7 ideas
| 15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
| Full Idea: Zermelo realised that the Axiom of Choice (based on arbitrary functions) could be used to 'count', in the Cantorian sense, those collections that had given Cantor so much trouble, which restored a certain unity to set theory. | |
| From: report of Ernst Zermelo (Proof that every set can be well-ordered [1904]) by Shaughan Lavine - Understanding the Infinite I |
| 18617 | Substances, unlike aggregates, can survive a change of parts [Mumford] |
| Full Idea: Substances can survive a change in their parts in a way that a mere aggregate of parts. | |
| From: Stephen Mumford (Metaphysics: a very short introduction [2012], 3) | |
| A reaction: A simple but very important idea. If we then distinguish between 'substances' and 'aggregates' we get a much clearer grip on things. Is the Ship of Theseus a substance or an aggregate? There is no factual answer to that. What do you want to explain? |
| 18618 | Maybe possibilities are recombinations of the existing elements of reality [Mumford] |
| Full Idea: It has been suggested that we could think of possibilities as recombinations of all the existing elements of reality. | |
| From: Stephen Mumford (Metaphysics: a very short introduction [2012], 8) | |
| A reaction: [Armstrong 1989 is the source] The obvious problem would be that the existence of an entirely different reality would be impossible, if this was all possibility could be. It seems to cramp the style of the possible too much. Are properties elements? |
| 18619 | Combinatorial possibility has to allow all elements to be combinable, which seems unlikely [Mumford] |
| Full Idea: The combinatorial account only works if you allow that the elements are recombinable. ...But could Lincoln really have been green? It seems possible that you could jump to the moon, unless we impose some restrictions. | |
| From: Stephen Mumford (Metaphysics: a very short introduction [2012], 8) | |
| A reaction: Mumford suggests different combination rules for logical and natural possibility. The general objection is that combinatorial possibility is too permissive - which it clearly is. |
| 18620 | Combinatorial possibility relies on what actually exists (even over time), but there could be more [Mumford] |
| Full Idea: Can combinatorial possibility deliver enough possibilities? It uses the existing elements, but there might have been one more particular or one more property. Even extended over time, the elements seem finite, yet there could have been more. | |
| From: Stephen Mumford (Metaphysics: a very short introduction [2012], 8) | |
| A reaction: [compressed] One objection is that the theory allows too much, and now the objection is that it allows too little. Both objections are correct, so that's the end of that. But I admire the attempt to base modality on actuality. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |