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[It would appear from what follows that non-demonstrative inference is largely a matter of common sense.]

I returned to England in June 1944, after three weeks on the Atlantic. Trinity had awarded me a five-years lectureship and I chose as the subject of my annual course, ‘Non-Demonstrative Inference.’ I had become increasingly aware of the very limited scope of deductive inference as practised in logic and pure mathematics. I realized that all the inferences used both in common sense and in science are of a different sort from those in deductive logic, and are such that, when the premises are true and the reasoning correct, the conclusion is only probable...

I found the subject of non-demonstrative inference much larger and much more interesting than I had expected. I found that it had in most discussions been unduly confined to the investigation of induction. I came to the conclusion that inductive arguments, unless they are confined within the limits of common sense, will lead to false conclusions much more often than to true ones. The limitations imposed by common sense are easy to feel but very difficult to formulate. In the end, I came to the conclusion that, although scientific inference needs indemonstrable extra-logical principles, induction is not one of them. It has a part to play, but not as a premise.

Another conclusion which was forced upon me was that not only science, but a great deal that no one sincerely doubts to be knowledge, is impossible if we only know what can be experienced and verified. I felt that much too much emphasis had been laid upon experience, and that, therefore, empiricism as a philosophy must be subjected to important limitations.

Bertrand Russell (from My Philosophical Development, 1959)

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