On Mathematical Proofs of the Vacuity of Compositionality

There is a widespread feeling among formal semanticists that, with suitable manipulations, any semantics can be made compositional. The following quote is representative: “. . . it [compositionality] being a methodological starting point, it is always possible to satisfy compositionality by simply adjusting the syntactic and/or semantic tools one uses, unless that is, the latter are constrained on independent grounds.” (Groenendijk and Stokhof [4], p. 93). Sometimes this feeling is backed by a mathematical proof, purportedly showing compositionality to be vacuous, or without empirical content. A recent instance is W. Zadrozny’s paper [9] in this journal, where he takes a fact about hypersets (non-wellfounded sets) to show that “. . . any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous.” (p. 329). In this note I will examine this claim, as well as two earlier ones in the same vein.