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Full Idea
Ontological commitment is carried by first-order quantifiers; a second-order quantifier needn't be taken to be a first-order quantifier in disguise, having special items, collections, as its range. They are two ways of referring to the same things.
Gist of Idea
First- and second-order quantifiers are two ways of referring to the same things
Source
George Boolos (To be is to be the value of a variable.. [1984], p.72)
Book Ref
Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.72
A Reaction
If second-order quantifiers are just a way of referring, then we can see first-order quantifiers that way too, so we could deny 'objects'.
| 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] |