A different form of pluralism about conceptual structure doesn’t employ atomic cores but simply says that the prototype, theory, etc. are all themselves concepts (Weiskopf 2009). Rather than holding that a single concept (e.g., the concept CAT) has multiple types of structure as components, as in the first form of pluralism, this form takes each type of structure to be a concept on its own, resulting in a plurality of concepts (CAT1, CAT2, CAT3, etc). On this view, it is wrong to suppose that there is such a thing as the concept CAT. Instead, there are many cat-concepts, each with a different type of structure, where each is involved in just a subset of the high-level psychological processes associated with cats. CAT1, for example, might explain some instances of categorization and some inferences, while CAT2, CAT3, etc. explain others. What’s more, on this form of pluralism, people might also differ with respect to which kinds of cat-concepts they possess. And even if two people have a cat-concept with the same general type of structure (e.g., prototype structure), the concepts might still be rather different (treating prototypical cats as having rather different sorts of properties). One challenge facing this version of pluralism is to explain why all of the different cat-concepts count as cat-concepts—that is, to explain what unifies the plurality of cat-concepts. A natural answer to this challenge is that what unifies them is that they all refer to the same category, the category of cats. But it is not so clear that they can all refer to the same category given the differences between the different cat-concepts and the way that they function in cognition. For example, a standard prototype structure would capture prototypical cats and exclude the highly unusual, atypical cats that a theory structure would cover, and consequently the two concepts would refer to distinct (though related) categories. Meow.

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