  Nevertheless, considerations of compositionality might still pose a significant challenge to the meaninglessness view. This is so because defenders of the meaninglessness view need to provide a compositional semantic theory that accounts for the meaning of those sentences that they do deem to be meaningful. The problem is that once such a theory provides a systematic recipe for how to assign meanings to benign sentences, there is a risk that an assignment of meanings to categorically mistaken combinations will automatically fall out. To illustrate the point, suppose that the semantic theory assigns objects to the names ‘Two’ and ‘Desky’ (the number two and a particular desk respectively), and the ordinary functions from objects to truth-values to the predicates ‘is green’ and ‘is prime’. Suppose further that the recursive specification of the theory say that the meaning of any sentence of the form ‘\(a\) is \(P\)’ is the claim that \(f(o)=\)true, where \(f\) is the function denoted by ‘\(P\)’ and \(o\) is the object denoted by ‘\(a\)’. Note that even if this theory was only designed to account for the meaning of standard combinations such as ‘Desky is green’ and ‘Two is prime’, it also inadvertently assigns a meaning to the category mistakes ‘Two is green’ and ‘Desky is prime’. Of course, one can try to amend the semantic theory so that it avoids this consequence, but the question is whether a semantic theory can be constructed that succeeds in assigning meanings to precisely all and only non-categorically mistaken sentences.