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Single Idea 7806

[filed under theme 5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification ]

Full Idea

Boolos virtually patented the new device of plural quantification.

Gist of Idea

Boolos invented plural quantification

Source

report of George Boolos (To be is to be the value of a variable.. [1984]) by José A. Benardete - Logic and Ontology

Book Ref

'A Companion of Philosophical Logic', ed/tr. Jacquette,Dale [Blackwell 2002], p.359


A Reaction

This would be 'there are some things such that...'


The 11 ideas from 'To be is to be the value of a variable..'

The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos]
Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro]
Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro]
We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro]
Boolos invented plural quantification [Boolos, by Benardete,JA]
Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo]
Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo]
Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos]
Plural forms have no more ontological commitment than to first-order objects [Boolos]
First- and second-order quantifiers are two ways of referring to the same things [Boolos]
Does a bowl of Cheerios contain all its sets and subsets? [Boolos]