25 ideas
| 19081 | Coherence with a set of propositions suggests we can know the proposition corresponds [Davidson, by Donnellan] |
| 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] |
| 8806 | The concepts of belief and truth are linked, since beliefs are meant to fit reality [Davidson] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 8252 | Davidson believes experience is non-conceptual, and outside the space of reasons [Davidson, by McDowell] |
| 8255 | Davidson says the world influences us causally; I say it influences us rationally [McDowell on Davidson] |
| 8804 | Reasons for beliefs are not the same as evidence [Davidson] |
| 8802 | Sensations lack the content to be logical; they cause beliefs, but they cannot justify them [Davidson] |
| 8801 | Coherent justification says only beliefs can be reasons for holding other beliefs [Davidson] |
| 8805 | Skepticism is false because our utterances agree, because they are caused by the same objects [Davidson] |
| 6172 | The Inverted Earth example shows that phenomenal properties are not representational [Block, by Rowlands] |
| 18703 | Davidson's Cogito: 'I think, therefore I am generally right' [Davidson, by Button] |