>When you apply Bayes rule, you are assuming that future outcomes will be
>drawn from the same distribution as past outcomes, i.e. you are assuming
>that induction works.
Not true! ALL I am assuming is basic, timeless Bayes Rule.
Bayes rule is deduction. It's a theorem. Using Bayes rule puts all the
onus of induction on the prior. As long as the prior is a good one, Bayes
rule works wonderfully well. But what's a good prior? If you have any
doubts about that, then Bayes can't help you.
People do induction. Hume agreed that he could not help but do it himself.
But, it isn't all that clear what induction IS. Once you define it, you
can program a computer to do "it". Even if it works it a wide variety of
circumstances, will it work in all of them? No. But, will it work well
enough? Maybe, perhaps probably. However, the probability of induction is
not the probability of Bayes. I think Hume said this when he
differentiated between the probability of causes and the probability of
chance.
Whatever gets called induction gets used as an element of faith. One may
perhaps show that an inductive method has a great tradition behind it.
Which kind of makes induction a religion. I think this is still the
probability of God thread.
