7 ideas
| 15923 | Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine] |
| Full Idea: Poincaré rejected the actual infinite. He viewed mathematics that is apparently concerned with the actual infinite as actually concerning the finite linguistic definitions the putatively describe actually infinite objects. | |
| From: report of Henri Poincaré (On the Nature of Mathematical Reasoning [1894]) by Shaughan Lavine - Understanding the Infinite |
| 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. |
| 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 |
| 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. |