Is Compositionality an Empirical Matter?
Jaroslav Peregrin · 2005
The principle of compositionality of meaning is often seen as a kind of a ‘natural law’ of semantics: we, finite being, so the story goes, cannot grasp an infinite stock of meanings otherwise than as composed out of a finite stock of primitive building blocks. Therefore we are restricted, out of the many possible kinds of languages, to the compositional kind. Hence although there might be noncompositional languages, they would not be intelligible for us. This received wisdom has not been substantially shattered by periodically appearing attempts at showing that, as a matter of fact, our factual natural language is not compositional. However, in 1983 there appeared a different kind of challenge which was taken more seriously: Janssen (1983) presented a proof of a theorem which suggested that the principle cannot be considered as a real law because it is simply vacuous. The theorem stated, in effect, that any range of expressions can be mapped on any range of entities in a compositional way, and hence appear to imply that the principle is not capable of excluding any kinds of meanings. Recently, a more sophisticated version of the same argument was presented by Zadrozny (1994), who gives a simple algoritm for constructing, given an alphabet A, a set M, and a mapping m (‘meaning assignment’) of A on M, a function μ mapping all concatenations of elements of A on M with the following properties: (i) The value of μ for the concatenation of s and t is always μ(s)(μ(t)) (hence μ is not only compositional in that its value for a whole is uniquely determined by the values of its parts; it is, moreover, the result of the application of the value of one of its parts to those of the others). (ii) The value of μ for a simple symbol is trivialy transformable into its antecedent ‘meaning’ m(s), namely μ(s)(s) = m(s). The upshot is taken to be that every assignment of any kinds of meanings to any kinds of expressions is trivially compositional; and