5 ideas
| 15938 | Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett] |
| Full Idea: The platonist destroys the whole essence of infinity, which lies in the conception of a structure which is always in growth, precisely because the process of construction is never completed. | |
| From: Michael Dummett (Elements of Intuitionism [1977], p.57), quoted by Thomas J. McKay - Plural Predication | |
| A reaction: I don't warm to intuitionism, but I warm to this conception of infinity. Completed infinities are convenient reifications for mathematicians. |
| 15939 | For intuitionists it is constructed proofs (which take time) which make statements true [Dummett] |
| Full Idea: For an intuitionist a mathematical statement is rendered true or false by a proof or disproof, that is, by a construction, and constructions are effected in time. | |
| From: Michael Dummett (Elements of Intuitionism [1977], p.336), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
| A reaction: Lavine is quoting this to draw attention to the difficulties of thinking of it as all taking place 'in time', especially when dealing with infinities. |
| 3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
| Full Idea: Even the gods cannot strive against necessity. | |
| From: report of Pittacus (reports [c.610 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 01.5.4 |
| 12719 | Clearly, force is that from which action follows, when unimpeded [Leibniz] |
| Full Idea: The notion of force is as clear as that of action and passion, because it is that from which action follows when nothing prevents it. | |
| From: Gottfried Leibniz (Letters to Paul Pellison-Fontinier [1691], A1.6.226), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 4 | |
| A reaction: For Leibniz, force seems to be a metaphysical notion, rather than a feature of the physical world. I take it to be the bottom level of explanation, and it equates with Aristotelian form and essence. |
| 12720 | Time doesn't exist, since its parts don't coexist [Leibniz] |
| Full Idea: Time never exists, since all of its parts never exist together. | |
| From: Gottfried Leibniz (Letters to Paul Pellison-Fontinier [1691], A1.6.226), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 4 | |
| A reaction: The problem here is that he seems to be admitting that time has 'parts'. Can something have parts and not exist? Events will also fail to exist by this criterion, though we could hardly deny that events (or some such) 'happen'. |