The Demise of Number and Axiomatic Systems
Michael Heather & Nick Rossiter
University of Northumbria UK
Post-modern mathematics needed for non-local applications in a global age has to reject the logical positivism of earlier methodology if it is to cope with the science and technology of the twenty first century. The principle of naturality replaces the axiomatic method and the local concept of number. Euclid and the ideals of Plato are inadequate for global reality as argued by Aristotle. Goedel showed the limitations of formal numerical modelling based on axiomatic systems. Twentieth century science carried on with these methods regardless but the reality of global problems now show the urgency to pursue the consequences of Goedel's results for the rational solutions of what faces us all.