21 ideas
19740 | A very hungry man cannot choose between equidistant piles of food [Aristotle] |
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
10283 | A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W] |
10284 | There are three different standard presentations of semantics [Hodges,W] |
10285 | I |= φ means that the formula φ is true in the interpretation I [Hodges,W] |
10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W] |
10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W] |
10287 | If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
398 | Each thing that has a function is for the sake of that function [Aristotle] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
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] |
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] |