47 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] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
12756 | Substance is a force for acting and being acted upon [Leibniz] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
12755 | Final causes can help with explanations in physics [Leibniz] |
12760 | Something rather like souls (though not intelligent) could be found everywhere [Leibniz] |
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] |
12759 | There are atoms of substance, but no atoms of bulk or extension [Leibniz] |
12718 | Secondary matter is active and complete; primary matter is passive and incomplete [Leibniz] |
11854 | If there is some trace of God in things, that would explain their natural force [Leibniz] |
12758 | It is plausible to think substances contain the same immanent force seen in our free will [Leibniz] |
19408 | To say that nature or the one universal substance is God is a pernicious doctrine [Leibniz] |