26 ideas
| 8349 | The best way to do ontology is to make sense of our normal talk [Davidson] |
| 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] |
| 8348 | If we don't assume that events exist, we cannot make sense of our common talk [Davidson] |
| 16978 | If conceivability is a priori coherence, that implies possibility [Tahko] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 8347 | Explanations typically relate statements, not events [Davidson] |
| 16975 | Essences are used to explain natural kinds, modality, and causal powers [Tahko] |
| 10371 | Distinguish causation, which is in the world, from explanations, which depend on descriptions [Davidson, by Schaffer,J] |
| 8403 | Either facts, or highly unspecific events, serve better as causes than concrete events [Field,H on Davidson] |
| 8346 | Full descriptions can demonstrate sufficiency of cause, but not necessity [Davidson] |
| 4778 | A singular causal statement is true if it is held to fall under a law [Davidson, by Psillos] |
| 16976 | Scientific essentialists tend to characterise essence in terms of modality (not vice versa) [Tahko] |
| 16977 | If essence is modal and laws are necessary, essentialist knowledge is found by scientists [Tahko] |