Probability Theory

Nevertheless, the proper logical connection is not in the uncertain causal direction (clouds ⇒ rain), but rather (rain ⇒ clouds), which is certain, although noncausal.

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

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.

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

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.

You insist that there is something a machine cannot do. If you will tell me precisely what it is that a machine cannot do, then I can always make a machine which will do just that!

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

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

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.