Formal theories of mental representation have receded from the importance they had in the early days of cognitive science. I argue that such theories are crucial in any mental domain, not just for their own sake, but to guide experimental inquiry, as well as to integrate the domain into the mind as a whole. To illustrate the criteria of adequacy…

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. We show that although these sentences are known to have a diagrammatic expression (in the form of the Gergonne…