Aerts et al. provide a valuable model to capture the interactive nature of conceptual combination in conjunctions and disjunctions. The commentary provides a brief review of the interpretation of these interactions that has been offered in the literature, and argues for a closer link between the more traditional account in terms of concept intensions, and the parameters that emerge from the fitting of the Quantum Probability model.

Understanding novel phrases (e.g. upside‐down daisy) and classifying objects in categories named by phrases ought to have common properties, but you'd never know it from current theories. The best candidate for both jobs is the Theory Theory, but it faces difficulties when theories are impoverished. A potential solution is a dual approach that couples theories (representations‐about categories) with fixed mentalese expressions (representations‐of categories). Both representations combine information in parallel when understanding phrases. Although there are objections to the notion that theories (...) can combine, some of them lose their force when applied to a suitable dual model. (shrink)

1 There is a Standard Objection to the idea that concepts might be prototypes (or exemplars, or stereotypes): Because they are productive, concepts must be compositional. Prototypes aren't compositional, so concepts can't be prototypes (see, e.g., Margolis, 1994).2 However, two recent papers (Osherson and Smith, 1988; Kamp and Partee, 1995) reconsider this consensus. They suggest that, although the Standard Objection is probably right in the long run, the cases where prototypes fail to exhibit compositionality are relatively exotic and involve phenomena (...) which any account of compositionality is likely to find hard to deal with; for example, the effects of quantifiers, indexicals, contextual constraints, etc. KP are even prepared to indulge a guarded optimism: "... when a suitably rich compositional theory... is developed, prototypes will be seen ... as one property among many which only when taken altogether can support a compositional theory of combination" (p.56). In this paper, we argue that the Standard Objection to prototype theory was right after all: The problems about compositionality are insuperable in even the most trivial sorts of examples; it is therefore as near to certain as anything in cognitive science ever gets that the structure of concepts is not statistical. Theories of categorization, concept acquisition, lexical meaning and the like, which assume the contrary simply don't work. We commence with a general discussion of the constraints that an account of concepts must meet if their compositionality is to explain their productivity. We'll then turn to a criticism of proposals that OS2 and KP make for coping with some specific cases. (shrink)