22 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] |
16756 | Substantial forms must exist, to explain the stability of metals like silver and tin [Albertus Magnus] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
19513 | A contextualist coherentist will say that how strongly a justification must cohere depends on context [DeRose] |
19514 | Classical invariantism combines fixed truth-conditions with variable assertability standards [DeRose] |
19515 | We can make contextualism more precise, by specifying the discrimination needed each time [DeRose] |
19510 | In some contexts there is little more to knowledge than true belief. [DeRose] |
19516 | Contextualists worry about scepticism, but they should focus on the use of 'know' in ordinary speech [DeRose] |
19511 | If contextualism is about knowledge attribution, rather than knowledge, then it is philosophy of language [DeRose] |