Peter Fritz (Oslo): The Consistency of Structured Propositions

Abstract: An argument going back to Bertrand Russell’s “The Principles of Mathematics” (1903) threatens the consistency of the popular view that propositions are structured. What exactly the argument establishes is not a straightforward matter, since there are compelling reasons to think that not all theoretical roles of propositions can be jointly satisfied. I argue in particular that it is plausible that quantifiers binding variables in sentence position do not range over the compositional semantic values of sentences. Since the most natural formulation of Russell’s argument employs such quantifiers, it does not obviously threaten the view that compositional semantic values of sentences are structured. I further defend the consistency of the view that compositional semantic values of sentences are structured using simple models. Returning to Russell, I also use these distinctions and models to shed some light on the relation between simple and ramified type theories.