25 ideas
19740 | A very hungry man cannot choose between equidistant piles of food [Aristotle] |
14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
14240 | The empty set is something, not nothing! [Oliver/Smiley] |
14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
398 | Each thing that has a function is for the sake of that function [Aristotle] |
23104 | Dworkin believed we should promote equality, to increase autonomy [Dworkin, by Kekes] |
23257 | We can treat people as equals, or actually treat them equally [Dworkin, by Grayling] |
18621 | Treating people as equals is the one basic value of all plausible political theories [Dworkin, by Kymlicka] |
394 | An unworn sandal is in vain, but nothing in nature is in vain [Aristotle] |
396 | There has to be some goal, and not just movement to infinity [Aristotle] |
16102 | Aether moves in circles and is imperishable; the four elements perish, and move in straight lines [Aristotle, by Gill,ML] |
17463 | An element is what bodies are analysed into, and won't itself divide into something else [Aristotle] |
399 | If the more you raise some earth the faster it moves, why does the whole earth not move? [Aristotle] |
20918 | Void is a kind of place, so it can't explain place [Aristotle] |
403 | The earth must be round and of limited size, because moving north or south makes different stars visible [Aristotle] |
402 | The Earth must be spherical, because it casts a convex shadow on the moon [Aristotle] |
1498 | Everyone agrees that the world had a beginning, but thinkers disagree over whether it will end [Aristotle] |
395 | It seems possible that there exists a limited number of other worlds apart from this one [Aristotle] |