  As an initial gloss, a universal semantics, whatever else it may be, is intended to be a framework able to express everything that can be expressed. As in Section 2.1, there should not be any artificial constraints placed on what we might be able to reason well about (or, by extension, think about or imagine), nonsense or not. And a universal logic should not have, as theorems, anything that is patently incorrect. Putting these two ideas together, Sylvan was already convinced that “classical logic” is too strong to serve as the basis for any universal semantics, because it cannot express everything that is expressible, such as many intensional notions; and it does deliver apparently nonsensical theses such as the paradoxes of material implication (see Section 2.2.2 below). (These two aspects of a logic—the extent of the class of models it can describe, and the set of validities it yields—are inversely proportional; cf. Priest 2008, 36–7.)