47 ideas
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] |
10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
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] |
13134 | We negate predicates but do not negate names [Westerhoff] |
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] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
13117 | How far down before we are too specialised to have a category? [Westerhoff] |
13116 | Maybe objects in the same category have the same criteria of identity [Westerhoff] |
13118 | Categories are base-sets which are used to construct states of affairs [Westerhoff] |
13125 | Categories are held to explain why some substitutions give falsehood, and others meaninglessness [Westerhoff] |
13126 | Categories systematize our intuitions about generality, substitutability, and identity [Westerhoff] |
13130 | Categories as generalities don't give a criterion for a low-level cut-off point [Westerhoff] |
13124 | Categories can be ordered by both containment and generality [Westerhoff] |
13131 | The aim is that everything should belong in some ontological category or other [Westerhoff] |
13123 | All systems have properties and relations, and most have individuals, abstracta, sets and events [Westerhoff] |
13115 | Ontological categories are like formal axioms, not unique and with necessary membership [Westerhoff] |
13119 | Categories merely systematise, and are not intrinsic to objects [Westerhoff] |
13135 | A thing's ontological category depends on what else exists, so it is contingent [Westerhoff] |
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] |
13129 | Essential kinds may be too specific to provide ontological categories [Westerhoff] |
3364 | All mental phenomena contain an object [Brentano] |
3225 | Mental unity suggests that qualia and intentionality must connect [Brentano, by Rey] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |