5 ideas
| 9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
| Full Idea: The terms 'set' and 'is a member of' are primitives of Zermelo's 1908 axiomatization of set theory. They are not given model-theoretic analyses or definitions. | |
| From: report of Ernst Zermelo (works [1920]) by Charles Chihara - A Structural Account of Mathematics 7.5 | |
| A reaction: This looks like good practice if you want to work with sets, but not so hot if you are interested in metaphysics. |
| 3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
| Full Idea: For Zermelo's set theory the empty set is zero and the successor of each number is its unit set. | |
| From: report of Ernst Zermelo (works [1920]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280 |
| 23218 | The brain has no responsibility for sensations, which occur in the heart [Aristotle] |
| Full Idea: And of course, the brain is not responsible for any of the sensations at all. The correct view is that the seat and source of sensation is the region of the heart. | |
| From: Aristotle (The Parts of Animals [c.345 BCE]), quoted by Matthew Cobb - The Idea of the Brain 1 | |
| A reaction: [Need a reference] Hippocrates's assertion a century earlier made no impression on the great man. I wish he had been a little more circumspect with his own view. |
| 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. |