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. |
| 14288 | 'If A,B' affirms that A⊃B, and also that this wouldn't change if A were certain [Jackson, by Edgington] |
| Full Idea: According to Jackson, in asserting 'If A,B' the speaker expresses his belief that A⊃B, and also indicates that this belief is 'robust' with respect to the antecedent A - the speaker would not abandon A⊃B if he were to learn that A. | |
| From: report of Frank Jackson (On Assertion and Indicative Conditionals [1979]) by Dorothy Edgington - Conditionals (Stanf) 4.2 | |
| A reaction: The point is that you must not believe A⊃B solely on the dubious grounds of ¬A. This is 'to ensure an assertable conditional is fit for modus ponens' - that is, that you really will affirm B when you learn that A is true. Nice idea. |
| 13769 | Conditionals are truth-functional, but should only be asserted when they are confident [Jackson, by Edgington] |
| Full Idea: Jackson holds that conditionals are truth-functional, but are governed by rules of assertability, rather like 'but' compared to 'and'. The belief must be 'robust' - the speaker would not abandon his belief that A⊃B if he were to learn that A. | |
| From: report of Frank Jackson (On Assertion and Indicative Conditionals [1979]) by Dorothy Edgington - Conditionals 17.3.2 | |
| A reaction: This seems to spell out more precisely the pragmatic approach to conditionals pioneered by Grice, in Idea 13767. The idea is make conditionals 'fit for modus ponens'. They mustn't just be based on a belief that ¬A. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |