Suszko's Thesis and the Evil Genius

There is a famous argument of the Evil Genius in Descartes' philosophy. When applied to modern multi-valued logic this argument claims a challenge to foundations of basic hypotheses about the nature of logical values, properties of languages of logical theories, and logic itself. Most part of finitely valued logics, thus, appear to be in some sense Cartesian, while there is no philosophical argument for such a necessity. Surprisingly, the property of "being a Cartesian" for an arbitrary logic is deeply related to the existence of an algorithm for construction of a Suszko-style bivalent semantics for this logic.