Chapter 7.                            Part D 

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

         In other words, the critics say, Bayesianism, as a way of describing what goes on in human thinking, is obviously not adequate. It can’t account for some of the ways of thinking that we know for sure we use. We do indeed test new theories against old, puzzling evidence all of the time, and we do feel much more impressed with a new theory if it can fully account for that same puzzling, old evidence.

       

        Now the response in defense of Bayesianism is complex, but not that complex. The thing that the critics seem not to grasp is the spirit of Bayesianism. What I mean is that in the deeply Bayesian way of seeing reality and our relationship to it, everything in the human mind is metamorphosing and floating. The Bayesian picture of the mind sees us as testing, re-assessing, and re-structuring all of our mental pictures and models of reality all of the time.

         In the formula above, the term for my degree of confidence in the evidence, taking only my background assumptions as being true and thus without letting the new hypothesis into my thinking – namely, the term Pr(E/B) – is never 100%. Not even for very familiar old evidence. Nor is the term for my degree of confidence in the evidence if I include the hypothesis in my set of mental assumptions, i.e. the term Pr(E/H&B), ever equal to 100%. I am never perfectly certain of anything, not my background assumptions and not even any of the evidence that I may have seen – sometimes repeatedly – with my own eyes.

        

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

                    

           When the hypothesis does successfully explain some old evidence, what the researcher is really considering and affirming to her satisfaction is that, in the term Pr(E/H&B), the evidence fits the hypothesis, the hypothesis fits the evidence, and the background set of assumptions can be integrated with the hypothesis in a consistent and comprehensive way. The thoughts that pass through her mind then include jubilation over the fact that if she does commit to this hypothesis, it will mean that she can be more confident that the old evidence really happened in the way that she and her fellow researchers saw it, that they were observing the evidence in the right way, and that they were not prey to some kind of mass hallucination or some form of mental lapse that might have caused them to misinterpret the old evidence situations or even misperceive them altogether. In short, she and her colleagues can feel a bit more confident that they weren’t deluded or sloppy in recording the old evidence data, a source of error that scientists know dogs all research.

   

         All of these things become even more apparent when we consider what the researcher does when she finds that a hypothesis does not successfully account for the old evidence. Rarely in scientific research does a researcher in this situation simply drop the new hypothesis. What she normally does is she examines the hypothesis, the old evidence, and even her background set of assumptions to see whether any or all of them may be adjusted, using new concepts or new calculations involving newly proposed and measured variables or different, closer observations of more replications of the old evidence, so that all of the elements in the Bayesian equation may be brought into harmony again. 

                          

 When I examine the old evidence in light of the new hypothesis, if I discover that the hypothesis does successfully explain that old evidence, my confidence in the hypothesis and my confidence in that old evidence both go up. Even if, prior to this test, my confidence in that old evidence was over 98%, if the hypothesis does successfully explain that old evidence, then I feel more confident that the evidence is as I saw it because I feel more confident that I and my colleagues – even ones in the distant past – did observe that old evidence correctly and did record our observations accurately.

   The value of this successful application of the new hypothesis to the old evidence may seem to be small – perhaps it has only raised the E value in the term Pr(E/H&B) a fraction of one percent. But that is still a positive increase in the value of the whole term and therefore a kind of proof of the explicative value, rather than the predictive value, of this hypothesis. 

  Meanwhile, my degree of confidence in this new hypothesis, namely the value of the term Pr(H/E&B), as a result of the increase in my confidence in the evidence, also goes up another notch. A scientist, like all of us, finds reassurance in the feeling that comes when more of her/his perceptions, memories, and concepts about the world can be brought into a mental harmony by their being made cognitively consonant with each other.