Bayes, Bayes' Theorem, Bayesian Approach to Philosophy of Science
The posthumous publication, in 1763, of Thomas Bayes's "Essay Towards Solving a Problem in the Doctrine of Chances" inaugurated a revolution in the understanding of the confirmation of scientific hypotheses—two hundred years later. Such a long period of neglect, followed by such a sweeping revival, ensured that it was the inhabitants of the latter half of the twentieth century above all who determined what it was to take a "Bayesian approach" to scientific reasoning.
Like most confirmation theorists, Bayesians alternate between a descriptive and a prescriptive tone in their teachings: They aim both to describe how scientific evidence is assessed and to prescribe how it ought to be assessed. This double message will be made explicit at some points, but passed over quietly elsewhere.
Subjective Probability
The first of the three fundamental tenets of Bayesianism is that the scientist's epistemic attitude to any scientifically significant proposition is, or ought to be, exhausted by the subjective probability the scientist assigns to the proposition. A subjective probability is a number between zero and one that reflects in some sense the scientist's confidence that the proposition is true. (Subjective probabilities are sometimes called degrees of belief or credences.)
A scientist's subjective probability for a proposition is then more a psychological fact about the scientist than an observer-independent fact about the proposition.
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