in the policeman’s syllogism (1.5), whether the plausibility for A increases by a large amount, raising it almost to certainty; or only a negligibly small amount, making the data B almost irrelevant? The object of the present work is to develop the mathematical theory which answers such questions, in the greatest depth and generality now possible.

We won’t try to understand it all at once, but we shall feel that progress has been made if we are able to construct idealized mathematical models which reproduce a few of its features.

Any successful model, even though it may reproduce only a few features of common sense, will prove to be a powerful extension of common sense in some field of application.

principles of logic, and not the principles of psychology or neurophysiology.

Good mathematicians see analogies between theorems; great mathematicians see analogies between analogies.

We can make progress only if we dissect it into little pieces and study them separately. Sometimes, we can invent a mathematical model which reproduces several features of one of these pieces, and whenever this happens we feel that progress has been made. These models are called physical theories.

this shows us how to ‘build a machine’, (i.e. write a computer program) which operates on incomplete information and, by applying quantitative versions of the above weak syllogisms, does plausible reasoning instead of deductive reasoning.

The evidence did not make the gentleman’s dishonesty certain, but it did make it extremely plausible.

The evidence does not prove that A is true, but verification of one of its consequences does give us more confidence in A.