Ockham’s razor, empirical complexity, and truth-finding efficiency

The nature of empirical simplicity and its relationship to scientific truth are long-standing puzzles. In this paper, empirical simplicity is explicated in terms of empirical effects, which are defined in terms of the structure of the inference problem addressed. Problem instances are classified according to the number of empirical effects they present. Simple answers are satisfied by simple worlds. An efficient solution achieves the optimum worst-case cost over each complexity class with respect to such costs as the number of retractions or errors prior to convergence and elapsed time to convergence. It is shown that always choosing the simplest theory compatible with experience and hanging on to it while it remains the simplest is both necessary and sufficient for efficiency.