28 ideas
| 19463 | Induction assumes some uniformity in nature, or that in some respects the future is like the past [Ayer] |
| 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] |
| 13445 | Descartes showed a one-one order-preserving match between points on a line and the real numbers [Descartes, by Hart,WD] |
| 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] |
| 16774 | Descartes thinks distinguishing substances from aggregates is pointless [Descartes, by Pasnau] |
| 19461 | Knowing I exist reveals nothing at all about my nature [Ayer] |
| 19459 | To say 'I am not thinking' must be false, but it might have been true, so it isn't self-contradictory [Ayer] |
| 19460 | 'I know I exist' has no counterevidence, so it may be meaningless [Ayer] |
| 7400 | Descartes said images can refer to objects without resembling them (as words do) [Descartes, by Tuck] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 19464 | We only discard a hypothesis after one failure if it appears likely to keep on failing [Ayer] |
| 19462 | Induction passes from particular facts to other particulars, or to general laws, non-deductively [Ayer] |
| 4310 | We have inner awareness of our freedom [Descartes] |
| 6553 | Descartes discussed the interaction problem, and compared it with gravity [Descartes, by Lycan] |
| 19676 | Nature is devoid of thought [Descartes, by Meillassoux] |
| 6518 | Matter can't just be Descartes's geometry, because a filler of the spaces is needed [Robinson,H on Descartes] |