73 ideas
| 12274 | Begin examination with basics, and subdivide till you can go no further [Aristotle] |
| 192 | Only one thing can be contrary to something [Plato] |
| 12260 | Dialectic starts from generally accepted opinions [Aristotle] |
| 12291 | There can't be one definition of two things, or two definitions of the same thing [Aristotle] |
| 12292 | Definitions are easily destroyed, since they can contain very many assertions [Aristotle] |
| 12272 | We describe the essence of a particular thing by means of its differentiae [Aristotle] |
| 12279 | The differentia indicate the qualities, but not the essence [Aristotle] |
| 12283 | In definitions the first term to be assigned ought to be the genus [Aristotle] |
| 12289 | The genera and the differentiae are part of the essence [Aristotle] |
| 12261 | Differentia are generic, and belong with genus [Aristotle] |
| 12263 | 'Genus' is part of the essence shared among several things [Aristotle] |
| 12285 | The definition is peculiar to one thing, not common to many [Aristotle] |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 11261 | Puzzles arise when reasoning seems equal on both sides [Aristotle] |
| 12273 | Unit is the starting point of number [Aristotle] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| 18182 | The extension of concepts is not important to me [Maddy] |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 12267 | There are ten categories: essence, quantity, quality, relation, place, time, position, state, activity, passivity [Aristotle] |
| 12282 | An individual property has to exist (in past, present or future) [Aristotle] |
| 12264 | An 'accident' is something which may possibly either belong or not belong to a thing [Aristotle] |
| 190 | If asked whether justice itself is just or unjust, you would have to say that it is just [Plato] |
| 12280 | Genus gives the essence better than the differentiae do [Aristotle] |
| 13269 | In the case of a house the parts can exist without the whole, so parts are not the whole [Aristotle] |
| 12284 | Everything that is has one single essence [Aristotle] |
| 12262 | An 'idion' belongs uniquely to a thing, but is not part of its essence [Aristotle] |
| 12290 | Destruction is dissolution of essence [Aristotle] |
| 12286 | If two things are the same, they must have the same source and origin [Aristotle] |
| 12266 | 'Same' is mainly for names or definitions, but also for propria, and for accidents [Aristotle] |
| 12287 | Two identical things have the same accidents, they are the same; if the accidents differ, they're different [Aristotle] |
| 12288 | Numerical sameness and generic sameness are not the same [Aristotle] |
| 12259 | Reasoning is when some results follow necessarily from certain claims [Aristotle] |
| 20184 | The only real evil is loss of knowledge [Plato] |
| 20185 | The most important things in life are wisdom and knowledge [Plato] |
| 12271 | Induction is the progress from particulars to universals [Aristotle] |
| 12293 | We say 'so in cases of this kind', but how do you decide what is 'of this kind'? [Aristotle] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 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] |
| 189 | If we punish wrong-doers, it shows that we believe virtue can be taught [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] |
| 12277 | Friendship is preferable to money, since its excess is preferable [Aristotle] |
| 12276 | Justice and self-control are better than courage, because they are always useful [Aristotle] |
| 12275 | We value friendship just for its own sake [Aristotle] |
| 12281 | Man is intrinsically a civilized animal [Aristotle] |
| 12265 | All water is the same, because of a certain similarity [Aristotle] |
| 12278 | 'Being' and 'oneness' are predicated of everything which exists [Aristotle] |