28 ideas
| 3993 | Arguments are nearly always open to challenge, but they help to explain a position rather than force people to believe [Lewis] |
| 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] |
| 3990 | The whole truth supervenes on the physical truth [Lewis] |
| 3991 | Where pixels make up a picture, supervenience is reduction [Lewis] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 3995 | A mind is an organ of representation [Lewis] |
| 3994 | Human pain might be one thing; Martian pain might be something else [Lewis] |
| 3989 | I am a reductionist about mind because I am an a priori reductionist about everything [Lewis] |
| 3992 | Folk psychology makes good predictions, by associating mental states with causal roles [Lewis] |
| 3996 | Folk psychology doesn't say that there is a language of thought [Lewis] |
| 3998 | If you don't share an external world with a brain-in-a-vat, then externalism says you don't share any beliefs [Lewis] |
| 3997 | Nothing shows that all content is 'wide', or that wide content has logical priority [Lewis] |
| 3999 | A spontaneous duplicate of you would have your brain states but no experience, so externalism would deny him any beliefs [Lewis] |
| 4000 | Wide content derives from narrow content and relationships with external things [Lewis] |
| 16746 | Principles of things are not hidden features of forms, but the laws by which they were formed [Newton] |