30 ideas
10653 | Maybe set theory need not be well-founded [Varzi] |
10648 | Mereology need not be nominalist, though it is often taken to be so [Varzi] |
10655 | Are there mereological atoms, and are all objects made of them? [Varzi] |
10659 | There is something of which everything is part, but no null-thing which is part of everything [Varzi] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
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] |
10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
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] |
10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
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] |
10661 | 'Composition is identity' says multitudes are the reality, loosely composing single things [Varzi] |
10647 | Parts may or may not be attached, demarcated, arbitrary, material, extended, spatial or temporal [Varzi] |
10651 | If 'part' is reflexive, then identity is a limit case of parthood [Varzi] |
10649 | 'Part' stands for a reflexive, antisymmetric and transitive relation [Varzi] |
10654 | The parthood relation will help to define at least seven basic predicates [Varzi] |
10658 | Sameness of parts won't guarantee identity if their arrangement matters [Varzi] |
10652 | Conceivability may indicate possibility, but literary fantasy does not [Varzi] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |