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Ideas of George Boolos, by Text

[American, 1940 - 1996, Professor of Philosophy at MIT.]

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