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Names, by contrast, succeed in their job because they aren't compositional; not even when they are syntactically complex. Consider ‘the Iron Duke’, to which ‘Iron’ does not contribute iron, and which you can therefore use to specifythe Iron Duke even if you don't know what he was made of. Names are nicer than descriptions because you don't haveto know much to specify their bearers, although you do have to know what their bearers are called. Descriptions arenicer than names because, although you do have to know a lot to specify their bearers, you don't have to know whattheir bearers are called. What's nicer than having the use of either names or descriptions is having the use of both. Iagree that, as a piece of semantic theory, this is all entirely banal; but that's my point, so don't complain. There is, torepeat, no need for fancy arguments that the representational systems we talk and think in are in large partcompositional; you find the effects of their compositionality just about wherever you look.


I must apologize for having gone on at such length about the arguments pro and con conceptual compositionality; the reason I've done so is that, in my view, the status of the statistical theory of concepts turns, practically entirely, on thisissue. And statistical theories are now the preferred accounts of concepts practically throughout cognitive science. Inwhat follows I will take the compositionality of conceptual repertoires for granted, and try to make clear how the thesisthat concepts are prototypes falls afoul of it.


Why Concepts Can't Be Prototypes^

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Here's why concepts can't be prototypes: whatever conceptual content is, compositionality requires that complex concepts inherit their contents from those of their constituents, and that they do so in a way that explains theirproductivity and systematicity. Accordingly, whatever is not inherited from its constituents by a complex concept is ipsofacto not the content of that concept. But: (i) indefinitely many complex concepts have no prototypes; a fortiori they donot inherit their prototypes from their constituents. And, (ii) there are indefinitely many complex concepts whoseprototypes aren't related to the prototypes of their constituents in the ways that the compositional explanation ofproductivity and systematicity requires. So, again, if concepts are compositional then they can't be prototypes.


In short, prototypes don't compose. Since this is the heart of the case against statistical theories of concepts, I propose to expatiate a bit on the examples.


(I) The Uncat Problem


For indefinitely many “Boolean” concepts,57there isn't any prototype even though: —their primitive constituent concepts all have prototypes,


and


--the complex concept itself has definite conditions of semantic evaluation (definite satisfaction conditions).


So, for example, consider the concept NOT A CAT (mutatis mutandis, the predicate ‘is not a cat’ and let's suppose (probably contrary to fact) that CAT isn't vague; i.e. that ‘is a cat’ has either the value S or the value U for every objectin the relevant universe of discourse. Then, clearly, there is a definite semantic interpretation for NOT A CAT; i.e. itexpresses the property of not being a cat, a property which all and only objects in the extension of the complement of theset of cats instantiate.

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However, although NOT A CAT is semantically entirely well behaved on these assumptions, it's pretty clear that it hasn't got a stereotype or an exemplar. For consider: a bagel is a pretty good example of a NOT A CAT, but a bagelcouldn't be NOT A CAT's prototype. Why not? Well, if bagels are the prototypic NOT A CATs, it follows that themore a thing is like a bagel the less it's like a cat; and the more a thing isn't like a cat, the more it's like a bagel. But the secondconjunct is patently not true. Tuesdays and erasers, both of which are very good examples of NOT A CATs, aren't atall like bagels. An Eraser is not more a Bagel for being a bad Cat. Notice that the same sort of argument goes throughif you are thinking of stereotypes in terms of features rather than exemplars. There is nothing that non-cats qua noncats as such are likely to have in common (except, of course, not being cats).58

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