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Full Idea
Standard second-order existential quantifiers pick out a class or a property, but Boolos suggests that they be understood as a plural quantifier, like 'there are objects' or 'there are people'.
Gist of Idea
We should understand second-order existential quantifiers as plural quantifiers
Source
report of George Boolos (To be is to be the value of a variable.. [1984]) by Stewart Shapiro - Philosophy of Mathematics 7.4
Book Ref
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.234
A Reaction
This idea has potential application to mathematics, and Lewis (1991, 1993) 'invokes it to develop an eliminative structuralism' (Shapiro).
| 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] |