46 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] |
10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
10857 | Set theory made a closer study of infinity possible [Clegg] |
10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
10871 | Axiom of Existence: there exists at least one set [Clegg] |
10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
10860 | An ordinal number is defined by the set that comes before it [Clegg] |
10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
13766 | 'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey] |
19143 | Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson] |
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] |
22704 | Immorality may or may not be an artistic defect [Davies,S] |
22706 | A work which seeks approval for immorality, but alienates the audience, is a failure [Davies,S] |