¹⁰ A more charitable way to put things would be that compositionality—which really amounts to semantic recursiveness—has been confused with the semantic sub-formula property. Thus Jerry Fodor and Ernest Lepore’s The Compositionality Papers (Oxford University Press, 2002) opens with this definition: “Compositionality is the property that a system of representations has when (i) it contains both primitive symbols and symbols that are syntactically and semantically complex; and (ii) the latter inherit their syntactic/semantic properties from the former” (p.1). On this definition, the incompatibility semantics is fully compositional. But Fodor and Lepore go on to draw atomistic consequences from compositionality that in fact only follow from the semantic sub-formula property. So the confusion I am concerned to point out is in play, however we decide to specify it.