10 ideas
| 18200 | Very large sets should be studied in an 'if-then' spirit [Putnam] |
| Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example), should today be investigated in an 'if-then' spirit. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.347), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Quine says the large sets should be regarded as 'uninterpreted'. |
| 18199 | Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam] |
| Full Idea: We may say that indispensability is a pretty strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.346), quoted by Penelope Maddy - Naturalism in Mathematics II.2 |
| 8857 | We must quantify over numbers for science; but that commits us to their existence [Putnam] |
| Full Idea: Quantification over mathematical entities is indispensable for science..., therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.57), quoted by Stephen Yablo - Apriority and Existence | |
| A reaction: I'm not surprised that Hartry Field launched his Fictionalist view of mathematics in response to such a counterintuitive claim. I take it we use numbers to slice up reality the way we use latitude to slice up the globe. No commitment to lines! |
| 12295 | 3-D says things are stretched in space but not in time, and entire at a time but not at a location [Fine,K] |
| Full Idea: Three-dimensionalist think a thing is somehow 'stretched out' through its location at a given time though not through the period during which it exists, and it is present in its entirety at a moment when it exists though not at a position of its location. | |
| From: Kit Fine (In Defence of Three-Dimensionalism [2006], p.1) | |
| A reaction: This definition is designed to set up Fine's defence of the 3-D view, by showing that various dubious asymmetries show up if you do not respect the distinctions offered by the 3-D view. |
| 12298 | Genuine motion, rather than variation of position, requires the 'entire presence' of the object [Fine,K] |
| Full Idea: In order to have genuine motion, rather than mere variation in position, it is necessary that the object should be 'entirely present' at each moment of the change. Thus without entire presence, or existence, genuine motion will not be possible. | |
| From: Kit Fine (In Defence of Three-Dimensionalism [2006], p.6) | |
| A reaction: See Idea 4786 for a rival view of motion. Of course, who says we have to have Kit Fine's 'genuine' motion, if some sort of ersatz motion still gets you to work in the morning? |
| 12296 | 4-D says things are stretched in space and in time, and not entire at a time or at a location [Fine,K] |
| Full Idea: Four-dimensionalists have thought that a material thing is as equally 'stretched out' in time as it is in space, and that there is no special way in which it is entirely present at a moment rather than at a position. | |
| From: Kit Fine (In Defence of Three-Dimensionalism [2006], p.1) | |
| A reaction: Compare his definition of 3-D in Idea 12295. The 4-D is contrary to our normal way of thinking. Since I don't think the future exists, I presume that if I am a 4-D object then I have to say that I don't yet exist, and I disapprove of such talk. |
| 18882 | You can ask when the wedding was, but not (usually) when the bride was [Fine,K, by Simons] |
| Full Idea: Fine says it is acceptable to ask when a wedding was and where it was, and it is acceptable to ask or state where the bride was (at a certain time), but not when she was. | |
| From: report of Kit Fine (In Defence of Three-Dimensionalism [2006], p.18) by Peter Simons - Modes of Extension: comment on Fine p.18 | |
| A reaction: This is aimed at three-dimensionalists who seem to think that a bride is a prolonged event, just as a wedding is. Fine is, interestingly, invoking ordinary language. When did the wedding start and end? When was the bride's birth and death? |
| 12297 | Three-dimensionalist can accept temporal parts, as things enduring only for an instant [Fine,K] |
| Full Idea: Even if one is a three-dimensionalist, one might affirm the existence of temporal parts, on the grounds that everything merely endures for an instant. | |
| From: Kit Fine (In Defence of Three-Dimensionalism [2006], p.2) | |
| A reaction: This seems an important point, as belief in temporal parts is normally equated with four-dimensionalism (see Idea 12296). The idea is that a thing might be 'entirely present' at each instant, only to be replaced by a simulacrum. |
| 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. |