49 ideas
| 14179 | The finest branch of wisdom is justice and moderation in ordering states and families [Plato] |
| 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] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 18190 | Completed infinities resulted from giving foundations to calculus [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] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [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] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic 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] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [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] |
| 1607 | Diotima said the Forms are the objects of desire in philosophical discourse [Plato, by Roochnik] |
| 15642 | If kinds depend only on what can be observed, many underlying essences might produce the same kind [Eagle] |
| 15645 | Nominal essence are the observable properties of things [Eagle] |
| 15643 | Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle] |
| 174 | True opinion without reason is midway between wisdom and ignorance [Plato] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 180 | We call a person the same throughout life, but all their attributes change [Plato] |
| 181 | Only the gods stay unchanged; we replace our losses with similar acquisitions [Plato] |
| 173 | Beauty and goodness are the same [Plato] |
| 172 | Love of ugliness is impossible [Plato] |
| 4026 | Beauty is harmony with what is divine, and ugliness is lack of such harmony [Plato] |
| 184 | Progress goes from physical beauty, to moral beauty, to the beauty of knowledge, and reaches absolute beauty [Plato] |
| 183 | Stage two is the realisation that beauty of soul is of more value than beauty of body [Plato] |
| 171 | Music is a knowledge of love in the realm of harmony and rhythm [Plato] |
| 14177 | Love assists men in achieving merit and happiness [Plato] |
| 179 | Love is desire for perpetual possession of the good [Plato] |
| 176 | Love follows beauty, wisdom is exceptionally beautiful, so love follows wisdom [Plato] |
| 177 | If a person is good they will automatically become happy [Plato] |
| 14178 | Happiness is secure enjoyment of what is good and beautiful [Plato] |
| 170 | The only slavery which is not dishonourable is slavery to excellence [Plato] |
| 182 | The first step on the right path is the contemplation of physical beauty when young [Plato] |
| 15641 | Kinds are fixed by the essential properties of things - the properties that make it that kind of thing [Eagle] |
| 175 | Gods are not lovers of wisdom, because they are already wise [Plato] |