30 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] |
14508 | A 'thisness' is a thing's property of being identical with itself (not the possession of self-identity) [Adams,RM] |
14511 | There are cases where mere qualities would not ensure an intrinsic identity [Adams,RM] |
12031 | Essences are taken to be qualitative properties [Adams,RM] |
12034 | If the universe was cyclical, totally indiscernible events might occur from time to time [Adams,RM] |
14510 | Two events might be indiscernible yet distinct, if there was a universe cyclical in time [Adams,RM] |
16455 | Black's two globes might be one globe in highly curved space [Adams,RM] |
14507 | Are possible worlds just qualities, or do they include primitive identities as well? [Adams,RM] |
11964 | Possible worlds are world-stories, maximal descriptions of whole non-existent worlds [Adams,RM, by Molnar] |
16451 | Adams says anti-haecceitism reduces all thisness to suchness [Adams,RM, by Stalnaker] |
11901 | Haecceitism may or may not involve some logical connection to essence [Adams,RM, by Mackie,P] |
14512 | Moderate Haecceitism says transworld identities are primitive, but connected to qualities [Adams,RM] |
22449 | When we say 'is red' we don't mean 'seems red to most people' [Foot] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
12032 | Direct reference is by proper names, or indexicals, or referential uses of descriptions [Adams,RM] |
22451 | All people need affection, cooperation, community and help in trouble [Foot] |
22452 | Do we have a concept of value, other than wanting something, or making an effort to get it? [Foot] |