27 ideas
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 13152 | We can talk of 'innumerable number', about the infinite points on a line [Newton] |
| 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] |
| 13151 | Not all infinites are equal [Newton] |
| 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] |
| 18529 | Relations are expressed either as absolute facts, or by a relational concept [William of Ockham] |
| 16779 | Cut wood doesn't make a new substance, but seems to make separate subjects [William of Ockham] |
| 16757 | Hot water naturally cools down, which is due to the substantial form of the water [William of Ockham] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 9102 | If an animal approached from a distance, we might abstract 'animal' from one instance [William of Ockham] |
| 9114 | There are no secure foundations to prove the separate existence of mind, in reason or experience [William of Ockham] |
| 15863 | The principles of my treatise are designed to fit with a belief in God [Newton] |
| 8340 | I do not pretend to know the cause of gravity [Newton] |
| 13150 | The motions of the planets could only derive from an intelligent agent [Newton] |
| 12178 | That gravity should be innate and essential to matter is absurd [Newton] |
| 9115 | To love God means to love whatever God wills to be loved [William of Ockham] |