45 ideas
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
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] |