What I mean by productivity is linguistic productivity: roughly, the fact that a finite human mind is capable of producing and understanding potentially infinitely many different linguistic expressions on equally many different occasions. Ordinary speakers perform the miracles of productivity on the fly and without even being aware of it: they produce new expressions not encountered before and use old expressions for new purposes.
The received wisdom of the last forty or so years is that recursive syntactic rules and semantic compositionality may be the core of an explanation for productivity. However, infinity of the set of expressions really is not the point, and that's why recursion can at most be part of the story and is in fact a little misleading as a showpiece of an explanation of linguistic productivity. The point, I want to suggest, is projectibility: projecting properties from the known to the unknown, and in a fashion that other speakers can follow.
One may reasonably doubt that the familiar category-based rules will suffice to account for processes of word formation, there are problems about the compositionality of certain syntactic constructions and, of course, pragmatics isn't really compositional either. I will not touch upon most of these problems though, but I will concentrate on problems of the context dependence of the semantic interpretation of linguistic utterances. I shall argue that there is no way of accounting for sentence contents, i.e. for the truth conditions sentences have under particular circumstances of utterance, in a compositional a priori fashion. I shall argue that, in addition to familiar category-based compositional mechanisms, representations of linguistic experience are required that cannot be formulated in terms of a denumerable set of categories. Such representations are mapped onto other situations of language use via relations of similarity, and I will argue that category-based rules are here no serious alternative - even though they are still required for other purposes in a theory of projectibility.