25 ideas
19740 | A very hungry man cannot choose between equidistant piles of food [Aristotle] |
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
398 | Each thing that has a function is for the sake of that function [Aristotle] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
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] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
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] |