24 ideas
19740 | A very hungry man cannot choose between equidistant piles of food [Aristotle] |
10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
398 | Each thing that has a function is for the sake of that function [Aristotle] |
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] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
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] |
402 | The Earth must be spherical, because it casts a convex shadow on the moon [Aristotle] |
403 | The earth must be round and of limited size, because moving north or south makes different stars visible [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] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |