contact@onbelief.orgReader Responses Page 5
Laura: I suspect that I hold a fairly similar Weltanschauung to yourself, and think that it is brave of you to commit to what is in many senses a fairly personal thing on to a very public format. Although I agree with the overall direction of the "strength of belief" page, I think that as a coherent argument, it does not always make logical sense - especially out of context of the rest of the website.
I think that my main problem with it was the conceptual overlap between the ideas of belief, strength of belief, probabilities and value systems. I think that it is an interesting idea to try and equate strength of belief with Bayesian probability, but I just don't agree that it is the same. Take for example the second paragraph in the section "what is this page about" at the beginning of the article. Assuming that both the doctor and patient have a superb understanding of probability, I think that it is reasonable to suppose that they have the same beliefs. That is; it is good if the patient gets better, it is bad if he dies (or gets side effects). If the doctor and patient have a good understanding of probability, they will believe that there is a 95% probability that the medicine will work. I don't see what this has to do with strength of belief - they do not have a stronger belief because there is a 95% rather than an 80% chance that the medicine will work; they simply hold the belief that there is a precisely 95% chance that it will work.
Where the patient and doctor may differ could be:
• The different values that they attribute to life vs intolerable side effects.
• Their different approaches in life to risk - e.g. would they gamble on the stock exchange or are all of their savings in an ISA?
• The experiences that they have had - for example, the doctors may have just lost a patient to that drug. Or a patient may have just finished another course of medication with intolerable side effects.
There is a complex relationship between attitudes, beliefs and actual behaviour, which is notoriously "illogical". (By which I mean non-algorithmic. A computer could not make sense of human behaviour. But if we sit down with people and ask them why they have behaved in a certain way; taking into account their background, their experiences, their beliefs and their emotions, the behaviour usually makes some sort of sense.) A single personal experience generally counts for far more than logical analysis in life.
The doctor and patient may also differ in the degree to which they understand probability - there was some work written in the BMJ looking at how well doctors and patients understand probability and risk. If I remember correctly, they concluded that neither doctors nor patients were all that great.
Taking all of this into account, I don't believe that the case that you describe is really about strength of belief; it is just about life.
Having said that I do not agree with the logic of your first example, I agree that it is a fascinating idea that you could apply the mathematical rules of Bayesian probability to "strength of belief". I am just not sure how one could "prove" (or I suppose more to the point, "disprove") that this was the case. You would have to argue convincingly that "strength of belief" was on a reasonably linear/ratio scale - for example, having a 40% strength of belief was around double as effective as having a 20% strength of belief. Also, on a personal level, I am not entirely convinced that my own belief system works like this. I think that I either believe something or I don't. Doubt is already written into that system by my belief in probability. I believe that there is a 95% chance that my husband will be back for lunch by 1.15pm, and a 90% chance that I will have made the white sauce for the gammon by then. I could haggle over the exact figures, but I don't have any actual doubt. I believe that there is a very small chance that the road home will be blocked by a car crash and that my husband will be stuck at a particular point on the road. Because I still haven't persuaded him to get a mobile phone, I will be left worrying that he has had an accident. All a bit disconcerting, but not as far as I can see much to do with my strength of belief.
A slightly pointless digression: Maybe humans just aren't supposed to do "doubt"? From an evolutionary perspective, it wouldn't be a particular useful trait at all. Probability, adaptability and contingency planning is all very well, but actual doubt doesn't get us anywhere. There is some work out there looking at the evolutionary advantage of mental disorder which is probably relevant. E.g. having sickle cell anaemia is a bad thing, but having sickle cell trait is a good thing because you don't die of malaria. Perhaps the same can be said for trait mental illness? Perhaps mental illness is doubt just gone too far? OK, well not all mental illness. Just a thought and digression into the nature of "belief" whatever it is.)
Some more digressions - as far as I can see, one of the core features of Autistic spectrum disorder is the reliance on a logarithmic progression of thinking. This is good in certain circumstances (like being an academic or a doctor) but bad in other circumstances (like relationships, unpredictability and life in general). "Neuro-typical" people usually use heuristics to draw rapid inferences, depending on experience and emotion - and this does them very well. People on the autistic spectrum just cannot do probability, and as a consequence become very anxious. Is this what happens when the brain is directly confronted with "doubt" - or less than 100% strength of belief?
I would apply the same sort of argument to some of the other examples in your article. For example, the 4*4 table that is used to calculate specificity and sensitivity. Or the ROC curve. I see both of these as useful examples of how to interpret test results based on pre and post test probability, and think that they are a huge scientific leap forwards in how we use statistics to interpret our experimental results. However, I am still not convinced that the section should be labeled"how to interpret test of beliefs". On the whole, our belief is that there is a "truth" or "gold standard" test or reality out there, and that we are just working our imperfect ways towards finding it. For the most part, and certainly over the past several years, I think that doctors have an increasingly sophisticated understanding that the "reality" of disease manifests itself through a range of symptoms, signs and investigations. In our imperfect human way, we must integrate and interpret all of these as best as we can to try and identify the underlying pathology or problem. Being human, we use a combination of logic, neural networks and heuristic reasoning to come to what we feel is the most sensible explanation for the combination of presentation and test results. We may have more or less faith in our conclusion depending on our previous knowledge and experience, but I wouldn't describe this as "belief" in the philosophical sense.
Incidentally, your ECG example. Can I try to reassure you, there is a very strong effort in medical school to teach students to treat the patient and not the test. There are exceptions to this - mostly in the field of renal medicine - where it has been shown that patients just do better if you treat their test results rather than asking them how they feel. Even in cardiology, if you treated everybody who had the symptoms of a heart attack with thrombolysis, you would overtreat and quite possibly kill thousands every year. By trial and error, they have worked out exactly what combination of ECG and blood test changes are associated with successful thrombolysis. So that is what they do. Not that I am defending cardiologists. Or in fact hospital doctors in general. But there are times when it is best to treat patients as individuals, and other times when it is in their interests to assume that their pathology fits a common pattern of pathology, and treat them according to the results of randomised controlled trials. If you felt strongly enough, and wanted to know more, there is a fairly extensive literature knocking evidence based medicine, not all of which is logically flawed.)
Finally, the bit about quantum mechanics. It is getting a bit close to lunch time - and I need to hang the washing out - but in a nutshell, my understanding is that quantum mechanics is about very very small things. At present, there is no grand unified theory that brings us up to reality. I have no problem in accepting the possibility of parallel-probability universes existing side by side. I just thought that as things stand, as soon as observation in any form (i.e. a decision point at molecular level) is encountered, the probability becomes a reality. Therefore it is not reasonable to use quantum mechanics to argue for multiple realities in this universe at the macro-molecular level, whether or not you can use Bayesian mathematics to describe quantum phenomena?
Commentary: Many thanks for your comments and the effort involved in your reply. Yes, we seem to have the same 'world view' or Weltanschauung (see reference page).
Your references to renal medicine and cardiology are truly illuminating because of the 2 very important generalities to which you point: 1) the value of considering statistical descriptors (such as some measure of the average) versus the value of considering the unique individual. 2) the value of subjective or personal experience versus systematic repeatable observation.
Readers might like to execute the following search of the British Medical Journal to see articles of the kind to which you refer concerned the assessment of risk. Click here to search or here. Full text is free at the BMJ so give it a go.
I also like your development of John Maynard Smith's speculation about the evolutionary trade-off between evolutionary fitness, creativity and mental illness (see video on links page). I wonder what he or his interlocutor, Robert Wright, would have made of your idea on autism.
You, like me, have undoubtedly been schooled largely in the 'frequentist' mode of statistical thinking. Bayesianism (see philosophy reference page) can therefore seem out of place in our 'world view' (or Weltanschauung). Indeed I would argue that the difficulties you have with the Bayesian approach is an excellent example of the cultural and educational dependence of our Weltanschauung. 'Frequentism', after you have performed many statistical tests, seems as 'real' as breathing. I would argue that in the field of diagnostic testing Bayes theorem, which is after all derived from the very fundamental Product Rule of probability, is indispensable. If it applies there why not elsewhere.
Clearly I have not persuaded you that the lessons learned in the diagnostic testing of medicine and science are indeed transferable beyond the immediate the bounds of interpretation of the test. I would encourage you to think of 'the facts' in everyday life or the 'gold standard' in testing as 'provisional observations' that are distinct from truth or probabilities. I also feel that when one considers the concepts of Conditional probability, Posterior probability, and Likelihood function, 'strength of belief' can meaningfully have a probabilistic basis. Of course the problem we have is to compute these probabilities in any real world situation or with regard to any particular belief.
We seem to be both in agreement that humans (and other animals) are not rule abiding computational machines, but instead make preference decisions based often on ignorance and using unreliable and highly variable weighting systems. However I have also argued that in the future our ability to act in a more computationally logical manner will become more important as technology develops and perhaps constrains as well as widens our apparent scope for action in the world. (see speculations on logic)
Even if I have not persuaded you of the usefulness in this particular way of thinking I hope that you would agree that 'strength of belief' is a very useful concept in the real world.
You are right to imply that we need a synthetic or integrative view on "ideas of belief, strength of belief, probabilities and value systems". I hope that as this internet site develops such an integration will become more evident.
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On the Nature of Belief
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