Now, all of this may begin to seem intuitive, but once we have a formula set down it also is open to attack and criticism, and the critics of Bayesianism see a flaw in it that they consider fatal. The flaw they point to is usually called “the problem of old evidence.”

One of the ways a new hypothesis gets more respect among experts in the field the hypothesis covers is by its ability to explain old evidence that no other theories in the field have been able to explain. For example, physicists all over the world felt that the probability that Einstein’s theory of relativity was right took a huge jump upward when Einstein used the theory to account for the changes in the orbit of the planet Mercury—changes that were familiar to physicists, but that had long defied explanation by the old familiar Newtonian model.

   

                           Representations of the solar system (credit: Wikimedia Commons) 

                       https://commons.wikimedia.org/wiki/File%3AOort_cloud_Sedna_orbit.svg

The constant, gradual shift in that planets’ orbit had baffled astronomers for decades since they had first acquired the instruments that enabled them to detect that shift. This shift could not be explained by any pre-relativity models. But relativity theory could describe this gradual shift and make predictions about it that were extremely accurate. Examples of hypotheses that worked to explain old anomalous evidence in other branches of science can easily be listed. Kuhn, in his book, gives many of them.¹

What is wrong with Bayesianism, then, according to its critics, is that it cannot explain why we give more credence to a theory when we realize it can be used to explain pieces of old, anomalous evidence that had long defied explanation by the established theories in the field. When the formula given above is applied to this situation, critics say Pr(E/B) has to be considered equal to 100 percent, or absolute certainty, since the old evidence (E) has been accepted as having been accurately observed for a long time.

For the same reasons, Pr(E/H&B) has to be thought of as equal to 100 percent because the evidence has been reliably observed and recorded many times – since long before we ever had this new theory to consider.

When these two 100% quantities are put into the equation, according to the critics, it looks like this:

Pr(H/E&B) = Pr(H/B)

This new version of the formula emerges because Pr(E/B) and Pr(E/H&B) are now both equal to 100 percent, or a probability of 1.0, and thus they can be cancelled out of the equation. But that means that when I realize this new theory that I’m considering adding to my mental programming can be used to explain some old, nagging problems in my field, my overall confidence in the new theory is not raised at all. Or to put the matter another way, after seeing the new theory explain some troubling old evidence, I trust the theory not one jot more than I did before I realized it might explain that old evidence.

This is simply not what happens in real life. When we suddenly realize that a new theory or model can be used to solve some old problems that were previously not solvable, we are impressed and definitely more inclined to believe that this new theory or model of reality is a true one.