Shapiro and Taschek have argued that simply using intuitionistic logic and its Heyting semantics, one can show that there are no gaps in warranted assertability. That is, given that a discourse is faithfully modelled using Heyting’s semantics for the logical constants, then if a statement S is not warrantedly assertable, its negation ∼S is. Tennant has argued for this conclusion on similar grounds. I show that these arguments fail, albeit in illuminating ways. An appeal to constructive logic does not commit one to this strong epistemological thesis, but appeals to semantics of intuitionistic logic none the less do give us certain conclusions about the connections between warranted assertability and truth.