29 ideas
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] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
22330 | Grice said patterns of use are often semantically irrelevant, because it is a pragmatic matter [Grice, by Glock] |
18045 | Grice's maxim of quality says do not assert what you believe to be false [Grice, by Magidor] |
18044 | Grice's maxim of manner requires one to be as brief as possible [Grice, by Magidor] |
18046 | Grice's maxim of quantity says be sufficiently informative [Grice, by Magidor] |
2705 | How can intuitionists distinguish universal convictions from local cultural ones? [Hare] |
2712 | You can't use intuitions to decide which intuitions you should cultivate [Hare] |
2706 | Emotivists mistakenly think all disagreements are about facts, and so there are no moral reasons [Hare] |
2709 | Prescriptivism sees 'ought' statements as imperatives which are universalisable [Hare] |
2704 | If morality is just a natural or intuitive description, that leads to relativism [Hare] |
2703 | Descriptivism say ethical meaning is just truth-conditions; prescriptivism adds an evaluation [Hare] |
2707 | If there can be contradictory prescriptions, then reasoning must be involved [Hare] |
2708 | An 'ought' statement implies universal application [Hare] |
2711 | Prescriptivism implies a commitment, but descriptivism doesn't [Hare] |
2710 | Moral judgements must invoke some sort of principle [Hare] |