I have just rediscovered an article by Max Albert on my hard drive which I never got around to reading that might interest others on Less Wrong. You can find the article here. It is an argument against Bayesianism and for Critical Rationalism (of Karl Popper fame).
Abstract:
Economists claim that principles of rationality are normative principles. Nevertheless,
they go on to explain why it is in a person’s own interest to be rational. If this were true,
being rational itself would be a means to an end, and rationality could be interpreted in
a non-normative or naturalistic way. The alternative is not attractive: if the only argument
in favor of principles of rationality were their intrinsic appeal, a commitment to
rationality would be irrational, making the notion of rationality self-defeating. A comprehensive
conception of rationality should recommend itself: it should be rational to be
rational. Moreover, since rational action requires rational beliefs concerning means-ends
relations, a naturalistic conception of rationality has to cover rational belief formation including
the belief that it is rational to be rational. The paper considers four conceptions
of rationality and asks whether they can deliver the goods: Bayesianism, perfect rationality
(just in case that it differs from Bayesianism), ecological rationality (as a version of
bounded rationality), and critical rationality, the conception of rationality characterizing
critical rationalism.
Any thoughts?
Well, to some extent every system must have unquestionable foundations, even maths must assume the axioms. The principle of induction (the more something has happened in the past, the more likely it is to happen in the future, all else being equal), cannot be justified without the justification being circular, but I doubt you could get through a single day without it. Ultimately every approach must fall back on an infinite regress as you put it, this doesn't prevent that system from working.
However, both Bayes' Theorem and Solomonoff Induction can be justified:
Bayes' Theorem is an elementary deductive consequence of basic probability theory, particular the fairly obvious (at least it seems that way to me) that P(A&B) = P(A)*P(B|A). If it doesn't seem obvious to you, then I know of at least two approaches for proving it. One is the Cox theorems, which begin by saying we want to rank statements by their plausibility, and we want certain things to be true this ranking (it must obey the laws of logic, it must treat hypotheses consistently etc), and from these derive probability theory.
Another approach is the Dutch Book arguments, which show that if you are making bets based on your probability estimates of certain things being true, then unless your probability estimates obey Bayes Theorem you can be tricked into a set of bets which result in a guaranteed loss.
To justify Solomonoff Induction, we imagine a theoretical predictor which bases its prior on Solomonoff Induction and updates by Bayes Theorem. Given any other predictor, we can compare our predictor to this opponent by comparing the probability estimates they assign to the actual outcome, then Solomonoff induction will at worst lose by a constant factor based on the complexity of the opponent.
This is the best that can be demanded of any prior, it is impossible to give perfect predictions in every possible universe, since you can always be beaten by a predictor taylor-made for that universe (which will generally perform very badly in most others).
(note: I am not an expert, it is possible that I have some details wrong, please correct me if I do)
"Well, to some extent every system must have unquestionable foundations"
No, Popper's epistemology does not have unquestionable foundations.
You doubt I could get by without induction, but I can and do. Popper's epistemology has no induction. It also has no regress.
Arguing that there is no choice but these imperfect concepts only works if there really is no choice. But there are alternatives.
I think that things like unquestionable foundations, or an infinite regress, are flaws. I think we should reject flawed things when we have better options. And... (read more)