[_0w8t]

The article has not mentioned Bayesian inference, which allows to make sound decisions under uncertainty.

For example, in practice the raven problem is not to guess if all ravens are black but to predict the color of the next raven if that color affects a decision.

From that perspective if one knows absolutely nothing about ravens and has seen a single black raven, then it is mathematically sound to guess that the next raven will be black, not white, and make a decision accordingly.

[zalyalov]

What do you mean by sound? Mathematically sound means "there exists a model validating it", and of course it exists, but so what? If you mean you can bound the probability of error, then in your formulation you actually can't.

[_0w8t]

Bayesian inference is mathematically sound as it is based on a very generic postulates and allows to compare probabilities based in the current information and made a decision accordingly. With the proper approach the errors are automatically accounted for. I.e. if the errors are large, then one will see that probabilities are too close each other to make a sound decision. Still if one must made a decision, then one can just use the answer based on Bayesian reasoning.

The problem in practice is that accounting for the existing information is hard with guessing of priors etc. But that is the problem of applicability of Bayesian inference, not the problem with the principle itself.

I.e. Bayesian inference is a good answer to the philosophical problem of induction. It is sad that the article has not even touched on that subject.