26 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] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 23514 | The cerbellum has a huge number of neurons, but little involvement in consciousness [Seth] |
| 23513 | Single neurons can carry out complex functions [Seth] |
| 23516 | Maybe a system is conscious if the whole generates more information than its parts [Seth] |
| 23519 | The self is embodied, perspectival, volitional, narrative and social [Seth, by PG] |
| 23518 | Modern AI is mostly machine-based pattern recognition [Seth] |
| 23517 | Volition is felt as doing what you want, with possible alternatives, and a source from within [Seth] |
| 23515 | Human exceptionalism plagues biology, and most other human thinking [Seth] |
| 22375 | Moral judgements need more than the relevant facts, if the same facts lead to 'x is good' and 'x is bad' [Foot] |
| 22378 | We can't affirm a duty without saying why it matters if it is not performed [Foot] |
| 22377 | Whether someone is rude is judged by agreed criteria, so the facts dictate the value [Foot] |
| 22376 | Facts and values are connected if we cannot choose what counts as evidence of rightness [Foot] |