4 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. |
| 490 | Everything happens by reason and necessity [Leucippus] |
| Full Idea: Nothing happens at random; everything happens out of reason and by necessity. | |
| From: Leucippus (fragments/reports [c.435 BCE], B002), quoted by (who?) - where? |
| 22601 | Laissez-faire individualism doesn't work, especially in troublesome times [Keynes] |
| Full Idea: It is obvious that an individualist society left to itself does not work well or even tolerably. The more troublesome the times, the worse does a laissez-faire system work. | |
| From: Maynard Keynes (The General Theory of Employment [1936]), quoted by Ian Dunt - How to be a Liberal 7 | |
| A reaction: I thought I was a Communitarian, but I may be a Keynesian Liberal, committed to a safety net welfare system. I haven't quite decided yet. Political philosophy is hopeless, if the ideas actually have to be implemented. What is the criterion of 'work'? |