Jeffrey Goldstein, Aldelphi University, Garden City, NY

Abstract: This article examines recent attempts to gain insight into philosophical paradoxes through using NDS models employing iterated difference equations and resulting phase portraits and escape time diagrams. The temporal nature of such models is contrasted with an alternative approach based on the a-temporal and non-dynamical construct of a lattice. Finally, there is a discussion of how such strategies for understanding paradox transcend the realm of empirical research and enter territory in the philosophy of mathematics.

Keywords: difference equations, escape diagrams, lattice, logical paradox, model, nonlinear dynamical systems theory (NDS), phase portraits, philosophy of mathematics, self-reference