Chapter 7       Bayesianism:  A Major Theoretical Criticism And A Response              Part A

The Bayesian way of explaining how we think about, test, and then adopt a new model of reality has been given a number of mathematical formulations. They look complicated, but they really aren’t that hard. I have chosen one of the more intuitive ones below because I intend to use it to discuss the theoretical criticism of Bayesianism which I mentioned in the last chapter.

The Bayesian model of how a human being’s thinking evolves can be broken down into a few basic components. When I, as a typical, modern human, am examining a new way of explaining what I see going on in the world, I am considering a new hypothesis, and as I try to judge just how true – and therefore how useful – a picture of the world this new hypothesis may give me, I look for ways of testing the hypothesis that will tend to show decisively one way or the other whether this new hypothesis and the model of reality that it is based on really work. What I am trying to determine is whether or not this hypothesis will help me to understand, anticipate, and respond effectively to, events in my world.

When I encounter a test situation that fits within the range of events that the hypothesis is supposed to be able to explain and make predictions about, I tend to become more convinced that the hypothesis is a true one if it does indeed enable me to make accurate predictions. (And I tend to be more likely to discard the hypothesis if the predictions that it leads me to make keep failing to be realized.) I am especially more inclined to accept the hypothesis and the model of reality that it is based on, if it enables me to make reliable predictions about the outcomes of these test situations and, if also, in the meantime, all of my other theories and models are silent or inaccurate when it comes to explaining my observations of these same test situations.

It is worth noting again here that this same process can also occur in a whole nation when increasing numbers of citizens become convinced that a new way of doing things is more effective than the status quo practices. "Popular" ideas, the few that really work, last. In other words, both individuals and whole societies really do learn, grow, and change by the Bayesian model. 

In the case of a whole society, the clusters of ideas that an individual sorts through and tries to shape into a larger idea-system become clusters of citizens, forming factions within society, each arguing for the way of thinking that it favors. The leaders of each faction search for reasoning and evidence to support their positions in ways that are closely analogous to the ways in which the various biases in an individual mind struggle to become the idea system that the individual follows. The difference is that the individual usually does not settle very heated internal debates by blinding his right eye with his left hand. (i.e. Each of us, usually, chooses to set aside unresolvable internal disputes rather than letting them make him crazy. Societies, on the other hand, have riots and, sometimes, revolutions.) 

In societies, factions sometimes work out their differences, reach consensus, and move on without violence. But sometimes, of course, as noted above, they seem to have to fight it out. Then violence between factions within society, or violence with the neighboring society that is perceived as being the carrier of the threatening new ideas, settles the matter. But Bayesian calculations are always in play in the minds of the participants, and these same calculations almost always eventually dictate the outcome. One side gives in and learns the new ways. The most extreme alternative, one tribe’s complete and genocidal extermination of the other, is only rarely the final outcome.

But let us now deal with the flaw that is seen - mistakenly, I will argue - by the critics of Bayesianism in the mathematical formula that purports to model the Bayesian decision-making process.