64 ideas
| 10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
| 10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
| 18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
| 7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
| 10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
| 10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
| 13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
| 10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| 10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| 10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
| 10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| 10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| 13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
| 10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
| 10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
| 7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| 10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
| 10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
| 10833 | Many concepts can only be expressed by second-order logic [Boolos] |
| 10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
| 10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| 10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
| 10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 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] |