64 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] |
10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
12010 | Is the meaning of 'and' given by its truth table, or by its introduction and elimination rules? [Forbes,G] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
12023 | Vagueness problems arise from applying sharp semantics to vague languages [Forbes,G] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
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] |
12014 | An individual essence is a set of essential properties which only that object can have [Forbes,G] |
12015 | Non-trivial individual essence is properties other than de dicto, or universal, or relational [Forbes,G] |
12013 | Essential properties depend on a category, and perhaps also on particular facts [Forbes,G] |
13804 | A property is essential iff the object would not exist if it lacked that property [Forbes,G] |
13805 | Properties are trivially essential if they are not grounded in a thing's specific nature [Forbes,G] |
12012 | Essential properties are those without which an object could not exist [Forbes,G] |
13808 | A relation is essential to two items if it holds in every world where they exist [Forbes,G] |
13806 | Trivially essential properties are existence, self-identity, and de dicto necessities [Forbes,G] |
13807 | A property is 'extraneously essential' if it is had only because of the properties of other objects [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] |
13809 | One might be essentialist about the original bronze from which a statue was made [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] |
13810 | The source of de dicto necessity is not concepts, but the actual properties of the thing [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] |
7295 | Maybe induction is only reliable IF reality is stable [Mitchell,A] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |