This is a very strange criticism—he says the proposition is provably false but also has nonzero probability.
He said it has zero probability but is still useful, not nonzero probability.
“It relies on the provably false probabilistic induction”. Popper was a scientific irrationalist because he denied the rationality of induction. If you deny the rationality of induction, then you must be sceptical about all scientific theories that purport to be confirmed by observational evidence. Inductive sceptics must hold that if you jumped out of a tenth floor balcony, you would be just as likely to float upwards as fall downwards. Equally, do you think that smoking causes lung cancer? Do you think that scientific knowledge has increased over the last 200 years? If you do, then you’re not an inductive sceptic. Inductive scepticism can’t be used to ground a criticism that distinguishes uncertain long-termist probability estimates from probability estimates based on “hard data”.
I think you’re overinterpreting the claim (or Ben’s claim is misleading, based on what’s cited). You don’t have to give equal weight to all hypotheses. You might not even define their weights. The proof cited shows that the ratio of probabilities between two hypotheses doesn’t change in light of new evidence that would be implied by both theories. Some theories are ruled out or made less likely in light of incompatible evidence. Of course, there are always “contrived” theories that survive, but it’s further evidence in the future, Occam’s razor or priors that we use to rule them out.
It also assigns very low probability to some hypotheses that are not logically or analytically false but have little to no observational support, such as “smoking does not increase the risk of lung cancer”. If ‘reject’ means “assigns <0.001% probability to”, then Bayesianism obviously does reject some hypotheses.
This depends on your priors, which may be arbitrarily skeptical of causal effects.
He said it has zero probability but is still useful, not nonzero probability.
I think you’re overinterpreting the claim (or Ben’s claim is misleading, based on what’s cited). You don’t have to give equal weight to all hypotheses. You might not even define their weights. The proof cited shows that the ratio of probabilities between two hypotheses doesn’t change in light of new evidence that would be implied by both theories. Some theories are ruled out or made less likely in light of incompatible evidence. Of course, there are always “contrived” theories that survive, but it’s further evidence in the future, Occam’s razor or priors that we use to rule them out.
This depends on your priors, which may be arbitrarily skeptical of causal effects.
Yes thanks my mistake—edited above