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] |
17488 | Empiricist theories are sets of laws, which give explanations and reductions [Glennan] |
17493 | Modern mechanism need parts with spatial, temporal and function facts, and diagrams [Glennan] |
17487 | Mechanistic philosophy of science is an alternative to the empiricist law-based tradition [Glennan] |
17489 | Mechanisms are either systems of parts or sequences of activities [Glennan] |
17490 | 17th century mechanists explained everything by the kinetic physical fundamentals [Glennan] |
17491 | Unlike the lawlike approach, mechanistic explanation can allow for exceptions [Glennan] |
22693 | The works we value most are in sympathy with our own moral views [John,E] |
22694 | We should understand what is morally important in a story, without having to endorse it [John,E] |
22695 | We value morality in art because that is what we care about - but it is a contingent fact [John,E] |
22692 | A work can be morally and artistically excellent, despite rejecting moral truth [John,E] |
17494 | Since causal events are related by mechanisms, causation can be analysed in that way [Glennan] |