24 ideas
| 13966 | Analytic philosophy loved the necessary a priori analytic, linguistic modality, and rigour [Soames] |
| 13974 | If philosophy is analysis of meaning, available to all competent speakers, what's left for philosophers? [Soames] |
| 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] |
| 13969 | Kripkean essential properties and relations are necessary, in all genuinely possible worlds [Soames] |
| 13973 | A key achievement of Kripke is showing that important modalities are not linguistic in source [Soames] |
| 13968 | Kripkean possible worlds are abstract maximal states in which the real world could have been [Soames] |
| 21227 | The Cogito demands a bridge to the world, and ends in isolating the ego [Velarde-Mayol] |
| 21215 | The representation may not be a likeness [Velarde-Mayol] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 13972 | Two-dimensionalism reinstates descriptivism, and reconnects necessity and apriority to analyticity [Soames] |
| 21219 | Find the essence by varying an object, to see what remains invariable [Velarde-Mayol] |