7 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 19896 | It is not a law if not endorsed by the public [Hooker,R] |
| Full Idea: Laws they are not which public approbation hath not made so. | |
| From: Richard Hooker (Of the Laws of Ecclesiastical Polity [1593], I s.10), quoted by John Locke - Second Treatise of Government 134 n1 | |
| A reaction: Margaret Thatcher's Poll Tax, rejected by public rebellion, illustrates the point. |
| 19891 | Rule of law is superior to autonomy, because citizens can see what is expected [Hooker,R] |
| Full Idea: Men saw that to live by one man's will became the cause of all men's misery. This contrained them to come unto laws wherein all men might see their duty beforehand, and know the penalties of transgressing them. | |
| From: Richard Hooker (Of the Laws of Ecclesiastical Polity [1593], I s.10), quoted by John Locke - Second Treatise of Government 111 n1 | |
| A reaction: One British school has a single rule, that pupils 'shall always treat other people with respect'. Presumably the rulers, as well as the pupils, must decide when this is transgressed. The rule of law may be preferable. |
| 19897 | Human laws must accord with the general laws of Nature [Hooker,R] |
| Full Idea: Laws human must be made according to the general laws of Nature. | |
| From: Richard Hooker (Of the Laws of Ecclesiastical Polity [1593], III s.9), quoted by John Locke - Second Treatise of Government | |
| A reaction: The point simply seems to be that they won't get assent from the public if they are not in accord with natural justice. Positivists say you can make any damned law you like. |
| 17005 | Natural things observe certain laws, and things cannot do otherwise if they retain their forms [Hooker,R] |
| Full Idea: Things natural …do so necessarily observe their certain laws, that as long as they keep those forms which give them their being they cannot possibly be apt or inclinable to do otherwise than they do. | |
| From: Richard Hooker (Of the Laws of Ecclesiastical Polity [1593], 1.3.4), quoted by Marc Lange - Laws and Lawmakers 1.2 | |
| A reaction: Cited by some as the beginnings of the idea of 'laws of nature', but it is striking that Hooker says the laws are controlled by 'forms' (which are Aristotelian essences). This is an essentialist view of laws, not a regularity or divine power one. |