29 ideas
192 | Only one thing can be contrary to something [Plato] |
13430 | Infinity: there is an infinity of distinguishable individuals [Ramsey] |
13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
13427 | Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey] |
23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
13334 | Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey] |
23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
190 | If asked whether justice itself is just or unjust, you would have to say that it is just [Plato] |
20185 | The most important things in life are wisdom and knowledge [Plato] |
20184 | The only real evil is loss of knowledge [Plato] |
22328 | I just confront the evidence, and let it act on me [Ramsey] |
22325 | A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey] |
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] |
197 | Some pleasures are not good, and some pains are not evil [Plato] |
200 | People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [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] |