The Dempster–Shafer approach to expressing beliefabout a parameter in a statistical model is notconsistent with the likelihood principle. Thisinconsistency has been recognized for some time, andmanifests itself as a non-commutativity, in which theorder of operations (combining belief, combininglikelihood) makes a difference. It is proposed herethat requiring the expression of belief to be committed to the model (and to certain of itssubmodels) makes likelihood inference very nearly aspecial case of the Dempster–Shafer theory.

In 1980 Morris Kline wrote this engaging book, in which he took on many of the myths about the nature and history of mathematics. This new edition will probably be as seldom read as the original, which is too bad because it contains important messages, including perhaps some comfort for anomalies researchers. I will briefly present an overview of the book’s contents, and then say what I think these comforts are. · · · The ancient Greeks developed the seed of (...) what we now think of as mathematics. Kline points out that their mathematical concepts arose from consideration of the natural world, and then the fact that numbers, shapes, and relationships corresponded to things in the real world convinced them that reality itself was in some mystical way generated by numerical principles. The regular patterns that they found in geometric forms and simple integers reflected the regularities of nature, and so provided keys to understanding how things were, and why they were that way. The faith that mathematics lay behind the mundane world of observations became an unquestioned truth, at least as important as the practical techniques the Greeks devised, and passed along through the Middle East and the medieval period to modern Europe. (shrink)

The great problem in writing a theory of everything is that it may turn out to be a theory of nothing. Here is how it works. If you develop a theory that only explains some small, simple Thing, then the theory is very strong. It is precise, understandable, and it always works. As you expand the theory to encompass another Thing, it becomes weaker. It may still be precise and understandable, but it is now more complicated, and because it involves (...) two things rather than one, it starts to become conditional. This means that in order for it to work with regard to the second Thing, we may have to take into account something about the first Thing. And so it goes. As the theory covers more and more Things, it becomes less precise, less understandable, and parts need to be added on in order cover multiple contingencies. People who go down this path inevitably come to a critical point, at which their theory has become so precisely complicated that it can barely be understood, and gargantuan efforts become necessary to make it work at all. To resolve this impasse, they have a terminological epiphany. They suddenly find a language (that is, an arcane vocabulary) which confers the appearance of simplicity to the morass they have created. Precision is replaced by undefined terms and relationships, described in forceful but impenetrable prose. Argumentation becomes not an activity of rational thought, but a magical experience in which a swirling array of undefined concepts assembles itself in just the right way to come to whatever conclusion is desired. In the mouth of its inventor the theory does indeed explain everything, but in the ears of the audience it explains nothing. (shrink)