Positive evidence for non-arbitrary assignments of probability

How to assign numerical values for probabilities that do not seem artificial or arbitrary is a central question in Bayesian statistics. The case of assigning a probability to the truth of a proposition or event for which there is no evidence other than that the event is contingent, is contrasted with the assignment of probability in the case where there is definte evidence that the event can happen in a finite set of ways. The truth of a proposition of this kind is frequently assigned a probability via arguments of ignorance, symmetry, randomness, the Principle of Indiffernce, the Principal Principal, non-informativeness, or by other methods. These concepts are all shown to be flawed or to be misleading. The statistical syllogism introduced by Williams in 1947 is shown to fix the problems that the other arguments have. An example in the context of model selection is given.