 First, although this article has focused on Liar-type paradoxes, and although the medieval literature did too, it also included other kinds of puzzles. For example (the ‘no’-‘no’ paradox), where a = ‘b is false’ and b = ‘a is false’, no Liar-type paradox arises; contradiction can be avoided by simply taking one of the two propositions as true and the other as false. But medieval logicians regarded such cases as problematic because they require us to assign different truth values to propositions that are semantically exactly alike; there is no reason to pick a as the true proposition rather than b or conversely (see Read 2006). Cases like this, which violate only a kind of semantic “principle of sufficient reason”, were often included under the heading “insolubles” (for example, Buridan, Sophismata VIII.8). A variety of epistemic and pragmatic puzzles were often included as  well.[32]  There was rarely any attempt, as is usual in present-day literature on the paradoxes, to ignore all the inessentials and focus in on a single paradigmatic case that gets at the kernel of the issue. For medieval authors, the issue was a broad one. Many did not attempt to give any precise and rigorous characterization of what it takes to be an insoluble. Often, the definitions they did give are quite general and include much more than Liar-type paradoxes. In contrast, Bradwardine’s definition is precise: an insoluble is “a difficult paralogism secundum quid et simpliciter arising from some [speech-] act’s reflection on itself with a privative determination” (Bradwardine [B-I]: §2.1).