On reflection scientists have rejected many past theories. It is also true that those theories were highly effective within the contexts in which they had been developed and tested. The old earth-centred model of the solar system was supremely accurate at predicting the locations of stars and planets.

Even now Newton's law of gravity is used to calculate satellite trajectories and to go to the moon. Beliefs are made on the basis of the evidence on hand. Philosophers and statisticians have, over a period of time, developed ways of thinking about the relationship between belief, action and evidence that captures this pragmatism.

Beliefs come in degrees and measure how likely we think something to be true. The evidence we gather should influence these degrees of belief. The character of the evidence makes us confident.

We can use a branch of probability theory to map out a precise relationship between what we observe and what we ought to believe. A formula known as Bayes' rule allows you to calculate your degree of belief, or credence, after learning of some evidence, taking into account what you believed before you saw the evidence. Bayes' rule is a unique and rational way to update your beliefs.