26 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] |
19216 | Propositions (such as 'that dog is barking') only exist if their items exist [Williamson] |
7096 | We may still admire a person's character even if the traits are involuntary [Statman] |
7098 | There is a new sort of moral scepticism, about the possibility of moral theories [Statman] |
7099 | With a broad concept of flourishing, it might be possible without the virtues [Statman] |
7100 | Virtue theory isn't a genuine ethical theory, because it doesn't have universal application [Statman] |
7102 | Promises create moral duties that have nothing to do with character [Statman] |
7095 | Moral education is better by concrete example than abstract principle [Statman] |
7094 | Friends express friendship even when no utility is involved [Statman] |
7093 | Behaviour may be disgusting or inhumane, but violate no duty [Statman] |
7104 | The ancients recognised imperfect duties, but we have added perfect duties like justice [Statman] |
7103 | Abortion issues focus on the mother's right over her body, and the status of the foetus [Statman] |