Q&A: Your opinion on the Bayesian approach
Your opinion on the Bayesian approach
Question
Hello,
I heard you say in an interview that Hume’s problem of induction is an open problem. In my view, the Bayesian interpretation of probability theory, as well as machine learning theory, provide good explanations for induction, and they also prove themselves in practice (although it’s clear to me that they too have assumptions that a sufficiently stubborn skeptic could pretend to challenge, and could point to the No Free Lunch theorems that follow from the absence of those assumptions). More generally, it seems to me that in recent years there has been a major movement of people hoping to solve the problems of philosophy (especially in epistemology and philosophy of language, but also concepts like causality) from a probabilistic-computational point of view. I would be glad to read your opinion about this approach in general, and about its results so far in particular.
Answer
If you want to raise a specific argument here and discuss it, you’re welcome to.
Discussion on Answer
That is the standard justification, and I don’t see how it justifies induction. There are infinitely many theories that will fit all the results of the experiments. You choose the simplest one, and the question is what justifies that.
What do you think of the claim that scientific induction is justified by the following argument:
According to Bayes’ formula, every observation that matches the theory raises its probability relative to theories that predicted a lower probability for that observation, and in the limit of a large number of observations, the probability of the correct theory approaches 1 if it was positive to begin with. From this it follows that in order *not* to converge in the end to the correct theory, one has to assign it an initial probability of 0 dogmatically.