 A geometrical development is the application to explaining the phenomenon of inconsistent pictures. The best known of these are perhaps M. C. Escher’s masterpieces Belvedere, Waterfall and Ascending and Descending. In fact the tradition goes back millennia to Pompeii. Escher seems to have derived many of his intuitions from the Swedish artist Oscar Reutersvärd, who began his inconsistent work in 1934. Escher also actively collaborated with the English mathematician Roger Penrose. There have been several attempts to describe the mathematical structure of inconsistent pictures using classical consistent mathematics, by theorists such as Cowan, Francis and Penrose. As argued in Mortensen (1997), however, no consistent mathematical theory can capture the sense that one is seeing an impossible thing. Only an inconsistent theory can capture the content of that perception. This amounts to an appeal to a cognitive justification of paraconsistency. One can then proceed to display inconsistent theories which are candidates for such inconsistent contents. There is an analogy with classical mathematics on this point: projective geometry is a classical consistent mathematical theory which is interesting because we are creatures with an eye, since it explains why it is that things look the way they do in perspective.