48 ideas
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
20489 | Human beings can never really flourish in a long-term state of nature [Wolff,J] |
20532 | Should love be the first virtue of a society, as it is of the family? [Wolff,J] |
20483 | Collective rationality is individuals doing their best, assuming others all do the same [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] |
23565 | Our obedience to the king erases any crimes we commit for him [Shakespeare] |