There are some difficulties to overcome in order to convince persons that the subject of this book is worth knowing something about. George Boole's theory of probability has had an extremely bad press for more than 100 years. It has almost universally been considered to be too complicated to understand, too difficult to calculate, and wrong in addition. As evidence that this is true, try and find a book on probability in, say, the 20th century which has any material on Boole's theory of probability. This is quite remarkable treatment for a person as distinguished as George Boole. In fact, his theory is not wrong, it is quite easy to make the calculations after a few simple emendations, it can solve a number of important problems which cannot be handled by the orthodox theory of probability, and there are quite a few areas in which these problems arise. We will try and convince skeptics that there are good reasons for believing that a book on the subject is justified.

The Last Challenge Problem: George Boole's Theory of Probability

Science & Math

Miller, David W.

Mathematics

Miller Ideas

The theory of arguments is developed as it was actually practiced by the early Greek probabilists. It is then illustrated by a number of examples of actual arguments. How does one handle facts, simple or complex, introduced by one's opponent in an argument? How can one use antitheses and reversals in an argument? How does one handle analogies, or slippery slope arguments, or dilemmas? This book is addressed to persons who are interested in learning appropriate methods for handling ordinary catch-as-catch-can arguments that arise so often in the usual processes of exchanging opinions about the world and all that goes on within it.

Everyday Arguments and the Theory of Argumentation

Reference

There are a great many named theoretical distributions but a large proportion of them have no known justification for their existence. There are two main reasons for this. First, it is very easy to create a "new" theoretical distribution or family of distributions. For many years any such "creation" was sufficient to achieve an academic publication. Second, no one ever, to our knowledge, acted upon the most elementary principles that might afford some justification for a proposed suggestion: namely, does the new distribution provide a good fit to some observed data that cannot be fitted by the standard, better known distributions? The result is that periodicals are full of suggested theoretical distributions that in many cases are of breathtaking worthlessness. This set of two books attempts to remedy this situation: 1. A very large number of theoretical distributions is repeatedly fitted to some 200 observed distributions. 2. I do not hesitate to conclude that a distribution is without value in fitting. Examples are McKay's Bessel function distributions, Fisher's quartic exponential distribution, most of Johnson's system, a distribution due to Ramberg et al. 3. I emphasize some theoretical distributions of major usefulness in fitting which do not seem to be so well known among practitioners. Examples are the immensely powerful Kapteyn system, the Burr distribution, the Evered distribution, and the Craig system. 4. My goal throughout is to enable any practitioner to be able to recognize the most likely possibilities as theoretical distributions for his or her observed dist and to eliminate the unlikely ones without waste of time.

Fitting Frequency Distributions: Philosophy and Practice

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Books by Miller Ideas

See the best price to sell, buy or rent books by the Miller Ideas publisher. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

The Last Challenge Problem: George Boole's Theory of Probability

Everyday Arguments and the Theory of Argumentation

Fitting Frequency Distributions: Philosophy and Practice