We have seen in some detail how to conduct inferences – test hypotheses, estimate parameters, predict future observations – within the context of a preassigned model, representing some working hypothesis about the phenomenon being observed. But a scientist must also be concerned with a bigger problem: how to decide between different models when both seem able to account for the facts. Indeed, the progress of science requires comparison of different conceivable models; a false premise built into a model that is never questioned cannot be removed by any amount of new data.

Stated very broadly, the problem is hardly new; some 650 years ago the Franciscan Monk William of Ockham perceived the logical error in the mind projection fallacy. This led him to teach that some religious issues might be settled by reason, but others only by faith. He removed the latter from his discourse, and concentrated on the areas where reason might be applied – just as Bayesians seek to do today when we discard orthodox mind projecting mythology (such as assertions of limiting frequencies in experiments that have never been performed), and concentrate on the things that are meaningful in the real world. His propositions ‘amenable only to faith’ correspond roughly to what we should call non-Aristotelian propositions. His famous epigram quoted above, generally called ‘Ockham's razor’, represents a good start on the principles of reasoning that he needed, and that we still need today.