72 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] |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| 10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
| 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] |
| 5937 | The goodness of opinions depends on their grounds, and corresponding degrees of conviction [Ross] |
| 5936 | Knowledge is superior to opinion because it is certain [Ross] |
| 5927 | I prefer the causal theory to sense data, because sensations are events, not apprehensions [Ross] |
| 5940 | Two goods may be comparable, although they are not commensurable [Ross] |
| 5924 | Identical objects must have identical value [Ross] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 5933 | Aesthetic enjoyment combines pleasure with insight [Ross] |
| 5928 | Beauty is neither objective nor subjective, but a power of producing certain mental events [Ross] |
| 5911 | Moral duties are as fundamental to the universe as the axioms of mathematics [Ross] |
| 5926 | The beauty of a patch of colour might be the most important fact about it [Ross] |
| 7259 | Ross said moral principles are self-evident from the facts, but not from pure thought [Ross, by Dancy,J] |
| 5913 | The moral convictions of thoughtful educated people are the raw data of ethics [Ross] |
| 5920 | Value is held to be either a quality, or a relation (usually between a thing and a mind) [Ross] |
| 5923 | The arguments for value being an objective or a relation fail, so it appears to be a quality [Ross] |
| 5918 | The thing is intrinsically good if it would be good when nothing else existed [Ross] |
| 5930 | All things being equal, we all prefer the virtuous to be happy, not the vicious [Ross] |
| 5922 | An instrumentally good thing might stay the same, but change its value because of circumstances [Ross] |
| 5921 | We can ask of pleasure or beauty whether they are valuable, but not of goodness [Ross] |
| 5910 | The three intrinsic goods are virtue, knowledge and pleasure [Ross] |
| 5932 | The four goods are: virtue, pleasure, just allocation of pleasure, and knowledge [Ross] |
| 5898 | 'Right' and 'good' differ in meaning, as in a 'right action' and a 'good man' [Ross] |
| 5899 | If there are two equally good acts, they may both be right, but neither a duty [Ross] |
| 5904 | In the past 'right' just meant what is conventionally accepted [Ross] |
| 5919 | Goodness is a wider concept than just correct ethical conduct [Ross] |
| 5941 | Motives decide whether an action is good, and what is done decides whether it was right [Ross] |
| 5938 | Virtue is superior to pleasure, as pleasure is never a duty, but goodness is [Ross] |
| 5931 | All other things being equal, a universe with more understanding is better [Ross] |
| 5939 | Morality is not entirely social; a good moral character should love truth [Ross] |
| 5905 | We clearly value good character or understanding, as well as pleasure [Ross] |
| 5929 | No one thinks it doesn't matter whether pleasure is virtuously or viciously acquired [Ross] |
| 5906 | Promise-keeping is bound by the past, and is not concerned with consequences [Ross] |
| 18622 | Promises create a new duty to a particular person; they aren't just a strategy to achieve well-being [Ross] |
| 5908 | Prima facie duties rest self-evidently on particular circumstance [Ross] |
| 5917 | People lose their rights if they do not respect the rights of others [Ross] |
| 5900 | We should do our duty, but not from a sense of duty [Ross] |
| 5909 | Be faithful, grateful, just, beneficent, non-malevolent, and improve yourself [Ross, by PG] |
| 5942 | We like people who act from love, but admire more the people who act from duty [Ross] |
| 5914 | An act may be described in innumerable ways [Ross] |
| 5912 | We should use money to pay debts before giving to charity [Ross] |
| 5916 | Rights were originally legal, and broadened to include other things [Ross] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 5915 | Rights can be justly claimed, so animals have no rights, as they cannot claim any [Ross] |