I agree with your point that the question of the validity of Bayesian inference and the question about whether the future will be “like” the past are two logically independent questions. I also agree that it is convenient to use “the problem of induction” as a label for questions related to the “similarity” of past and future. Hence, I agree that the posting does not really help to solve “the problem of induction”.
What does help? Well one argument goes like this: “If you believe the future is not like the past, then you must believe that the present is very special; that it is a boundary point between a stretch of time which is one way, and a stretch of time which is quite different. What is your justification for your belief in the special quality of the present?
Perhaps your only possible move is to claim that the present is not special; that all points in time are boundary points. But we have evidence that this is not the case; the first half of the past is visibly similar to the second half of the past, for example.”
This, of course is not an airtight argument. But it does show that someone who denies the validity of induction is likely to be forced into much more convoluted explanations of the evidence than would someone who adopts the simple hypothesis that “all points in time are pretty much alike”. So, in a sense, induction reduces to Occam’s razor.
Response to ETA 2.
I agree with your point that the question of the validity of Bayesian inference and the question about whether the future will be “like” the past are two logically independent questions. I also agree that it is convenient to use “the problem of induction” as a label for questions related to the “similarity” of past and future. Hence, I agree that the posting does not really help to solve “the problem of induction”.
What does help? Well one argument goes like this: “If you believe the future is not like the past, then you must believe that the present is very special; that it is a boundary point between a stretch of time which is one way, and a stretch of time which is quite different. What is your justification for your belief in the special quality of the present? Perhaps your only possible move is to claim that the present is not special; that all points in time are boundary points. But we have evidence that this is not the case; the first half of the past is visibly similar to the second half of the past, for example.”
This, of course is not an airtight argument. But it does show that someone who denies the validity of induction is likely to be forced into much more convoluted explanations of the evidence than would someone who adopts the simple hypothesis that “all points in time are pretty much alike”. So, in a sense, induction reduces to Occam’s razor.