34 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] |
| 6472 | Continuity is a sufficient criterion for the identity of a rock, but not for part of a smooth fluid [Russell] |
| 6473 | Physical things are series of appearances whose matter obeys physical laws [Russell] |
| 6465 | We need not deny substance, but there seems no reason to assert it [Russell] |
| 6471 | The assumption by physicists of permanent substance is not metaphysically legitimate [Russell] |
| 6466 | Where possible, logical constructions are to be substituted for inferred entities [Russell] |
| 6467 | No sensibile is ever a datum to two people at once [Russell] |
| 6483 | Russell held that we are aware of states of our own brain [Russell, by Robinson,H] |
| 8244 | Sense-data are qualities devoid of subjectivity, which are the basis of science [Russell, by Deleuze/Guattari] |
| 6462 | Sense-data are not mental, but are part of the subject-matter of physics [Russell] |
| 6463 | Sense-data are objects, and do not contain the subject as part, the way beliefs do [Russell] |
| 6464 | Sense-data are usually objects within the body, but are not part of the subject [Russell] |
| 6459 | We do not know whether sense-data exist as objects when they are not data [Russell] |
| 6460 | 'Sensibilia' are identical to sense-data, without actually being data for any mind [Russell] |
| 6461 | Ungiven sense-data can no more exist than unmarried husbands [Russell] |
| 6458 | Individuating sense-data is difficult, because they divide when closely attended to [Russell] |
| 6469 | Sense-data may be subjective, if closing our eyes can change them [Russell] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 22818 | Liberals are not too individualistic, because people recognise and value social relations [Kymlicka] |
| 6470 | Matter is the limit of appearances as distance from the object diminishes [Russell] |
| 6468 | There is 'private space', and there is also the 'space of perspectives' [Russell] |