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. |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles. | |
From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro' | |
A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture? |
20890 | Why do sexual relationships need permanence, if other relationships don't? [Punzo] |
Full Idea: What is the reason for demanding permanence in the relationship of sexual partners when we do not see such permanence as being importance to other human relationships? | |
From: Vincent C. Punzo (Morality and Human Sexuality [1969], p.220) | |
A reaction: The distinction may not be that simple. 'Loyalty' must certainly be mentioned. Friends can legitimately drift apart, but to desert a close friend at a time of great need might be as great a crime as adultery. When is loyalty particularly needed? |
20891 | Does engaging in sexual intercourse really need no more thought than playing tennis? [Punzo] |
Full Idea: It seems strange for a man and a woman to give no more thought to the question of whether they should engage in sexual intercourse than to the question of whether they shoud play tennis. | |
From: Vincent C. Punzo (Morality and Human Sexuality [1969], p.221) | |
A reaction: This strikes me as a reasonable point, but times have moved on since 1969, and for plenty of people nowadays playing tennis is a bigger issue than having sex, because of the time, equipment and effort involved. |