Despite the context, I didn’t have Deutsch specifically in mind. Just a general observation over the years.
The issue under discussion here is wider than Popper and appears elsewhere, in the disagreement between small-world and large-world Bayesians, the former being the side that I guess Popper would have been on. (It’s a very long time since I read Popper, and I do not recall if he ever says anything about Bayesian inference.) Must Bayesian inference of the sort that takes a parameterised model and a prior distribution on the parameters, and fits it to a data set (a process whose validity everyone except a few hard-core frequentists agree on) be subordinate to some other process when the data do not fit your model at all, for any parameters, and you need to find a different model? The small-worlders say yes, and the large-worlders say no. The small-worlders scoff at the large-worlders, the large-worlders exhibit the Solomonoff universal prior, and if the small-worlders are still paying attention, they usually just scoff some more. Sometimes they will point out that Solomonoff induction is uncomputable, and that computable approximations are exponentially unfeasible, relying as they do on merely enumerating all possible hypotheses in order of size. I haven’t seen a large-worlder response to that anywhere, not even here on LessWrong, where large-worldism is the default view.
But then the small worlders, asked just what it is that they put above Bayes, reply only with magic names, such as “human judgement”, “criticism”, or “argument”. All they are doing is describing what the process feels like, not what it is. In chapter 7 of The Fabric of Reality, Deutsch circles around and around the point, but the point never appears.
ETA: And they generally deny that the process can be elucidated any further. Popper himself says (as quoted elsewhere in these threads) that there is no method.
So for me, that is where things stand, and I am not convinced by either side.
Some further context for the above. I’ve been drafting a posting on this for a while, which this comment and that one are based on.
Despite the context, I didn’t have Deutsch specifically in mind. Just a general observation over the years.
The issue under discussion here is wider than Popper and appears elsewhere, in the disagreement between small-world and large-world Bayesians, the former being the side that I guess Popper would have been on. (It’s a very long time since I read Popper, and I do not recall if he ever says anything about Bayesian inference.) Must Bayesian inference of the sort that takes a parameterised model and a prior distribution on the parameters, and fits it to a data set (a process whose validity everyone except a few hard-core frequentists agree on) be subordinate to some other process when the data do not fit your model at all, for any parameters, and you need to find a different model? The small-worlders say yes, and the large-worlders say no. The small-worlders scoff at the large-worlders, the large-worlders exhibit the Solomonoff universal prior, and if the small-worlders are still paying attention, they usually just scoff some more. Sometimes they will point out that Solomonoff induction is uncomputable, and that computable approximations are exponentially unfeasible, relying as they do on merely enumerating all possible hypotheses in order of size. I haven’t seen a large-worlder response to that anywhere, not even here on LessWrong, where large-worldism is the default view.
But then the small worlders, asked just what it is that they put above Bayes, reply only with magic names, such as “human judgement”, “criticism”, or “argument”. All they are doing is describing what the process feels like, not what it is. In chapter 7 of The Fabric of Reality, Deutsch circles around and around the point, but the point never appears.
ETA: And they generally deny that the process can be elucidated any further. Popper himself says (as quoted elsewhere in these threads) that there is no method.
So for me, that is where things stand, and I am not convinced by either side.
Some further context for the above. I’ve been drafting a posting on this for a while, which this comment and that one are based on.