Chapter 7.                                      Part F 

It is also worth noting here that even the idea behind “H&B” is more complex than the equation can capture. “If I integrate the hypothesis into my whole background concept set” is how this part of the term  should be read. It is an expression that is trying to capture in symbols something that is almost not capturable. This is so because the whole point of positing a hypothesis, H, is that it does not fit neatly into my background set of beliefs. It is built around a new way of seeing and comprehending reality, and therefore, it will only be integrated into my background set of concepts and beliefs if some of those old background concepts and beliefs are removed, by careful, gradual tinkering and adjusting of many concepts.

  Similarly, in the term Pr(H/E&B), the “E&B” part is trying to capture something that no formula can capture. “E&B” is trying to say something like “if I take both the evidence and my set of background concepts and beliefs to be 100% reliable”. But that way of stating the “E&B” part of the term merely highlights the whole point with problematic old evidence. This evidence is problematic because I can’t make it consistent with my set of background concepts and beliefs, no matter how I tinker with them or push them.

   Thus, all that the whole formula really does is try to capture the general gist of human thinking and learning. It is a useful approximation, but we can’t get confident or complacent about this formula for the Bayesian model of human thinking and learning any more than we can get complacent about any of our concepts. And that thought is consistent with the spirit of Bayesianism. It tells us not to become too blindly attached to any of our concepts; any of them may have to be radically updated and revised at any time.

   In short, this whole criticism of Bayesianism — which says that the Bayesian model can’t explain why we find a fit between a hypothesis and some problematic old evidence so reassuring – this whole criticism, on closer examination, turns out to be not a fatal criticism, but more like a useful tool, one that we may use to deepen and broaden our understanding of the Bayesian model of human thinking. We can hold onto the Bayesian model if we accept that all of the concepts, the thought patterns, all of the patterns of neuron firings, in the brain – hypotheses, evidence, and assumed background concepts – are forming, re-forming, aligning and re-aligning, and floating in and out of each other all of the time.

            And what of the spirit of Bayesianism? What Bayesian thinking requires of us is this willingness to float all of our concepts, even our most deeply held ones. Some are more central and we can stand on them with more confidence, more of the time. A few we may believe almost, but not quite, absolutely. But in the end, none of our concepts is irreplaceable. 

            For our species, the mind is our means of surviving. It will adapt, if it has to, to almost anything. I just choose to gamble most heavily on the concepts that I have been using to organize most of my sense data and memories most of the time.

  I use my concepts to organize both the memories already stored in my brain and the new sense data that are flooding into my brain all of the time. I keep trying to acquire more concepts, including concepts for organizing other concepts, that will enable me to utilize my memories more efficiently so that I can make faster and better decisions and perform more and more effective actions. In this constant restless, searching mental life of mine, I never trust anything absolutely. If I did, a simple magic show would mesmerize and paralyze me. Or reduce me to catatonia.

       

  When I see elephants disappear, ladies get sawn in half, and men defy gravity, and all come through their ordeals in fine shape, obviously some of my most basic and trusted concepts are being violated. But I choose to stand by my concepts in almost every such case, not because I am certain that they are perfect, but because they have been tested and found effective over so many trials and for so long that I am willing to keep gambling on them. I don’t know they are “sure things”, but they do seem like the most promising of the options that I have available to me. 

   Life is constantly making demands on me to move and keep moving; I have to gamble on something. I go with my best horses. And sometimes, I change my mind.

   What this mental flexibility on my part means is that the critics of Bayesianism simply haven’t grasped its spirit. What Bayesianism is telling us is pretty much what Thomas Kuhn was saying in his very influential book “The Structure of Scientific Revolutions”. We are constantly adjusting all of our mental constructs to try to make our ways of dealing with reality more efficacious, all of the time. 

   And when a researcher begins to grasp a new hypothesis, and the model or theory that the hypothesis is based on, the resulting experience is like a philosophical or religious awakening – profound, all encompassing, and even life-altering. Everything changes when we accept a new model or theory because we change. In order to “get it”, we have to. We have to cut some of our old beliefs out of our familiar background set.

   And what of the shifting nature of our view of reality and the gambling spirit that is implicit in the Bayesian model? Most of our instincts, along with the general tone of all of our experience, tell us that this overall view of our world and ourselves, though it may seem scary, or perhaps for some more confident individuals, challenging ...it’s just life.

   We have now arrived at a point where we can feel confident that Bayesianism does give us a solid base on which to build further reasoning. It can answer its critics, decisively as it turns out, both the ones who attack it with real world counter-examples and the ones who attack it in the abstract world with pure logic.

     For now then, let's be content to sum up our points in a new chapter devoted solely to that summing up. 

          Notes 

1. Kuhn, Thomas; "The Structure of Scientific Revolutions"; University of Chicago; 1996