5 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 |
22518 | The actual must be possible, because it occurred [Aristotle] |
Full Idea: Actual events are evidently possible, otherwise they would not have occurred. | |
From: Aristotle (The Poetics [c.347 BCE], 1451b18) | |
A reaction: [quoted online by Peter Adamson] Seems like common sense, but it's important to have Aristotle assert it. |
16566 | Poetry is more philosophic than history, as it concerns universals, not particulars [Aristotle] |
Full Idea: Poetry is something more philosophic and of graver import than history, since its statements are rather of universals, whereas those of history are singulars. | |
From: Aristotle (The Poetics [c.347 BCE], 1451b05) | |
A reaction: Hm. Characters in great novels achieve universality by being representated very particularly. Great depth of mind seems required to be a poet, but less so for a historian (though there is, I presume, no upward limit on the possible level of thought). |
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. |