Reflexivity, Contradiction, Paradox and M. C. Escher

Abstract

The paradoxes that have been studied by philosophers and logicians are arguments that lead from plausible premises to impossible conclusions. For example, in the Liar Paradox, the assumption that “This statement is false” is either true or false leads to the conclusion that it is both true and false. Depictions of sc-called “impossible objects” in the late works of M. C. Escher are visually paradoxical. There are deep similarities between visual and logico-semantic paradoxes. In the case of the visual paradoxes, knowledge of various means of representing distance enables us to explain how the paradoxical effect is achieved. A novel approach to solving the Liar and other logico-semantic paradoxes consists of coming to understand how the impossibility of their conclusions arises by means analogous to those by which visually impossible objects are produced.