36 ideas
4036 | What matters is not how many entities we postulate, but how many kinds of entities [Armstrong, by Mellor/Oliver] |
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] |
15754 | Without properties we would be unable to express the laws of nature [Armstrong] |
18430 | We accept properties because of type/tokens, reference, and quantification [Edwards] |
4034 | Whether we apply 'cold' or 'hot' to an object is quite separate from its change of temperature [Armstrong] |
8535 | To the claim that every predicate has a property, start by eliminating failure of application of predicate [Armstrong] |
18432 | Quineans say that predication is primitive and inexplicable [Edwards] |
8537 | Tropes fall into classes, because exact similarity is symmetrical and transitive [Armstrong] |
8538 | Trope theory needs extra commitments, to symmetry and non-transitivity, unless resemblance is exact [Armstrong] |
8539 | Universals are required to give a satisfactory account of the laws of nature [Armstrong] |
8529 | Deniers of properties and relations rely on either predicates or on classes [Armstrong] |
8532 | Resemblances must be in certain 'respects', and they seem awfully like properties [Armstrong] |
18437 | Resemblance nominalism requires a second entity to explain 'the rose is crimson' [Edwards] |
8530 | Change of temperature in objects is quite independent of the predicates 'hot' and 'cold' [Armstrong] |
8536 | We want to know what constituents of objects are grounds for the application of predicates [Armstrong] |
8531 | In most sets there is no property common to all the members [Armstrong] |
18434 | That a whole is prior to its parts ('priority monism') is a view gaining in support [Edwards] |
15753 | Essences might support Resemblance Nominalism, but they are too coarse and ill-defined [Armstrong] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
8533 | Predicates need ontological correlates to ensure that they apply [Armstrong] |
4035 | There must be some explanation of why certain predicates are applicable to certain objects [Armstrong] |
8541 | Regularities theories are poor on causal connections, counterfactuals and probability [Armstrong] |
8540 | The introduction of sparse properties avoids the regularity theory's problem with 'grue' [Armstrong] |