that rights support each other. Protective and welfare rights provide a basis for a political role. This underpins a sense of membership, and an obligation to provide welfare. Rights confer equal status and self-respect. | |
| From: David Miller (Community and Citizenship [1989], 3) | |
| A reaction: A helpful eludation of what a richer concept of citizenship than mere membership might look like. Communitarians have a different concept of rights from that of liberals. |
| 22816 | Socialists reject nationality as a false source of identity [Miller,D] |
| Full Idea: The socialist tradition has been overwhelmingly hostile to nationality as a source of identity, usually regarding it merely as an artificially created impediment to the brotherhood of man. | |
| From: David Miller (Community and Citizenship [1989], 2) | |
| A reaction: I have some sympathy with this, especially when nationalism is expressed in terms of enemies, but the question of what community a person can plausibly identify with is difficult. We start in hunter gather tribes of several hundred. |