Communication and the Complexity of Semantics

In W. Hinzen, E. Machery & Werning (eds.), Oxford Handbook of Compositionality (forthcoming)
A celebrated argument for the claim that natural languages are compositional is the learnability argument. Briefly: for it to be possible to learn an entire natural language, which has infinitely many sentences, the language must have a compositional semantics. This argument has two main problems: One of them concerns the difference between compositionality and computability: if the argument is good at all, it only shows that the language must have a computable semantics, which allows speakers to compute the meanings of new sentences. But a semantics may be computable without being compositional (and vice versa). Why would we want the semantics to be compositional over and above being computable? The learnability argument doesn’t tell us.
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