5 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. |
| 6003 | Galen showed by experiment that the brain controls the body [Galen, by Hankinson] |
| Full Idea: Galen established by experiments in neural anatomy that the brain really is, contra the Stoics and Aristotelians, the body's control centre. | |
| From: report of Galen (On Hippocrates and Plato [c.170]) by R.J. Hankinson - Galen (damaged) | |
| A reaction: And about time too. This is one of the most significant events in the development of human understanding. No one has been able to go back to the old view, even Descartes, no matter how much they may long to do so. |
| 6030 | Each part of the soul has its virtue - pleasure for appetite, success for competition, and rectitude for reason [Galen] |
| Full Idea: We have by nature these three appropriate relationships, corresponding to each form of the soul's parts - to pleasure because of the appetitive part, to success because of the competitive part, and to rectitude because of the rational part. | |
| From: Galen (On Hippocrates and Plato [c.170], 5.5.8) | |
| A reaction: This is a nice combination of Plato's tripartite theory of soul (in 'Republic') and Aristotle's derivation of virtues from functions. Presumably, though, reason should master the other two, and there is nothing in Galen's idea to explain this. |
| 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. |