106 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] |
| 22355 | In the realist view, the real external world explains how it (and perceptions of it) are possible [Williams,B] |
| 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] |
| 23283 | Necessity implies possibility, but in experience it matters which comes first [Williams,B] |
| 4244 | It is very confused to deduce a nonrelativist morality of universal toleration from relativism [Williams,B] |
| 4243 | Our ability to react to an alien culture shows that ethical thought extends beyond cultural boundaries [Williams,B] |
| 3238 | 'Dead person' isn't a contradiction, so 'person' is somewhat vague [Williams,B] |
| 3239 | You can only really love a person as a token, not as a type [Williams,B] |
| 7946 | The memory criterion has a problem when one thing branches into two things [Williams,B, by Macdonald,C] |
| 2181 | It is an absurd Kantian idea that at the limit rationality and freedom coincide [Williams,B] |
| 2176 | There is only a problem of free will if you think the notion of 'voluntary' can be metaphysically deepened [Williams,B] |
| 24008 | Reference to a person's emotions is often essential to understanding their actions [Williams,B] |
| 24009 | Moral education must involve learning about various types of feeling towards things [Williams,B] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 4317 | We judge weakness of will by an assessment after the event is concluded [Williams,B, by Cottingham] |
| 9284 | Reasons are 'internal' if they give a person a motive to act, but 'external' otherwise [Williams,B] |
| 2174 | Responsibility involves cause, intention, state of mind, and response after the event [Williams,B] |
| 22455 | Many ethical theories neglect the power of regretting the ought not acted upon [Williams,B] |
| 8239 | If the King likes music then there is hope for the state [Mengzi (Mencius)] |
| 4114 | Philosophers try to produce ethical theories because they falsely assume that ethics can be simple [Williams,B] |
| 22453 | Moral conflicts have a different feeling and structure from belief conflicts [Williams,B, by Foot] |
| 22454 | We tolerate inconsistency in ethics but not in other beliefs (which reflect an independent order) [Williams,B, by Foot] |
| 22450 | If moral systems can't judge other moral systems, then moral relativism is true [Williams,B, by Foot] |
| 2178 | In bad actions, guilt points towards victims, and shame to the agent [Williams,B] |
| 20168 | Blame usually has no effect if the recipient thinks it unjustified [Williams,B] |
| 20167 | Blame partly rests on the fiction that blamed agents always know their obligations [Williams,B] |
| 4128 | Intuitionism has been demolished by critics, and no longer looks interesting [Williams,B] |
| 4366 | We can't accept Aristotle's naturalism about persons, because it is normative and unscientific [Williams,B, by Hursthouse] |
| 4132 | The category of person is a weak basis for ethics, because it is not fixed but comes in degrees [Williams,B] |
| 23398 | Human nature is naturally compassionate and good (as a 'sprout'), but people may not be good [Mengzi (Mencius), by Norden] |
| 24007 | Emotivism saw morality as expressing emotions, and influencing others' emotions [Williams,B] |
| 4134 | The weakness of prescriptivism is shown by "I simply don't like staying at good hotels" [Williams,B] |
| 4135 | Some ethical ideas, such as 'treachery' and 'promise', seem to express a union of facts and values [Williams,B] |
| 23400 | Righteousness is extending the unthinkable, to reveal what must be done [Mengzi (Mencius)] |
| 22410 | Maybe the unthinkable is a moral category, and considering some options is dishonourable or absurd [Williams,B] |
| 22408 | Consequentialism assumes that situations can be compared [Williams,B] |
| 22411 | For a consequentialist massacring 7 million must be better than massacring 7 million and one [Williams,B] |
| 4120 | It is an error of consequentialism to think we just aim at certain states of affairs; we also want to act [Williams,B] |
| 23282 | If all that matters in morality is motive and intention, that makes moral luck irrelevant [Williams,B] |
| 4252 | Promise keeping increases reliability, by making deliberation focus on something which would be overlooked [Williams,B] |
| 4116 | A weakness of contractual theories is the position of a person of superior ability and power [Williams,B] |
| 2169 | Greek moral progress came when 'virtue' was freed from social status [Williams,B] |
| 4112 | A crucial feature of moral thought is second-order desire - the desire to have certain desires [Williams,B] |
| 24010 | An admirable human being should have certain kinds of emotional responses [Williams,B] |
| 23279 | It is important that a person can change their character, and not just be successive 'selves' [Williams,B] |
| 23280 | Kantians have an poor account of individuals, and insist on impartiality, because they ignore character [Williams,B] |
| 23399 | Each correct feeling relies on an underlying virtue [Mengzi (Mencius)] |
| 8235 | Should a coward who ran fifty paces from a battle laugh at another who ran a hundred? [Mengzi (Mencius)] |
| 3236 | Equality of opportunity without equality of respect would create a very inhuman society [Williams,B] |
| 4113 | 'Deon' in Greek means what one must do; there was no word meaning 'duty' [Williams,B] |
| 4250 | The concept of a 'duty to myself' is fraudulent [Williams,B] |
| 4110 | Obligation and duty look backwards (because of a promise or job), although the acts are in the future [Williams,B] |
| 4249 | "Ought implies can" is a famous formula in connection with moral obligation [Williams,B] |
| 2172 | The modern idea of duty is unknown in archaic Greece [Williams,B] |
| 4248 | Not all moral deliberations lead to obligations; some merely reveal what 'may' be done [Williams,B] |
| 4121 | Why should I think of myself as both the legislator and the citizen who follows the laws? [Williams,B] |
| 22409 | We don't have a duty to ensure that others do their duty [Williams,B] |
| 4122 | If the self becomes completely impartial, it no longer has enough identity to worry about its interests [Williams,B] |
| 2180 | If reason cannot lead people to good, we must hope they have an internal voice [Williams,B] |
| 24012 | Kant's love of consistency is too rigid, and it even overrides normal fairness [Williams,B] |
| 2179 | If the moral self is seen as characterless, then other people have a very limited role in our moral lives [Williams,B] |
| 22407 | Utilitarianism cannot make any serious sense of integrity [Williams,B] |
| 23278 | For utilitarians states of affairs are what have value, not matter who produced them [Williams,B] |
| 4124 | Utilitarian benevolence involves no particular attachments, and is immune to the inverse square law [Williams,B] |
| 4245 | Ethical conviction must be to some extent passive, and can't just depend on the will and decisions [Williams,B] |
| 4246 | Taking responsibility won't cure ethical uncertainty by; we are uncertain what to decide [Williams,B] |
| 8240 | A true king shares his pleasure with the people [Mengzi (Mencius)] |
| 8237 | Extend the treatment of the old and young in your family to the rest of society [Mengzi (Mencius)] |
| 3233 | Equality implies that people are alike in potential as well as in needs [Williams,B] |
| 3234 | Equality seems to require that each person be acknowledged as having a significant point of view [Williams,B] |
| 3235 | It is a mark of extreme exploitation that the sufferers do not realise their plight [Williams,B] |
| 8241 | Only put someone to death if the whole population believes it is deserved [Mengzi (Mencius)] |
| 8238 | Seeking peace through war is like looking for fish up a tree [Mengzi (Mencius)] |
| 4247 | It is a mark of our having ethical values that we aim to reproduce them in our children [Williams,B] |
| 4131 | Most women see an early miscarriage and a late stillbirth as being very different in character [Williams,B] |
| 8236 | Avoid the animals you are going to eat, as it is hard once you have got to know them [Mengzi (Mencius)] |
| 4133 | Speciesism isn't like racism, because the former implies a viewpoint which belongs to no one [Williams,B] |
| 2175 | There is a problem of evil only if you expect the world to be good [Williams,B] |