25 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] |
21516 | We want certainty in order to achieve secure results for action [Dewey] |
20298 | The traditional a priori is justified without experience; post-Quine it became unrevisable by experience [Rey] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
20300 | Externalist synonymy is there being a correct link to the same external phenomena [Rey] |
20294 | 'Married' does not 'contain' its symmetry, nor 'bigger than' its transitivity [Rey] |
20293 | Analytic judgements can't be explained by contradiction, since that is what is assumed [Rey] |
20297 | Analytic statements are undeniable (because of meaning), rather than unrevisable [Rey] |
20301 | The meaning properties of a term are those which explain how the term is typically used [Rey] |
20302 | An intrinsic language faculty may fix what is meaningful (as well as grammatical) [Rey] |
20303 | Research throws doubts on the claimed intuitions which support analyticity [Rey] |
20299 | If we claim direct insight to what is analytic, how do we know it is not sub-consciously empirical? [Rey] |