68 ideas
| 12124 | Metaphysics is the best knowledge, because it is the simplest [Bacon] |
| 12123 | Natural history supports physical knowledge, which supports metaphysical knowledge [Bacon] |
| 12119 | Physics studies transitory matter; metaphysics what is abstracted and necessary [Bacon] |
| 12120 | Physics is of material and efficient causes, metaphysics of formal and final causes [Bacon] |
| 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] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [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] |
| 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] |
| 12121 | We don't assume there is no land, because we can only see sea [Bacon] |
| 12117 | Science moves up and down between inventions of causes, and experiments [Bacon] |
| 12127 | Many different theories will fit the observed facts [Bacon] |
| 12126 | People love (unfortunately) extreme generality, rather than particular knowledge [Bacon] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 20489 | Human beings can never really flourish in a long-term state of nature [Wolff,J] |
| 20483 | Collective rationality is individuals doing their best, assuming others all do the same [Wolff,J] |
| 20532 | Should love be the first virtue of a society, as it is of the family? [Wolff,J] |
| 20490 | For utilitarians, consent to the state is irrelevant, if it produces more happiness [Wolff,J] |
| 20493 | Social contract theory has the attracton of including everyone, and being voluntary [Wolff,J] |
| 20494 | Maybe voting in elections is a grant of legitimacy to the winners [Wolff,J] |
| 20500 | We can see the 'general will' as what is in the general interest [Wolff,J] |
| 20497 | How can dictators advance the interests of the people, if they don't consult them about interests? [Wolff,J] |
| 20506 | 'Separation of powers' allows legislative, executive and judicial functions to monitor one another [Wolff,J] |
| 20530 | Political choice can be by utility, or maximin, or maximax [Wolff,J] |
| 20487 | A realistic and less utopian anarchism looks increasingly like liberal democracy [Wolff,J] |
| 20488 | It is hard for anarchists to deny that we need experts [Wolff,J] |
| 20529 | Utilitarianism probably implies a free market plus welfare [Wolff,J] |
| 20510 | A system of democracy which includes both freedom and equality is almost impossible [Wolff,J] |
| 20511 | Democracy expresses equal respect (which explains why criminals forfeit the vote) [Wolff,J] |
| 20502 | Democracy has been seen as consistent with many types of inequality [Wolff,J] |
| 20496 | A true democracy could not tolerate slavery, exploitation or colonialism [Wolff,J] |
| 20498 | We should decide whether voting is for self-interests, or for the common good [Wolff,J] |
| 20499 | Condorcet proved that sensible voting leads to an emphatically right answer [Wolff,J] |
| 20509 | Occasional defeat is acceptable, but a minority that is continually defeated is a problem [Wolff,J] |
| 20524 | Market prices indicate shortages and gluts, and where the profits are to be made [Wolff,J] |
| 20518 | Liberty principles can't justify laws against duelling, incest between siblings and euthanasia [Wolff,J] |
| 20531 | Either Difference allows unequal liberty, or Liberty makes implementing Difference impossible [Wolff,J] |
| 20526 | Utilitarians argue for equal distribution because of diminishing utility of repetition [Wolff,J] |
| 20528 | Difference Principle: all inequalities should be in favour of the disadvantaged [Wolff,J] |
| 20503 | Political equality is not much use without social equality [Wolff,J] |
| 20512 | Standard rights: life, free speech, assembly, movement, vote, stand (plus shelter, food, health?) [Wolff,J] |
| 20513 | If natural rights are axiomatic, there is then no way we can defend them [Wolff,J] |
| 20514 | If rights are natural, rather than inferred, how do we know which rights we have? [Wolff,J] |
| 20522 | Utilitarians might say property ownership encourages the best use of the land [Wolff,J] |
| 20534 | Rights and justice are only the last resorts of a society, something to fall back on [Wolff,J] |
| 20492 | Following some laws is not a moral matter; trivial traffic rules, for example [Wolff,J] |
| 12125 | Teleological accounts are fine in metaphysics, but they stop us from searching for the causes [Bacon] |
| 12118 | Essences are part of first philosophy, but as part of nature, not part of logic [Bacon] |