 The point applies to more subtle attempts to trivialize compositionality as well. Consider a famous result due to Zadrozny (1994). Given a set S of strings generated from an arbitrary alphabet via concatenation and a meaning function m which assigns the members of an arbitrary set M to the members of S, we can construct a new meaning function \(\mu\) such that for all \(s, t \in S \mu(s{.}t) = \mu(s)(\mu(t))\) and \(\mu(s)(s) = m(s)\). What this shows is that we can turn an arbitrary meaning function into a compositional  one,[6]  as long as we replace the old meanings with new “meanings” from which they are uniformly  recoverable.[7] What is not clear is whether these new “meanings” really are meanings. After all, someone ignorant of m could assign entities to members of S following \(\mu\). Such a person would know what each expression in S “means” but would not necessarily know what any of them means. (For further discussion of Zadrozny’s result, see Kazmi and Pelletier (1998), Westerståhl (1998), Dever (1999).)