56 ideas
| 20388 | 'Necessary' conditions are requirements, and 'sufficient' conditions are guarantees [Davies,S] |
| 20389 | A definition of a thing gives all the requirements which add up to a guarantee of it [Davies,S] |
| 20391 | Feminists warn that ideologies use timeless objective definitions as a tool of repression [Davies,S] |
| 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] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 20387 | Aesthetic experience involves perception, but also imagination and understanding [Davies,S] |
| 20385 | The faculty of 'taste' was posited to explain why only some people had aesthetic appreciation [Davies,S] |
| 20386 | The sublime is negative in awareness of insignificance, and positive in showing understanding [Davies,S] |
| 20384 | The idea that art forms are linked into a single concept began in the 1740s [Davies,S] |
| 20390 | Defining art as representation or expression or form were all undermined by the avant-garde [Davies,S] |
| 20392 | 'Aesthetic functionalism' says art is what is intended to create aesthetic experiences [Davies,S] |
| 20405 | Music may be expressive by being 'associated' with other emotional words or events [Davies,S] |
| 20403 | It seems unlikely that sad music expresses a composer's sadness; it takes ages to write [Davies,S] |
| 20393 | The 'institutional' theory says art is just something appropriately placed in the 'artworld' [Davies,S] |
| 20402 | Music is too definite to be put into words (not too indefinite!) [Davies,S] |
| 20395 | The title of a painting can be vital, and the artist decrees who the portrait represents [Davies,S] |
| 20396 | We must know what the work is meant to be, to evaluate the artist's achievement [Davies,S] |
| 20399 | Intentionalism says either meaning just is intention, or ('moderate') meaning is successful intention [Davies,S] |
| 20401 | The meaning is given by the audience's best guess at the author's intentions [Davies,S] |
| 20397 | If we could perfectly clone the Mona Lisa, the original would still be special [Davies,S] |
| 20398 | Art that is multiply instanced may require at least one instance [Davies,S] |
| 20404 | Music isn't just sad because it makes the listener feel sad [Davies,S] |
| 22705 | If the depiction of evil is glorified, that is an artistic flaw [Davies,S] |
| 22707 | It is an artistic defect if excessive moral outrage distorts the story, and narrows our sympathies [Davies,S] |
| 22706 | A work which seeks approval for immorality, but alienates the audience, is a failure [Davies,S] |
| 22704 | Immorality may or may not be an artistic defect [Davies,S] |