24 ideas
| 20771 | Six parts: dialectic, rhetoric, ethics, politics, physics, theology [Cleanthes, by Diog. Laertius] |
| 13407 | All worthwhile philosophy is synthetic theorizing, evaluated by experience [Papineau] |
| 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] |
| 13409 | Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment [Papineau] |
| 13406 | A priori knowledge is analytic - the structure of our concepts - and hence unimportant [Papineau] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 13408 | Intuition and thought-experiments embody substantial information about the world [Papineau] |
| 6028 | Bodies interact with other bodies, and cuts cause pain, and shame causes blushing, so the soul is a body [Cleanthes, by Nemesius] |
| 20831 | The soul suffers when the body hurts, creates redness from shame, and pallor from fear [Cleanthes] |
| 13410 | Verificationism about concepts means you can't deny a theory, because you can't have the concept [Papineau] |
| 5993 | The ascending scale of living creatures requires a perfect being [Cleanthes, by Tieleman] |