What do you think about the Bayesian approach?
peace
I heard you talk in an interview about the problem of induction of a day as an open problem. In my opinion, the Bayesian interpretation of probability theory as well as the theory of machine learning give good explanations of induction, which also prove themselves in practice (although it is clear to me that they also have assumptions that a sufficiently stubborn skeptic could pretend to challenge, and refer to the No free lunch theorems that arise from the absence of these assumptions). In general, it seems to me that in recent years there has been a large movement of people who hope to solve the problems of philosophy (especially in epistemology and the philosophy of language, but also concepts such as causality) from a probabilistic-computational point of view. I would be happy to read your opinion on this approach in general, and on its products to date in particular.
If you want to raise a particular argument here and discuss it, you are welcome.
What do you think about the claim that scientific induction is justified by the following argument:
According to Bayes' rule, each observation that is consistent with the theory increases its probability relative to theories that predicted a lower probability for this observation, and in the limit of a large number of observations, the probability of the correct theory tends to 1 if it were positive to begin with. Hence, in order to *not* eventually converge to the correct theory, it must be dogmatically assigned a probability of 0 from the outset
That's the accepted justification, and I don't see how that justifies induction. There are an infinite number of theories that will fit all the results of the experiments. You pick the simplest one, and the question is what is the justification for it.
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