I wasn’t especially impressed by Aretae’s reasoning. For example,
Why would I not believe that the future will be different from the past? . . . This is silly. Bayes disposes of that rather rapidly. Unless one embraces radical skepticism (why should I believe in the past at all?), Bayesian statistics takes both theses (the future is different than/same as the past) and applies updating. What is left standing is the future resembles the past.
You will not be able to perform this updating unless you have already assigned prior probabilities to propositions connecting the past to the future. That’s why Bayesian updating will never get it right if you start out with the anti-induction prior. Hence, to address Hume’s problem, you have to come up with a justification for preferring certain prior distributions. We may have good reasons for preferring those distributions that posit that the past is like the future, but, contra Aretae, those reasons are outside the scope of mere Bayesian updating.
I had trouble understanding the quote out of context. The first sentence is fine. But, despite a prior understanding of Hume’s argument, I couldn’t see how Aretae got from the first sentence to the conclusion that “Hume’s argument goes up in smoke”. On the contrary, Hume’s point was that the connections we make in our minds might have little similarity to the actual connections, if any, that exist among things in the external world.
I had to go to the context to see that Aretae is making Hume out to be some kind of a-priorist. Aretae concludes that general arguments against a-priorists are therefore arguments against Hume. This is a bizarre misreading of Hume. Hume’s problem of induction is itself an attack on a-priorism. He refers to a-priori arguments only to show that they do not suffice to justify induction. This was big news in a day when practically all intellectuals were a-priorists.
I wasn’t especially impressed by Aretae’s reasoning. For example,
You will not be able to perform this updating unless you have already assigned prior probabilities to propositions connecting the past to the future. That’s why Bayesian updating will never get it right if you start out with the anti-induction prior. Hence, to address Hume’s problem, you have to come up with a justification for preferring certain prior distributions. We may have good reasons for preferring those distributions that posit that the past is like the future, but, contra Aretae, those reasons are outside the scope of mere Bayesian updating.
ETA: Better link on anti-induction.
Well that’s why I quoted one part and not the other.
I had trouble understanding the quote out of context. The first sentence is fine. But, despite a prior understanding of Hume’s argument, I couldn’t see how Aretae got from the first sentence to the conclusion that “Hume’s argument goes up in smoke”. On the contrary, Hume’s point was that the connections we make in our minds might have little similarity to the actual connections, if any, that exist among things in the external world.
I had to go to the context to see that Aretae is making Hume out to be some kind of a-priorist. Aretae concludes that general arguments against a-priorists are therefore arguments against Hume. This is a bizarre misreading of Hume. Hume’s problem of induction is itself an attack on a-priorism. He refers to a-priori arguments only to show that they do not suffice to justify induction. This was big news in a day when practically all intellectuals were a-priorists.