41 ideas
22496 | Wisdom only implies the knowledge achievable in any normal lifetime [Foot] |
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] |
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] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
23694 | All criterions of practical rationality derive from goodness of will [Foot] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
23686 | Moral reason is not just neutral, because morality is part of the standard of rationality [Foot, by Hacker-Wright] |
23693 | Practical rationality must weigh both what is morally and what is non-morally required [Foot] |
23687 | Moral virtues arise from human nature, as part of what makes us good human beings [Foot, by Hacker-Wright] |
22493 | Sterility is a human defect, but the choice to be childless is not [Foot] |
22492 | Virtues are as necessary to humans as stings are to bees [Foot] |
22491 | Moral evaluations are not separate from facts, but concern particular facts about functioning [Foot] |
22497 | Deep happiness usually comes from the basic things in life [Foot] |
22498 | Happiness is enjoying the pursuit and attainment of right ends [Foot] |
23695 | Good actions can never be justified by the good they brings to their agent [Foot] |
22499 | We all know that just pretending to be someone's friend is not the good life [Foot] |
22495 | Someone is a good person because of their rational will, not their body or memory [Foot] |
22502 | Refraining from murder is not made good by authenticity or self-fulfilment [Foot] |