53 ideas
| 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] |
| 7404 | Nations are not obliged to help one-another, but are obliged not to harm one another [Grotius, by Tuck] |
| 23928 | Good art produces exaltation and detachment [Bell,C] |
| 23922 | The word 'beauty' leads to confusion, because it denotes distinct emotions [Bell,C] |
| 23921 | Our feeling for natural beauty is different from the aesthetic emotion of art [Bell,C] |
| 23929 | We only see landscapes as artistic if we ignore their instrumental value [Bell,C] |
| 23923 | Visual form can create a sublime mental state [Bell,C] |
| 23932 | Art is the expression of an emotion for ultimate reality [Bell,C] |
| 23927 | Aestheticism invites artist to create beauty, but with no indication of how to do it [Bell,C] |
| 8115 | Only artists can discern significant form; other people must look to art to find it [Bell,C, by Gardner] |
| 23924 | Maybe significant form gives us a feeling for ultimate reality [Bell,C] |
| 23931 | Significant form is the essence of art, which I believe expresses an emotion about reality [Bell,C] |
| 20434 | 'Form' is visual relations, and it is 'significant' if it moves us aesthetically; art needs both [Bell,C, by Feagin] |
| 23934 | The only expression art could have is the emotion resulting from pure form [Bell,C] |
| 23925 | Mere copies of pictures are not significant - unless the copies are very exact [Bell,C] |
| 23926 | Art is distinguished by its aesthetic emotion, which produces appropriate form [Bell,C] |
| 23933 | Aesthetic contemplation is the best and most intense mental state [Bell,C] |
| 23935 | Aesthetic experience is an exaltation which increases the possibilities of life [Bell,C] |
| 22691 | Only artistic qualities matter in art, because they also have the highest moral value [Bell,C] |
| 7402 | Everyone has a right of self-preservation, and harming others is usually unjustifiable [Grotius, by Tuck] |
| 21938 | Democracy needs respect for individuality, but the 'community of friends' implies strict equality [Grotius] |
| 19845 | A person is free to renounce their state, as long as it is not a moment of crisis [Grotius, by Rousseau] |
| 22133 | Grotius and Pufendorf based natural law on real (rather than idealised) humanity [Grotius, by Ford,JD] |
| 7406 | A natural right of self-preservation is balanced by a natural law to avoid unnecessary harm [Grotius, by Tuck] |
| 7403 | Grotius ignored elaborate natural law theories, preferring a basic right of self-preservation [Grotius, by Tuck] |
| 23585 | It is permissible in a just cause to capture a place in neutral territory [Grotius] |
| 6892 | Moral principles have some validity without a God commanding obedience [Grotius, by Mautner] |
| 23930 | Religion sees infinite value in some things, and irrelevance in the rest [Bell,C] |