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. |
| 5998 | From the necessity of the past we can infer the impossibility of what never happens [Diod.Cronus, by White,MJ] |
| Full Idea: Diodorus' Master Argument inferred that since what is past (i.e. true in the past) is necessary, and the impossible cannot follow from the possible, that therefore if something neither is nor ever will be the case, then it is impossible. | |
| From: report of Diodorus Cronus (fragments/reports [c.300 BCE]) by Michael J. White - Diodorus Cronus | |
| A reaction: The argument is, apparently, no longer fully clear, but it seems to imply determinism, or at least a rejection of the idea that free will and determinism are compatible. (Epictetus 2.19) |
| 20832 | The Master Argument seems to prove that only what will happen is possible [Diod.Cronus, by Epictetus] |
| Full Idea: The Master Argument: these conflict 1) what is past and true is necessary, 2) the impossible does not follow from the possible, 3) something possible neither is nor will be true. Hence only that which is or will be true is possible. | |
| From: report of Diodorus Cronus (fragments/reports [c.300 BCE]) by Epictetus - The Discourses 2.19.1 | |
| A reaction: [Epictetus goes on to discuss views about which of the three should be given up] It is possible there will be a sea fight tomorrow; tomorrow comes, and no sea fight; so there was necessarily no sea fight; so the impossible followed from the possible. |
| 14304 | Conditionals are true when the antecedent is true, and the consequent has to be true [Diod.Cronus] |
| Full Idea: The connected (proposition) is true when it begins with true and neither could nor can end with false. | |
| From: Diodorus Cronus (fragments/reports [c.300 BCE]), quoted by Stephen Mumford - Dispositions 03.4 | |
| A reaction: [Mumford got the quote from Bochenski] This differs from the truth-functional account because it says nothing about when the antecedent is false, which fits in also with the 'supposition' view, where A is presumed. This idea adds necessity. |
| 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? |
| 6024 | Thought is unambiguous, and you should stick to what the speaker thinks they are saying [Diod.Cronus, by Gellius] |
| Full Idea: No one says or thinks anything ambiguous, and nothing should be held to be being said beyond what the speaker thinks he is saying. | |
| From: report of Diodorus Cronus (fragments/reports [c.300 BCE]) by Aulus Gellius - Noctes Atticae 11.12.2 | |
| A reaction: A key argument in favour of propositions, implied in this remark, is that propositions are never ambiguous, though the sentences expressing them may be |