This article reports on a new method for analysing self-referential and contradictory sentences. In a new paper, Kostis Vezerides of the American College of Thessaloniki, and Athanasios Kehagias of the Aristotle University of Thessaloniki, in Greece, show that, in almost all cases, paradoxes such as the Liar are resolvable with the use of "fuzzy logic". Earlier work had shown how assigning fuzzy values to self-referential sentences could give rise to mathematical chaos. This is because the systems of equations that must be solved to determine the truth-values are often "non-linear"--so attempts to find a solution can rarely be found in the general case, but must be found numerically, closing in on the answer through several iterations of trial and error. Dr Kehagias and Mr Vezerides, though, set out to find consistent solutions to fuzzy truth equations without chaotic oscillations. Dr Kehagias suggests two directions for further research. The first is to examine the various mathematical algorithms of fuzzy logic from the point of view of psychological authenticity. The second possibility is to devise a form of logic that is in between "fuzzy" logic and normal, true-or-false binary logic. Rather than the infinite choices of fuzzy logic, or the two in binary logic, this would have options for false, true, sort of true, sort of false, and exactly half-way.