Probability and Induction

Probability and Induction

Probability and Induction

Probability and Induction

Excerpt

This book is based on lectures I have given to students of philosophy, and it is intended for readers who are interested in the philosophical problems suggested by the title. I do not pretend that it is either a treatise on the mathematical theory of probability or a practical guide to scientific method. For I have not the ability to produce the former, and I do not think it is the business of a philosopher (or perhaps of anyone) to try to provide the latter. So far as mathematics and natural science are concerned, I shall be content if I have avoided howlers.

The philosophical problems discussed are elementary in the sense that they have to do with first principles, and I have tried to make my treatment of them elementary also in the other sense of the word, that is to say, intelligible without much previous reading about the subject. But some of the statements to which I have committed myself are very controversial, and it may be useful to make clear that I do not attach equal importance to them all. In Part I, for example, I have written of knowledge as though it were indefinable, but this is merely because I have seen no satisfactory analysis of knowledge and do not think it necessary for my present purpose to try to find one. In spite of what I have said, I should welcome a new attempt to analyse this notion. At the other extreme, the general account of induction given in Part IV seems to me substantially correct, and I wish to stand by it. The theory of natural necessity in Part II and the range theory of probability in Part III come between these contentions in order of importance. I am acutely conscious of the difficulties of my views and the insufficiency of my arguments, and yet I cannot at present see any other way of describing matters which seems at all plausible. If I am mistaken in what I have said about these topics, I hope that I have at least written clearly enough to be found out quickly.

In accordance with the conventions of the Clarendon Press, logical and mathematical symbols have been printed without quotation marks even where they are themselves the subjects of discourse. I hope no reader will be seriously distressed by this usage, which is almost universal in mathematical texts. In certain contexts it can lead to dangerous confusion, and my own preference is for a rigorous distinction between use and mention at all times . . .

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