28 ideas
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 4975 | A thought can be split in many ways, so that different parts appear as subject or predicate [Frege] |
| 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] |
| 9949 | There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman] |
| 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] |
| 18995 | Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo] |
| 10317 | It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale] |
| 10535 | Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett] |
| 15642 | If kinds depend only on what can be observed, many underlying essences might produce the same kind [Eagle] |
| 15645 | Nominal essence are the observable properties of things [Eagle] |
| 15643 | Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 9839 | Frege equated the concepts under which an object falls with its properties [Frege, by Dummett] |
| 4973 | As I understand it, a concept is the meaning of a grammatical predicate [Frege] |
| 9167 | Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam] |
| 4974 | For all the multiplicity of languages, mankind has a common stock of thoughts [Frege] |
| 15641 | Kinds are fixed by the essential properties of things - the properties that make it that kind of thing [Eagle] |