Does Compositionality Entail Complexity ?

The view that propositions are mereologically complex structured entities is the regnant paradigm in the philosophy of language and linguistics. As Steven Schiffer says, “Virtually every propositionalist accepts [compositionality] and rejects unstructured propositions”, and even the “new” theories of propositions defended by Peter Hanks, Jeffrey King, Scott Soames, and Jeff Speaks take propositions to be complex structured entities. Schiffer’s linking of structured propositions and compositionality is no accident: the most influential argument for structured propositions takes their existence to follow from the fact that language is compositional. In brief, it is argued that if language is compositional, the linguistic meanings of complex expressions must themselves be complex. Call the claim that language is compositional Compositionality, and the claim that the linguistic meanings of (many) complex expressions are themselves complex Complexity. Then we can say that, according to what we can call the Compositionality Argument, Compositionality entails Complexity. This argument dates back to Frege and Russell, and has had a lasting influence on theorizing about propositions ever since. The argument can be formulated in two ways: as a deductive argument that Compositionality entails Complexity, or as an inductive argument that Compositionality is best explained by Complexity. I show the deductive argument is unsound and that the inductive argument is weak. I also show that several arguments of the form ‘Compositionality + X entails (or is best explained by) Complexity’ are unconvincing, for several different substitution instances of ‘X’, including ‘truth-evaluability’, ‘representationality’, ‘direct reference’, ‘factual representationality’ (representing facts or states of affairs), and ‘recoverability’ (the fact that the semantic values of the meaningful parts of a sentence s sometimes need to be recovered for further semantic processing when s is embedded in some larger sentence s*).