Everything I Might Say Will Already Have Passed Through Your Mind*
Roger Koppl
Department of Economics and Finance
Fairleigh Dickinson University
Madison, NJ 07940 USA
Koppl@alpha.fdu.edu
J. Barkley Rosser, Jr.
Department of Economics
James Madison University
Harrisonburg, VA USA
Rosserjb@jmu.edu
March 1999
ABSTRACT
We establish three theorems on the limits to rationality, prediction, and control in economics, based on Morgenstern's analysis of the Holmes-Moriarty problem. The first uses a standard metamathematical theorem on computability to establish logical limits to forecasting the future. The second provides a nonconvergence result on Bayesian forecasting in infinite dimensional space. The third shows the impossibility of a computer perfectly forecasting an economy with agents knowing its forecasting program. Thus, economic order is partly the product of something other than calculative rationality.
*We thank Richard Langlois, Young Back Choi, and Larry Samuelson for useful comments, and Yaw Nyarko for providing research materials. Any limits or errors of analysis are our own.