28 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] |
17954 | Essence is a thing's necessities, but what about its possibilities (which may not be realised)? [Vetter] |
17953 | Real definition fits abstracta, but not individual concrete objects like Socrates [Vetter] |
17952 | Modal accounts make essence less mysterious, by basing them on the clearer necessity [Vetter] |
17959 | Metaphysical necessity is even more deeply empirical than Kripke has argued [Vetter] |
17955 | Possible worlds allow us to talk about degrees of possibility [Vetter] |
17957 | Maybe possibility is constituted by potentiality [Vetter] |
17958 | The apparently metaphysically possible may only be epistemically possible [Vetter] |
17956 | Closeness of worlds should be determined by the intrinsic nature of relevant objects [Vetter] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
22410 | Maybe the unthinkable is a moral category, and considering some options is dishonourable or absurd [Williams,B] |
22408 | Consequentialism assumes that situations can be compared [Williams,B] |
22411 | For a consequentialist massacring 7 million must be better than massacring 7 million and one [Williams,B] |
22409 | We don't have a duty to ensure that others do their duty [Williams,B] |
22407 | Utilitarianism cannot make any serious sense of integrity [Williams,B] |