4 ideas
| 9545 | Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara] |
| Full Idea: Near the end of his life, Frege completely abandoned his logicism, and came to the conclusion that the source of our arithmetical knowledge is what he called 'the Geometrical Source of Knowledge'. | |
| From: report of Gottlob Frege (Sources of Knowledge of Mathematics [1922]) by Charles Chihara - A Structural Account of Mathematics Intro n3 | |
| A reaction: We have, rather crucially, lost touch with the geometrical origins of arithmetic (such as 'square' numbers), which is good news for the practice of mathematics, but probably a disaster for the philosophy of the subject. |
| 7296 | 'Grue' is not a colour [Milsted] |
| Full Idea: 'Grue' is not a colour. | |
| From: Tom Milsted (talk [2006]), quoted by PG - Db (ideas) | |
| A reaction: This simple observation strikes me as rather crucial in assessing Goodman's paradox. Blue is a colour, but grue is some sort of behaviour. Blue is a secondary quality, but grue seems to be a primary quality. |
| 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. |