57 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] |
| 10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
| 20391 | Feminists warn that ideologies use timeless objective definitions as a tool of repression [Davies,S] |
| 10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| 10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo] |
| 10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
| 10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
| 10635 | Second-order quantification and plural quantification are different [Linnebo] |
| 10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
| 10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
| 10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
| 10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
| 10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| 14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
| 14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
| 14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
| 14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
| 14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
| 14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
| 14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
| 10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |
| 10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
| 14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
| 10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
| 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] |