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Full Idea
To put the predicate letter 'F' in a quantifier is to treat predicate positions suddenly as name positions, and hence to treat predicates as names of entities of some sort.
Gist of Idea
Putting a predicate letter in a quantifier is to make it the name of an entity
Source
Willard Quine (Philosophy of Logic [1970], Ch.5)
Book Ref
Quine,Willard: 'Philosophy of Logic' [Prentice-Hall 1970], p.66
A Reaction
Quine's famous objection to second-order logic. But Quine then struggles to give an account of predicates and properties, and hence is accused by Armstrong of being an 'ostrich'. Boolos 1975 also attacks Quine here.
10705 | Putting a predicate letter in a quantifier is to make it the name of an entity [Quine] |
9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
5740 | Second-order logic needs second-order variables and quantification into predicate position [Melia] |
13453 | Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano] |
18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
18763 | Basic variables in second-order logic are taken to range over subsets of the individuals [Anderson,CA] |