33 ideas
| 192 | Only one thing can be contrary to something [Plato] |
| 8472 | Sentential logic is consistent (no contradictions) and complete (entirely provable) [Orenstein] |
| 8476 | Axiomatization simply picks from among the true sentences a few to play a special role [Orenstein] |
| 8480 | S4: 'poss that poss that p' implies 'poss that p'; S5: 'poss that nec that p' implies 'nec that p' [Orenstein] |
| 8474 | Unlike elementary logic, set theory is not complete [Orenstein] |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| 8465 | Mereology has been exploited by some nominalists to achieve the effects of set theory [Orenstein] |
| 8452 | Traditionally, universal sentences had existential import, but were later treated as conditional claims [Orenstein] |
| 8475 | The substitution view of quantification says a sentence is true when there is a substitution instance [Orenstein] |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| 8454 | The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein] |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| 8473 | The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein] |
| 8458 | Just individuals in Nominalism; add sets for Extensionalism; add properties, concepts etc for Intensionalism [Orenstein] |
| 190 | If asked whether justice itself is just or unjust, you would have to say that it is just [Plato] |
| 20184 | The only real evil is loss of knowledge [Plato] |
| 20185 | The most important things in life are wisdom and knowledge [Plato] |
| 8457 | The Principle of Conservatism says we should violate the minimum number of background beliefs [Orenstein] |
| 191 | Everything resembles everything else up to a point [Plato] |
| 8477 | People presume meanings exist because they confuse meaning and reference [Orenstein] |
| 8471 | Three ways for 'Socrates is human' to be true are nominalist, platonist, or Montague's way [Orenstein] |
| 8484 | If two people believe the same proposition, this implies the existence of propositions [Orenstein] |
| 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] |