28 ideas
| 19090 | If we can't check our language against experience, philosophy is just comparing beliefs and words [Rorty] |
| 12619 | We have no successful definitions, because they all use indefinable words [Fodor] |
| 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] |
| 12620 | If 'exist' is ambiguous in 'chairs and numbers exist', that mirrors the difference between chairs and numbers [Fodor] |
| 12613 | Empiricists use dispositions reductively, as 'possibility of sensation' or 'possibility of experimental result' [Fodor] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 12617 | Associationism can't explain how truth is preserved [Fodor] |
| 12615 | Mental representations are the old 'Ideas', but without images [Fodor] |
| 6650 | Fodor is now less keen on the innateness of concepts [Fodor, by Lowe] |
| 12618 | It is essential to the concept CAT that it be satisfied by cats [Fodor] |
| 12614 | I prefer psychological atomism - that concepts are independent of epistemic capacities [Fodor] |
| 12621 | Definable concepts have constituents, which are necessary, individuate them, and demonstrate possession [Fodor] |
| 12622 | Many concepts lack prototypes, and complex prototypes aren't built from simple ones [Fodor] |
| 12623 | The theory theory can't actually tell us what concepts are [Fodor] |
| 12616 | English has no semantic theory, just associations between sentences and thoughts [Fodor] |