(3) Higher orders are achieved by allowing predicate functions as variables.
Theory of types, in logic, a theory introduced by the British philosopher Bertrand Russell in his Principia Mathematica (1910 13) to deal with logical paradoxes arising from the unrestricted use of predicate functions as variables.
The type of a predicate function is determined by the number and type of its arguments.
In philosophy "identity" is a predicate, which functions as an identifier, i.e. a marker that distinguishes and differentiates one object from another object.
In the complex predicate, an IA head functions as a matrix predicate and introduces an applied object for the secondary predicate to be predicated of.
All of these verbs may function as a predicate or occur as part of a predicate.
If the utterance particle is predicative, XP could be regarded as a secondary predicate and F functions as a coordinating conjunction that links the main clause and the secondary predicate, somewhat like and in Englishd.
In (3.11), very functions as a predicate modifier, in particular a subsective modifier, since the set of things that are very(P) is a subset of the things that are P. Do we need such modifiers in our logical forms?
And sentences like 4 are what, following Geach [1960], I'll call attributive uses of "good", because "good" functions as a predicate modifier, rather than as a predicate in its own right.
A predicate is represented as a function that has arguments in parenthesis, with each argument being a constant, a variable, or a predicate.
A structure contains interpretations of certain predicate, function and constant symbols; each predicate or function symbol has a fixed arity.
