25 ideas
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
17505 | Using proper names properly doesn't involve necessary and sufficient conditions [Putnam] |
13163 | Circles must be bounded, so cannot be infinite [Leibniz] |
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] |
11908 | Putnam bases essences on 'same kind', but same kinds may not share properties [Mackie,P on Putnam] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
17508 | Science aims at truth, not at 'simplicity' [Putnam] |
13162 | Sloth's Syllogism: either it can't happen, or it is inevitable without my effort [Leibniz] |
17506 | I now think reference by the tests of experts is a special case of being causally connected [Putnam] |
17507 | Natural kind stereotypes are 'strong' (obvious, like tiger) or 'weak' (obscure, like molybdenum) [Putnam] |
11904 | Express natural kinds as a posteriori predicate connections, not as singular terms [Putnam, by Mackie,P] |
19339 | Evil is a negation of good, which arises from non-being [Leibniz] |
13164 | God only made sin possible because a much greater good can be derived from it [Leibniz] |