41 ideas
12027 | There must be a plausible epistemological theory alongside any metaphysical theory [Forbes,G] |
12005 | The symbol 'ι' forms definite descriptions; (ιx)F(x) says 'the x which is such that F(x)' [Forbes,G] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
12010 | Is the meaning of 'and' given by its truth table, or by its introduction and elimination rules? [Forbes,G] |
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] |
8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
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] |
12023 | Vagueness problems arise from applying sharp semantics to vague languages [Forbes,G] |
12017 | In all instances of identity, there must be some facts to ensure the identity [Forbes,G] |
12024 | If we combined two clocks, it seems that two clocks may have become one clock. [Forbes,G] |
11885 | Only individual essences will ground identities across worlds in other properties [Forbes,G, by Mackie,P] |
12015 | Non-trivial individual essence is properties other than de dicto, or universal, or relational [Forbes,G] |
12014 | An individual essence is a set of essential properties which only that object can have [Forbes,G] |
12013 | Essential properties depend on a category, and perhaps also on particular facts [Forbes,G] |
12012 | Essential properties are those without which an object could not exist [Forbes,G] |
12025 | Artefacts have fuzzy essences [Forbes,G] |
12022 | Same parts does not ensure same artefact, if those parts could constitute a different artefact [Forbes,G] |
12020 | An individual might change their sex in a world, but couldn't have differed in sex at origin [Forbes,G] |
11888 | Identities must hold because of other facts, which must be instrinsic [Forbes,G, by Mackie,P] |
12003 | De re modal formulae, unlike de dicto, are sensitive to transworld identities [Forbes,G] |
12028 | De re necessity is a form of conceptual necessity, just as de dicto necessity is [Forbes,G] |
12008 | Unlike places and times, we cannot separate possible worlds from what is true at them [Forbes,G] |
12009 | The problem with possible worlds realism is epistemological; we can't know properties of possible objects [Forbes,G] |
12007 | Possible worlds are points of logical space, rather like other times than our own [Forbes,G] |
12011 | Transworld identity concerns the limits of possibility for ordinary things [Forbes,G] |
12016 | The problem of transworld identity can be solved by individual essences [Forbes,G] |
12004 | Counterpart theory is not good at handling the logic of identity [Forbes,G] |
12021 | Haecceitism attributes to each individual a primitive identity or thisness [Forbes,G] |
12029 | We believe in thisnesses, because we reject bizarre possibilities as not being about that individual [Forbes,G] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |