1971 | The iterative conception of Set |
p.59 | 18192 | Do the Replacement Axioms exceed the iterative conception of sets? |
1975 | On Second-Order Logic |
p.152 | 14249 | Boolos reinterprets second-order logic as plural logic |
p.245 | 13841 | Why should compactness be definitive of logic? |
p.44 | p.516 | 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets |
p.45 | p.518 | 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems |
p.46 | p.519 | 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed |
p.48 | p.521 | 10833 | Many concepts can only be expressed by second-order logic |
p.52 | p.525 | 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences |
1984 | To be is to be the value of a variable.. |
p. | 7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections |
p.105 | 10225 | Monadic second-order logic might be understood in terms of plural quantifiers |
p.201 | 13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology |
p.234 | 10267 | We should understand second-order existential quantifiers as plural quantifiers |
p.359 | 7806 | Boolos invented plural quantification |
Intro | p.71 | 10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic |
§1 | p.74 | 10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic |
p.54 | p.54 | 10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus |
p.66 | p.66 | 10698 | Plural forms have no more ontological commitment than to first-order objects |
p.72 | p.72 | 10699 | Does a bowl of Cheerios contain all its sets and subsets? |
p.72 | p.72 | 10700 | First- and second-order quantifiers are two ways of referring to the same things |
1989 | Iteration Again |
p.227 | 13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) |
1997 | Must We Believe in Set Theory? |
p.121 | p.121 | 10482 | The logic of ZF is classical first-order predicate logic with identity |
p.122 | p.122 | 10483 | Mathematics and science do not require very high orders of infinity |
p.126 | p.126 | 10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first |
p.127 | p.127 | 10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves |
p.128 | p.128 | 10488 | It is lunacy to think we only see ink-marks, and not word-types |
p.128 | p.128 | 10487 | I am a fan of abstract objects, and confident of their existence |
p.129 | p.129 | 10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. |
p.129 | p.129 | 10490 | Mathematics isn't surprising, given that we experience many objects as abstract |
p.129 | p.129 | 10491 | Infinite natural numbers is as obvious as infinite sentences in English |
p.130 | p.130 | 10492 | A few axioms of set theory 'force themselves on us', but most of them don't |
1997 | Is Hume's Principle analytic? |
p.75 | 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect |