 But this result depends on the fact that (pringle(sweater)) and (woollen(sweater)) are merely contingently coextensive. If ‘water’ and ‘H2O’ are necessarily co-extensive, then wanting a glass of water and wanting a glass of H2O will be indistinguishable in higher-order intensional type theory. This failure to make a distinction, however, traces to the intensionality of the semantics — to its being (merely) a possible-worlds semantics — not to its being higher-order or type-theoretic. So possible solutions include (i) augmenting higher-order intensional type theory with extra apparatus, or (ii) employing a different kind of higher-order type theory. In both cases the aim is to mark distinctions like that between wanting a glass of water and wanting a glass of H2O.