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Will_Sawin comments on Confidence levels inside and outside an argument - Less Wrong
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I have been toying with an idea for this based on an analogy to evolutionary biology.
An organism attempts to adapt to the environment it attempts to find itself in, up to the limits allowed by its genetic programming. But a population of organisms, all exposed to the same environment, can adapt even further - by mutating the genetic programming of some of its members, and then using natural selection to change the relative proportions of different genomes in the population.
Similarly, a Bayesian attempts to adjust his belief probabilities according to the evidence he is exposed to, up to the limits allowed by his system of core assumptions and priors. But a population of Bayesians, all exposed to the same evidence, can adjust even further - by mutating priors and core beliefs, and then using a selection process to extinguish those belief systems that don't work well in practice and to replicate variants that do perform well.
Now, imagine that this population of Bayesians exists within the head of a single rational agent (well, almost rational) and that decision making is done by some kind of proportional voting scheme (with neural-net-like back-feedback).
In this scheme, assigning probabilities of 0 or 1 to propositions is OK for a member of this Bayesian population. If that assignment is never refuted, then there is some efficiency in removing the epsilons from the calculations. However, such a sub-agent risks being extinguished should contradictory evidence ever arise.
A true Bayesian is epistemically perfect. I could have different subroutines computing estimates conditional on different chunks of my prior as a way to approximate true Bayesianism, but if you have access to one Bayesian, you don't need another.
Are you 100% sure about that?
I don't know how to compute beliefs, conditional on it being false.
My point is that there are some propositions - for instance the epistemic perfection of Bayesianism - to which you attach a probability of exactly 1.0. Yet you want to remain free to reject some of those "100% sure" beliefs at some future time, should evidence or argument convince you to do so. So, I am advising you to have one Bayesian in your head who believes the 'obvious', and at least one who doubts it. And then if the obvious ever becomes falsified, you will still have one Bayesian you can trust.
I don't think the other guy counts as a Bayesian.
That's definitely a good approximation of the organizational structure of the human mind of an imperfect Bayesian. You have a human consciousness simulating a Bayesian probability-computer, but the human contains heuristics powerful enough to, in some situations, overrule the Bayesian.
This has nothing to do with arguments, though.