30 ideas
| 19740 | A very hungry man cannot choose between equidistant piles of food [Aristotle] |
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| 8195 | Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett] |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| 8194 | Surely there is no exact single grain that brings a heap into existence [Dummett] |
| 10833 | Many concepts can only be expressed by second-order logic [Boolos] |
| 8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
| 8198 | A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett] |
| 8192 | I no longer think what a statement about the past says is just what can justify it [Dummett] |
| 8199 | The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett] |
| 8193 | Verification is not an individual but a collective activity [Dummett] |
| 8189 | Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett] |
| 8191 | The truth-conditions theory must get agreement on a conception of truth [Dummett] |
| 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] |
| 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] |
| 8197 | Maybe past (which affects us) and future (which we can affect) are both real [Dummett] |
| 8196 | The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett] |
| 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] |