30 ideas
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 13134 | We negate predicates but do not negate names [Westerhoff] |
| 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] |
| 13117 | How far down before we are too specialised to have a category? [Westerhoff] |
| 13116 | Maybe objects in the same category have the same criteria of identity [Westerhoff] |
| 13118 | Categories are base-sets which are used to construct states of affairs [Westerhoff] |
| 13125 | Categories are held to explain why some substitutions give falsehood, and others meaninglessness [Westerhoff] |
| 13126 | Categories systematize our intuitions about generality, substitutability, and identity [Westerhoff] |
| 13130 | Categories as generalities don't give a criterion for a low-level cut-off point [Westerhoff] |
| 13124 | Categories can be ordered by both containment and generality [Westerhoff] |
| 13131 | The aim is that everything should belong in some ontological category or other [Westerhoff] |
| 13123 | All systems have properties and relations, and most have individuals, abstracta, sets and events [Westerhoff] |
| 13115 | Ontological categories are like formal axioms, not unique and with necessary membership [Westerhoff] |
| 13119 | Categories merely systematise, and are not intrinsic to objects [Westerhoff] |
| 13135 | A thing's ontological category depends on what else exists, so it is contingent [Westerhoff] |
| 13129 | Essential kinds may be too specific to provide ontological categories [Westerhoff] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 8659 | The gods alone live forever with Shamash. The days of humans are numbered. [Anon (Gilg)] |