25 ideas
| 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] |
| 7440 | Secondary qualities are microscopic primary qualities of physical things [Armstrong] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 7437 | Consciousness and experience of qualities are not the same [Armstrong] |
| 7434 | Behaviourism is false, but mind is definable as the cause of behaviour [Armstrong] |
| 7436 | The manifestations of a disposition need never actually exist [Armstrong] |
| 7429 | Causal Functionalism says mental states are apt for producing behaviour [Armstrong] |
| 7438 | A causal theory of mentality would be improved by a teleological element [Armstrong] |
| 7431 | The identity of mental states with physical properties is contingent, because the laws of nature are contingent [Armstrong] |
| 7432 | One mental role might be filled by a variety of physical types [Armstrong] |
| 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] |