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Full Idea
Abandon the idea that use of plural forms must always be understood to commit one to the existence of sets of those things to which the corresponding singular forms apply.
Gist of Idea
Plural forms have no more ontological commitment than to first-order objects
Source
George Boolos (To be is to be the value of a variable.. [1984], p.66)
Book Ref
Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.66
A Reaction
It seems to be an open question whether plural quantification is first- or second-order, but it looks as if it is a rewriting of the first-order.
| 7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
| 10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
| 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] |
| 7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
| 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] |
| 10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
| 10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
| 10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
| 10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |