Böcker av Chris Mortensen

"The Impossible Arises explores the life and work of Oscar Reutersvèard (1916-2002), founder of the Impossible Figures movement. The movement began in Stockholm in 1934 when eighteen-year-old Reutersvèard drew the first impossible triangle. Over the course of his life he would go on to draw around 4000 impossible figures and be honored by the Swedish government with an issue of stamps showing his work. Based on a large collection of Reutersvèard's art and correspondence held at the Lilly Library at Indiana University Bloomington, the lavishly illustrated Impossible Arises examines the evolution of Reutersvèard's impossible figures and how they influenced other modern artists in the later twentieth century. The Impossible Arises offers a detailed look at the philosophy guiding Reutersvèard's art and presents a rich array of stories from his eccentric personal life. It is an essential introduction to the life and career of one of the most fascinating artists of the twentieth century"--

The Theory of Inconsistency has a long lineage, stretching back to Herakleitos, Hegel and Marx. In the late twentieth-century, it was placed on a rigorous footing with the discovery of paraconsistent logic and inconsistent mathematics. Paraconsistent logics, many of which are now known, are "inconsistency tolerant", that is, they lack the rule of Boolean logic that a contradiction implies every proposition. When this constricting rule was seen to be arbitrary, inconsistent mathematical structures were free to be described. This book continues the development of inconsistent mathematics by taking up inconsistent geometry, hitherto largely undeveloped. It has two main goals. First, various geometrical structures are shown to deliver models for paraconsistent logics. Second, the "impossible pictures" of Reutersvaard, Escher, the Penroses and others are addressed. The idea is to derive inconsistent mathematical descriptions of the content of impossible pictures, so as to explain rigorously how they can be impossible and yet classifiable into several basic types. The book will be of interest to logicians, mathematicians, philosophers, psychologists, cognitive scientists, and artists interested in impossible images. It contains a gallery of previously-unseen coloured images, which illustrates the possibilities available in representing impossible geometrical shapes. Chris Mortensen is Emeritus Professor of Philosophy at the University of Adelaide. He is the author of Inconsistent Mathrmatics (Kluwer 1995), and many articles in the Theory of Inconsistency.