I maintain that it isn't just hard, it is computationally impossible. We should all know that given a belief about the world, and evidence, Bayes' Theorem describes how to update our beliefs. But what if we have a network of interrelated beliefs? That's called a Bayesian net, and it turns out that Bayes' Theorem also prescribes a unique answer. However, unfortunately, it turns out that working out that answer is NP-h…
> We should all know that given a belief about the world, and evidence, Bayes' Theorem describes how to update our beliefs. Should we? What of the problem of induction?
And neither logic nor mathematics offers a solution. In practice, however, we do. But, as any parent should know, we don't do it through a rational process.