24 ideas
12772 | Philosophy is a value- and attitude-driven enterprise [Fraassen] |
12771 | Is it likely that a successful, coherent, explanatory ontological hypothesis is true? [Fraassen] |
12773 | Analytic philosophy has an exceptional arsenal of critical tools [Fraassen] |
12770 | We may end up with a huge theory of carefully constructed falsehoods [Fraassen] |
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] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
12769 | Inference to best explanation contains all sorts of hidden values [Fraassen] |
12768 | We accept many scientific theories without endorsing them as true [Fraassen] |
1477 | Being manly and brave is the result of convention, not of human nature [Plutarch] |
1478 | Animals don't value pleasure, as they cease sexual intercourse after impregnation [Plutarch] |
1479 | Animals have not been led into homosexuality, because they value pleasure very little [Plutarch] |