26 ideas
15544 | If what is actual might have been impossible, we need S4 modal logic [Armstrong, by Lewis] |
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] |
7024 | Properties are universals, which are always instantiated [Armstrong, by Heil] |
9478 | Even if all properties are categorical, they may be denoted by dispositional predicates [Armstrong, by Bird] |
10729 | Universals explain resemblance and causal power [Armstrong, by Oliver] |
4031 | It doesn't follow that because there is a predicate there must therefore exist a property [Armstrong] |
10024 | The type-token distinction is the universal-particular distinction [Armstrong, by Hodes] |
10728 | A thing's self-identity can't be a universal, since we can know it a priori [Armstrong, by Oliver] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
22375 | Moral judgements need more than the relevant facts, if the same facts lead to 'x is good' and 'x is bad' [Foot] |
22378 | We can't affirm a duty without saying why it matters if it is not performed [Foot] |
22377 | Whether someone is rude is judged by agreed criteria, so the facts dictate the value [Foot] |
22376 | Facts and values are connected if we cannot choose what counts as evidence of rightness [Foot] |