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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification

[quantifiyng over both objects, and features or sets of objects]

11 ideas
Putting a predicate letter in a quantifier is to make it the name of an entity [Quine]
First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Shapiro on Boolos]
If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K]
Second-order variables also range over properties, sets, relations or functions [Shapiro]
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
In second-order logic the higher-order variables range over all the properties of the objects [Read]
Second-order logic needs second-order variables and quantification into predicate position [Melia]
Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano]
Second-order variables need to range over more than collections of first-order objects [McGee]
Basic variables in second-order logic are taken to range over subsets of the individuals [Anderson,CA]