38 ideas
| 192 | Only one thing can be contrary to something [Plato] |
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| 190 | If asked whether justice itself is just or unjust, you would have to say that it is just [Plato] |
| 19712 | Maybe there is plain 'animal' knowledge, and clearly justified 'reflective' knowledge [Vahid] |
| 20185 | The most important things in life are wisdom and knowledge [Plato] |
| 20184 | The only real evil is loss of knowledge [Plato] |
| 19703 | Epistemic is normally marked out from moral or pragmatic justifications by its truth-goal [Vahid] |
| 19705 | 'Mentalist' internalism seems to miss the main point, if it might not involve an agent's access [Vahid] |
| 19706 | Strong access internalism needs actual awareness; weak versions need possibility of access [Vahid] |
| 19707 | Maybe we need access to our justification, and also to know why it justifies [Vahid] |
| 19709 | Internalism in epistemology over-emphasises deliberation about beliefs [Vahid] |
| 19704 | Externalism may imply that identical mental states might go with different justifications [Vahid] |
| 19710 | With a counterfactual account of the causal theory, we get knowledge as tracking or sensitive to truth [Vahid] |
| 19711 | Externalism makes the acquisition of knowledge too easy? [Vahid] |
| 191 | Everything resembles everything else up to a point [Plato] |
| 203 | Courage is knowing what should or shouldn't be feared [Plato] |
| 202 | No one willingly and knowingly embraces evil [Plato] |
| 193 | Some things are good even though they are not beneficial to men [Plato] |
| 200 | People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato] |
| 197 | Some pleasures are not good, and some pains are not evil [Plato] |
| 188 | Socrates did not believe that virtue could be taught [Plato] |
| 204 | Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato] |
| 189 | If we punish wrong-doers, it shows that we believe virtue can be taught [Plato] |