What about beliefs being justified by non-beliefs? If you're a traditional foundationalist, you think everything is ultimately grounded in sense-experience, about which we cannot reasonably doubt.

If a traditional foundationalist believes that beliefs are justified by sense-experience, he's a justificationalist. The argument in the OP works. How can he justify the belief that beliefs are justified by sense-experience without first assuming his conclusion?

Also, what about externalism? This is one of the major elements of modern epistemology, as a response to such skeptical arguments.

I had to look it up. It is apparently the position that the mind is a result of both what is going on inside the subject and outside the subject. Some of them seem to be concerned about what beliefs mean, and others seem to carefully avoid using the word "belief". In the OP I was more interested in whether the beliefs accurately predict sensory experience. So far as I can tell, externalism says we don't have a mind that can be considered as a separate object, so we don't know things, so I expect it to have little to say about how we know what we know. Can you explain why you brought it up?

I don't mean to imply that either of these is correct, but it seems that if one is going to attempt to use disjunctive syllogism to argue for anti-justificationism, you ought to be sure you've partitioned the space of reasonable theories.

I don't see any way to be sure of that. Maybe some teenage boy sitting alone in his bedroom in Iowa figured out something new half an hour ago; I would have no way to know. Given the text above, do think there are alternatives that are not covered?

Perhaps it is so structured that it is invulnerable to being changed after it is adopted, regardless of the evidence observed.

This example seems anomalous. If there exists some H such that, if P(H) > 0.9, you lose the ability to choose P(H), you might want to postpone believing in it for prudent reasons. But these don’t really bear on what the epistemically rational level of belief is (Assuming remaining epistemically rational is not part of formal epistemic rationality).

Furthermore, if you adopted a policy of never raising P(H) above 0.9, it’d be just like you were stuck with P(H) < 0.9 !

The point is that if a belief will prevent you from considering alternatives, that is a true and relevant statement about the belief that you should know when choosing whether to adopt it. The point is not that you shouldn't adopt it. Bayes' rule is probably one of those beliefs, for example.

Without a constraining external metric, there are many consistent sets [of preferences], and the only criticism you can ultimately bring to bear is one of inconsistency.

I presently believe there are many consistent sets of preferences, and maybe you do too. If that's true, we should find a way to live with it, and the OP is proposing such a way.

I don't know what the word "ultimately" means there. If I leave it out, your statement is obviously false -- I listed a bunch of criticisms of preferences in the OP. What did you mean?