4 ideas
8754 | Logic is dependent on mathematics, not the other way round [Heyting, by Shapiro] |
Full Idea: Heyting (the intuitionist pupil of Brouwer) said that 'logic is dependent on mathematics', not the other way round. | |
From: report of Arend Heyting (Intuitionism: an Introduction [1956]) by Stewart Shapiro - Thinking About Mathematics 7.3 | |
A reaction: To me, this claim makes logicism sound much more plausible, as I don't see how mathematics could get beyond basic counting without a capacity for logical thought. Logic runs much deeper, psychologically and metaphysically. |
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. |
16591 | Prime matter is nothing but its parts [Vanini] |
Full Idea: The whole of prime matter, considered as prime matter, is nothing other than its parts. | |
From: Julio Cesare Vanini (Amphitheatrum [1615], Ex 5:p.28), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.2 | |
A reaction: This is a late scholastic writer rejecting the traditional (and obscure) prime matter with the new corpuscularian approach. It signals the end of the Greek concept of matter. |
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. |