Just wanted to note that your point that I didn’t properly rebut “Whatever approximation you use, it works to the extent that it approximates the ideal Bayesian calculation—and fails to the extent that it departs.” was a good one, and it has nagged at me for a while. In general in this post I think he’s implying that Bayesianism is not only correct in the limit, but also relevant to the way we actually do thinking. But I agree that interpreting this particular quote in that way is a bit of a stretch, so I’ve replaced it with “You may not be able to compute the optimal [Bayesian] answer. But whatever approximation you use, both its failures and successes will be explainable in terms of Bayesian probability theory.” which more directly draws the link between methods we might actually use, and the ideal bayesian case.
Just wanted to note that your point that I didn’t properly rebut “Whatever approximation you use, it works to the extent that it approximates the ideal Bayesian calculation—and fails to the extent that it departs.” was a good one, and it has nagged at me for a while. In general in this post I think he’s implying that Bayesianism is not only correct in the limit, but also relevant to the way we actually do thinking. But I agree that interpreting this particular quote in that way is a bit of a stretch, so I’ve replaced it with “You may not be able to compute the optimal [Bayesian] answer. But whatever approximation you use, both its failures and successes will be explainable in terms of Bayesian probability theory.” which more directly draws the link between methods we might actually use, and the ideal bayesian case.