25 ideas
| 10397 | Abelard's mereology involves privileged and natural divisions, and principal parts [Abelard, by King,P] |
| 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] |
| 10396 | If 'animal' is wholly present in Socrates and an ass, then 'animal' is rational and irrational [Abelard, by King,P] |
| 10395 | Abelard was an irrealist about virtually everything apart from concrete individuals [Abelard, by King,P] |
| 15384 | Only words can be 'predicated of many'; the universality is just in its mode of signifying [Abelard, by Panaccio] |
| 8481 | The de dicto-de re modality distinction dates back to Abelard [Abelard, by Orenstein] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 15385 | Abelard's problem is the purely singular aspects of things won't account for abstraction [Panaccio on Abelard] |
| 15383 | Nothing external can truly be predicated of an object [Abelard, by Panaccio] |
| 20739 | Levinas took 'first philosophy' to begin with seeing the vulnerable faces of others [Levinas, by Aho] |
| 20445 | Levinas says Marxism is the replacement of individualist ethics, by solidarity and sociality [Levinas, by Critchley] |
| 10398 | Natural kinds are not special; they are just well-defined resemblance collections [Abelard, by King,P] |