38 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] |
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] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18207 | Maybe applications of continuum mathematics are all idealisations [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] |
20429 | Most of us are too close to our own motives to understand them [Fry] |
20424 | Imaginative life requires no action, so new kinds of perception and values emerge in art [Fry] |
20427 | Everyone reveals an aesthetic attitude, looking at something which only exists to be seen [Fry] |
20433 | 'Beauty' can either mean sensuous charm, or the aesthetic approval of art (which may be ugly) [Fry] |
20430 | In life we neglect 'cosmic emotion', but it matters, and art brings it to the fore [Fry] |
20431 | Art needs a mixture of order and variety in its sensations [Fry] |
20423 | If graphic arts only aim at imitation, their works are only trivial ingenious toys [Fry] |
20428 | Popular opinion favours realism, yet most people never look closely at anything! [Fry] |
20432 | When viewing art, rather than flowers, we are aware of purpose, and sympathy with its creator [Fry] |
20425 | In the cinema the emotions are weaker, but much clearer than in ordinary life [Fry] |
20426 | For pure moralists art must promote right action, and not just be harmless [Fry] |
467 | A virtue is a combination of intelligence, strength and luck [Ion] |