| Abstract: |
Both in learning and in natural science, one faces the problem of selecting among a range of theories, all of which are compatible with the available evidence. The traditional response to this problem has been to select the simplest such theory on the authority of ``Ockham's Razor''. But how can a fixed bias toward simplicity help us find the possibly complex truth? I survey the standard attempts to answer this question and find them all to be wishful, circular, or beside the point. Then I present a new approach based on minimizing the number of reversals of opinion prior to convergence to the truth. According to this approach, preferring simple theories minimizes changes of opinion even when the truth is quite complex, which explains how a fixed simplicity bias can help one find possibly complex truths. Time permitting, I will present a very general, topological definition of theoretical simplicity and will then show that choosing the uniquely simplest theory compatible with experience is the best possible strategy for minimizing reversals of opinion prior to convergence to the truth. |