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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] |