4 ideas
17606 | Axioms reveal the underlying assumptions, and reveal relationships between different areas [Kline] |
Full Idea: The axiomatic method ....revealed precisely what assumptions underlie each branch [of mathematics] and made possible the comparison and clarification of the relationships of various branches. | |
From: Morris Kline (Mathematical Thought from Ancient to Modern Times [1972], p.1027), quoted by Penelope Maddy - Defending the Axioms 1.3 | |
A reaction: I take this to be the 'fruitfulness' which marks out the discovery of the essence of something. |
20436 | Art leads to mental health, and mental clarity [Beardsley,M, by Carroll,N] |
Full Idea: Beardsley says aesthetic experience relieves tensions and quiet destructive emotions. It also aids us in sorting out the jumble in the flow of consciousness, by virtue of its tendencies toward heightened clarity and coherence. | |
From: report of Monroe Beardsley (Aesthetics: problems in the philosophy of criticism [1958]) by Noël Carroll - Monroe Beardsley p.162-3 | |
A reaction: I find this claim highly implausible. I like art, but I feel neither healthier nor clearer after experiencing it. |
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. |