Higher-order quantification and natural language property-talk

null, Cian Dorr (New York University)

Abstract: I will defend the view that the usage of words like ‘property’ in natural languages is correctly understood in higher-order terms. For example, the English sentence ’Socrates has some property’ literally means exactly the same as the higher-order sentence ∃X.X(Socrates).  This view implies that many natural-language expressions are highly type-ambiguous. I respond to an influential objection to such ambiguity by giving an account of sentences like ‘Athens and the property of being Athenian were both mentioned by Socrates’ in which a single word-occurrence seems to need to have several differently-typed interpretations simultaneously.  This account is most naturally stated using an extended form of higher-order language that allows for sum-types.  These may initially seem metaphysically suspect, but are in fact harmless, since given very weak logical assumptions, any theory stated using sum-types can be translated into a theory stated without them.