34 ideas
| 3123 | Science is in the business of carving nature at the joints [Segal] |
| 3125 | Psychology studies the way rationality links desires and beliefs to causality [Segal] |
| 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] |
| 3105 | Is 'Hesperus = Phosphorus' metaphysically necessary, but not logically or epistemologically necessary? [Segal] |
| 3106 | If claims of metaphysical necessity are based on conceivability, we should be cautious [Segal] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 6027 | From the fact that some men die, we cannot infer that they all do [Philodemus] |
| 3113 | The success and virtue of an explanation do not guarantee its truth [Segal] |
| 3112 | Folk psychology is ridiculously dualist in its assumptions [Segal] |
| 3108 | If 'water' has narrow content, it refers to both H2O and XYZ [Segal] |
| 3110 | Humans are made of H2O, so 'twins' aren't actually feasible [Segal] |
| 3124 | Externalists can't assume old words refer to modern natural kinds [Segal] |
| 3117 | Concepts can survive a big change in extension [Segal] |
| 3104 | Must we relate to some diamonds to understand them? [Segal] |
| 3103 | Maybe content involves relations to a language community [Segal] |
| 3111 | Externalism can't explain concepts that have no reference [Segal] |
| 3109 | If content is external, so are beliefs and desires [Segal] |
| 3116 | Maybe experts fix content, not ordinary users [Segal] |
| 3121 | If content is narrow, my perfect twin shares my concepts [Segal] |
| 3118 | If thoughts ARE causal, we can't explain how they cause things [Segal] |
| 3119 | Even 'mass' cannot be defined in causal terms [Segal] |