4 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 |
20082 | Bodily movements are not actions, which are really the tryings within bodily movement [Hornsby, by Stout,R] |
Full Idea: Hornsby claims the basic description of action is in terms of trying, that all actions (even means of doing other actions) are actions of trying, and that tryings (and therefore actions) are interior to bodily movements (which are thus not essential). | |
From: report of Jennifer Hornsby (Actions [1980]) by Rowland Stout - Action 9 'Trying' | |
A reaction: [compression of his summary] There is no regress with explaining the 'action' of trying, because it is proposed that trying is the most basic thing in all actions. If you are paralysed, your trying does not result in action. Too mentalistic? |
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. |