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. |
| 19378 | Early modern possibility is what occurs sometime; for Leibniz, it is what is not contradictory [Arthur,R] |
| Full Idea: For Descartes, Hobbes and Spinoza, if a state of things is possible, it must occur at some time, whether past, present or future. For Leibniz possibility makes no reference to time; an individual is possible if its concept contains no contradiction. | |
| From: Richard T.W. Arthur (Leibniz [2014], 4 'Contingent') | |
| A reaction: It has always struck me as fallacious to say that anything that is possible must at some time occur. If '6' is possible on the die, what will constrain it to eventually come up when thrown? Mere non-contradiction doesn't imply possibility either. |
| 19380 | Occasionalism contradicts the Eucharist, which needs genuine changes of substance [Arthur,R] |
| Full Idea: The Jesuits rejected occasionalism ... because it is incompatible with the Catholic interpretation of the Eucharist, which there is genuine change of substance of the bread into the substance of Christ (transubstantiation). | |
| From: Richard T.W. Arthur (Leibniz [2014], 5 'Substance') | |
| A reaction: Not sure I understand this, but I take it that the Eucharist needs a real relation across the substance-spirit boundary, and not just a co-ordination. |
| 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? |