Does the Bayesian degree of belief system result in absurd conclusions?

Question

In Bayesian epistemology, you are considered to have some sort of subjective prior probability of any hypothesis.

Then, when a piece of potential evidence comes about, you can update that credence by comparing the likelihood of that event on the hypothesis under test with the likelihood of that event on an alternative, usually accepted hypothesis. Bayesians recommend to set a non-zero prior for any hypothesis, no matter how ridiculous. For otherwise, no matter how much evidence is acquired, you can never fully believe in a hypothesis with a zero prior.

The problem with this, it seems, is that this seems to implicitly admit that certain forms of evidence should increase your credence in a belief even when it makes sense not to.

For example, suppose one is testing the hypothesis of a witch causing death to someone by casting a spell on them. Suppose one observes a witch casting a spell on them. And that person gets a disease and dies within the next 3 months. The likelihood of that person dying on the witch hypothesis may be much higher than the alternative hypothesis of naturalistic processes causing his disease and death within the next 3 months.

Now, Bayesian epistemology seems to tell you to now update your credence. It tells you that your P(Witches) must necessarily increase. Since its prior is considered to be non-zero, you are now forced to admit that it is reasonable to now, even infinitesimally, be more confident in the witch hypothesis.

But is it really reasonable to do so? Is one observation by itself ANY form of evidence? Do most humans update their credences in hypotheses this way? Do most humans become more confident in a person being a psychic who claims to guess coin results just because the next head/tail matched his guess? I doubt this.

It seems, rather, that most people (unless they grew up believing in psychics) would wait until a certain threshold of evidence before which they even consider the possibility of psychics being real.

So if human beings don’t actually update their credences as a matter of reality based on Bayesian epistemology in a continuous way, and nor does it seem to actually match reality in general, why should this epistemology be considered “true” in some sense?

Note that I’m asking why it makes sense to use this epistemology specifically for claims that we have not observed any evidence for, such as psychics/witches/etc. Of course, when priors are properly defined such as in the case of HIV tests, it may be wise to update credences this way.

Answer 1

There ARE problems with a Bayesian approach to epistemology, but they are the opposite of what you claim them to be.

Bayes correctly pointed out that Bayesian reasoning is how humans think. We assume a prior, assume a certainty for it, and we generally do not change our views quickly, even in the face of evidential falsifications, as we weight prior conviction pretty highly.

Bayes came up with a coherent mathematical way to do this, but it depends on judgement calls about the certainly of our "prior" and about the weight of new evidence. The advocates of Bayesian statistics point out its internal coherence, while frequentist statistics is not internally coherent, and depends on a series of judgement calls about thresholds and sufficiency of data to support or refute a claim.

There is a major problem with Bayesian statistics, and it lies in human psychology. We are highly susceptible to convince ourselves of what we want to believe in. This makes almost all human judgement on certainty of priors, and on evidence weight, VERY subject to confirmation bias. Give people license to select their own priors and weights, and they will, now with a clear conscience, then point to Bayesian statistics to show that their desired POV is not challenged by any evidence.

Note, all dogmatists and ideologues are good Bayesians. They are convinced of the very high prior of their worldview, to the point that no evidence will convince them otherwise, because a very high prior will not be COMPELETELY unaffected by counter evidence, but as a practical matter the difference between a 99.9999999 certainty and a 99.9999998 certainty is irrelevant to them, and to the world.

You are an atheist, and materialist, and have in prior questions noted that you have debated God questions with the religious. You have no doubt debated with Literalist Creationists, and experienced futility in doing so. That was because they have a Bayesian mindset. They have such high priors, that no matter what reasoning errors, errors of facts, or intrinsic dishonesty you may point out in their references sources, the certainty they have in their POV is unaffected by anything you might say or cite. This level of undue certainty is because they hold that there is a very high prior to their worldview, such that any contrary evidence CANNOT shake their faith.

Discussions between two ideological Bayesians demonstrate the\is failing of Bayesianism -- neither party can say or point to anything which can affect the other's views in any discernable way. This is apparent in multitudes of online discussions, in which neither party's views are affected in ANY discernable way by their dialog, no matter how one or both parties were "embarrassed".

Frequentist statistics was explicitly constructed to resist this human psychological flaw, and prioritize data and evidence over prior conviction. YES, frequentist statistics is a somewhat incoherent set of approximations to fully valid mathematics, but incoherence is intrinsic to our knowledge, which is based on building up multiple separate models that we apply to different aspects of our world. WE COULD reduce the incoherence of our overall worldview by one by using Bayesian statistics instead, but the Bayesian statistics provide no resistance to the far worse problem we face of our inherent tendency to dogmatism and confirmation bias.

The essence of the scientific project is to prioritize evidence over dogma, and the drift toward Bayesian statistics is one that science will eventually reverse. Science is a pragmatic endeavor, and pragmatism accepts mathematical incoherence when it provides more useful results, which is what frequentist statistics do.

The essence of a philosophic mindset is to learn to identify the walls of the boxes that one's thinking is being constrained by, and realize that those walls may not actually be built upon solid foundations. Examining their foundations, and the alternatives to that set of walls, may NOT always lead to one abandoning those walls, but WILL lead to one realizing they are not well grounded.

Your objection to Bayesianism -- that it leads to even INFINITESIMAL changes in the probability of a prior, while you think YOUR prior should have a certainty of one and that certainty should be unaffected by evidence, strongly suggests that you are in the grip of an ideology yourself. You are on a philosophy forum. And again, the essence of a philosophic mindset is to question the walls of the boxes that constrain one's thinking. You would be well served by trying to identify your assumption set, and examine the challenging evidence that may bring that set into question, rather than seeking for rationalizations to never question it.

My best guess of the ideology you hold, is that of reductive materialism. If you really want to practice philosophy, then questioning the assumptions behind reductive materialism, would be a very good way to advance your understanding of your self, and of how to do philosophy.

If you want to pursue identifying the challenges to reductive materialism, I can suggest a variety of avenues for you to pursue.

Materialism itself now has almost no adherents among philosophers. The developments of modern physics, to which matter is no longer central, but instead is derivative of more fundamental processes and phenomena, had led almost all materialists to switch to physicalism. The more recent discoveries that what we consider matter, "ordinary" matter, is no more than 5% of our universe, has just reinforced this switch.

Physicalism provides a problematic foundation for an ontology. Physics is a SCIENCE, not a dogma. It is the application of a pragmatic methodology to a subject field, and its boundaries are open. PhysicalISM, at least when it was first adopted, was the claim that all of science will eventually reduce to physics, and that what we can know about our universe is limited to science. These assumptions are, respectively, universal reductionism in science, and scientism relative to all other knowledge. Note that philosophers of science have now abandoned universal reductionism as untrue even of SCIENCE, much less the rest of knowledge (See section 5 of SEP's entry on scientific reduction: https://plato.stanford.edu/entries/scientific-reduction/), and virtually no educated people today defend scientism.

In the face of emergence, scientific pluralism, and pluralism outside science, PhyscalISTS have latched on to "causal closure of physics" as a last feature of the original reductionist dogma, to try to reject evidences for non-physical causation -- which seems to be what disturbs you so much about the possibly of witchcraft having real world effects. But physics CANNOT be closed, if there is scientific pluralism, and/or emergence. And pluralism plus emergence is what science now endorses. Plus even in physics, one cannot identify ANY closed space. All space in the universe is influenceable from anywhere else, thru fields that cross arbitrary boundaries, and even form outside our universe (all cosmology models treat our universe as a whole as not closed). To assert causal closure of physics, is to assert a dogma that is counter to science.

There is also a problem with the dogma of physicalism as a dogma, and that is spelled out in Hempel's Dilemma. One cannot define physics such that it excludes the things that physicalists want to deny are possible (causation by either non-physical mental of spiritual events, by or abstraction on physics), and not end up with a definition of physics that is refuted. An interesting recent book making this point is Stoljar's Physicalism: https://www.amazon.com/gp/customer-reviews/R13R2OUNXMIN6H/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0415452627 Stoljar, a former Physicalist, has now adopted an open ontological view, and is instead committed to an epistemology of methodological naturalism.

I hope this discussion, and the threads it provides, give you interesting and useful philosophic investigations to pursue.

Answer 2

No informed Bayesian believes that the brain performs exact Bayesian inference. The claim of Bayesianism is that the brain approximates (or ought to approximate) Bayesian inference. Exact Bayesian inference is NP-hard, so we cannot calculate it in practice for moderate-sized problems, and we are always dealing with approximations.

So, your witch casts a spell, and the person dies in 3 months, but your brain does not increase its credence in the witch having real magic. That isn't a problem; perhaps your brain is simply using zero increase in credence, to approximate the very small ideal Bayesian increase in credence. This approximation is an instance of "treating a very small factor as negligible," which we do all the time.

Answer 3

Almost any system of reasoning can lead to absurd results if you apply it uncritically. Suppose I hypothesised that whenever a seagull flies over my house it causes the value of a stock exchange index to change. Since the value of the index is changing almost all the time, my prediction is bound to come true. Does that make it a believable hypothesis? Your suggestion that a belief in witchcraft should be influenced purely by observing an extremely sparse correlation between the casting of spells and the timing of deaths is about as sensible as my seagull hypothesis. So the answer to your question about whether the Bayesian degree of believe system can lead to absurd consequences is of course it can if it is applied indiscriminately- you have proved that for yourself.