Epilogue
It is convenient to look back over what has been accomplished in this book and to put the development into perspective, examining both its strengths and its weaknesses. Essentially what has been done is to establish the
logic of uncertainty.
Ordinary logic deals with truth and falsehood, whereas our subject has been uncertainty, the situation where you do not know whether a statement is true or false. Since most statements are, for you, uncertain, whereas knowledge, either of truth or falsity, is rare, the new logic has more relevance to you than the old. Furthermore, it embraces the old since truth and falsity are merely the extreme values, 0 and 1, on a probability scale. Cromwell's rule (§6.8) is relevant here.
We have also seen what this logic consists of, namely, the calculus of probability with its three basic rules of convexity, addition and multiplication. Many people think of probability merely as a number lying between 0 and 1, the convexity rule, describing your uncertainty of an event. This is only part of the story, and a rather unimportant part at that, because in reality you typically need to consider many uncertain events at the same time before combining them, often with other features, like utility, to produce an answer to your problem. The result established in this book is that these combinations must be effected by the addition and multiplication rules and not in any other way. It is this method of calculation, this calculus, that uniquely provides ...
