First, there is some confusion here about what probability is. In any real problem you want the strength of implication of one binary proposition by another; and this quantity was proved in 1946 by RT Cox, from the Boolean calculus of the propositions, to obey the sum and product rules (and their immediate corollary Bayes' theorem). Since degree of implication is what we want and it obeys the sum and product rules, it seems sensible to take it as 'the probability' - but if anybody objects to this definition of the p-word, it is better not to engage them but simply sidestep and get on with solving the problem by calculating the degree of implication. That said, there is a mystery: Suppose you plot a theoretical curve, and it is a straight line having a particular gradient, and then you plot the experimental datapoints, and find that they fit beautifully on a straight line but of a very different gradient, then why do we reject the theory even if we don't have a competitor? This rejection is a problem for objective Bayesians, for whom theories can only be tested against each other on the basis of their predictions, and the probability for each theory we throw into the game must (conditioned identically) add up to unity. In contrast, frequentist hypothesis testing can happily take place in a vacuum with no predictive alternative. I think the answer is as follows. When our minds see the datapoints lying on a straight line of a very different gradient, they immediately invent a new hypothesis - that the correct curve is a straight line, but of a different gradient than that predicted by the formal theory. Then our minds intuitively perform an Ockham-type Bayesian analysis, in which "straight line with data-estimated gradient" wins out over "straight line with the gradient predicted by the formal theory". The capacity of our minds to invent a new hypothesis in the light of the data is something that the Bayesian calculation does not replicate, and this explains the discrepancy. Popper's concern that there are an infinite number of theories, all a priori equally improbable, is as confused as much that this over-rated philosopher wrote. It is only theories with testable predictions that get thrown into the Bayesian survival-of-the-fittest contest. A deeper problem with Popper's view of physical science is that he rejected inductive logic but accepted probability - yet inductive logic, when done correctly, IS (Bayesian) probabilistic reasoning. Probabilistic testing is the only practical way to compare theories; without it, you are left only with the black-and-white of True or False, whence Popper's 'falsifiability' criterion. Whoever thought that it was the height of scientific ambition to see your theory proved WRONG?