An indifferent reaction to a new theory’s handling of confusing old evidence is simply not what happens in real life. When physicists around the world realized that the Theory of Relativity could be used to explain the shift in the orbit of Mercury, their confidence that the theory was correct shot up. Most humans are exhilarated when a new theory they are just beginning to understand gives solutions to unsolved old problems. 

Hence, the critics say, Bayesianism  is obviously not adequate as a way of describing human thinking. It can’t account for some of the ways of thinking that we’re certain we use. We do indeed test new theories against old, puzzling evidence all the time, and we do feel much more impressed with a new theory if it can account for that same evidence when all the old theories can’t.

The response in defense of Bayesianism is complex, but not that complex. What the critics seem not to grasp is the spirit of Bayesianism. In the deeply Bayesian way of seeing reality and our relationship to it, everything in the human mind is morphing and floating. The Bayesian picture of the mind sees us as testing, reassessing, and restructuring all our mental models all the time.

In the formula above, the term for my degree of confidence in the evidence, taking only my background assumptions as true—namely, the term Pr(E/B)—is never 100 percent. Not even for very familiar old evidence. Nor is the term for my degree of confidence in the evidence if I do include the hypothesis in my set of mental assumptions—i.e. the term Pr(E/H&B)—ever equal to 100 percent. I am never perfectly certain of anything, not of my background assumptions and not even any of the evidence I have seen repeatedly with my own eyes.

To closely consider this situation in which a hypothesis is used to try to explain old evidence, we need to examine the kinds of things that occur in the mind of a researcher in both the situation in which the new hypothesis does fit the old evidence and the one in which it doesn’t.

When the hypothesis does successfully explain some old evidence, what the researcher is affirming is that, in the term Pr(E/H&B), the evidence fits the hypothesis, the hypothesis fits the evidence, and the background assumptions can be integrated with the hypothesis in a comprehensive way. She is delighted to see that, if she commits to this hypothesis and the theory underlying it, that will mean she can also feel reassured that the old evidence did happen in the way in which she and her colleagues observed it. In short, she and her colleagues can feel reassured that they did their work well. 

Sloppy observation is a fear for all scientists. It's nice to learn that you didn't mess up.  

All of these logical and psychological effects rising out of her testing the new theory against some troubling old evidence raise her confidence that this theory must be right.