66 ideas
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
| 9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
| 9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
| 9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
| 9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| 9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
| 9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
| 9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
| 9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
| 9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
| 9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| 9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
| 9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
| 9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
| 9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
| 9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
| 9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
| 9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
| 9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
| 9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| 9630 | The most brilliant formalist was Hilbert [Brown,JR] |
| 9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
| 9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
| 9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| 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] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |