Listening to this podcast made me revisit some topics that I haven't thought about in years.
It seems to me that the major points Prof Deutsch makes all boil down to - Bayesian priors, credencies as he calls them, are actually conditional on a pre determined set of outcomes but the true possible set of outcomes is not really known or knownable. So the input probabilities are conditional and not absolute. That also creates a self affirmation paradox.
He does admit that the paradigm Bayesian statistics provides applies very well in practice for certain types of problems but he is highly uncomfortable with the applications to major physics theories.
I understand his criticism from the point of view of logic, but I think it leads down a rabbit hole as his proposed alternatives (consistency as opposed to probability based) lack clarity or conviction as it became very obvious throughout the conversation.
For me the only takeout, and frankly not a very profound one, is that one has to be aware of the "infinite variance" challenge in certain types of problems.
What rubs me the wrong way is that Prof Deutsch seems to like being contrarian for the sake of it. It is extremely easy to find flaws with pretty much everything in life, infinitely harder to provide alternatives.
For example recently he posted the following on Twitter :
In an irrational education system, those who can best game the exams come out on top. Those who are actually competent can make it too but not as well.
In an irrational electoral system, those who can game it come out on top, and those who are competent do something else.
The statement is extreme and obviously ridiculous. What are the meanings of "irrational" or "competent" here? Yes - we all know that there are plenty of brilliant minds who dropped out of high school or college. Yes, there are people who are very good at passing tests but lack creativity. Education systems don't work for 100% of people. But implying that if you succeeded academically, that somehow makes you less competent ?? He is falling exactly into the same trap he tried to set up for others (the banker and feminist example).
The underlying theme in Deutsch's thinking seems to be that we have to blow up everything apart to accommodate corner cases and avoid inconsistencies. Yet, based on what I have seen, his attempts to provide answers as to what should come afterwards are so weak that it is hard for me to take him too seriously.