It’s worth noting that in the case of logical induction, there’s a more fleshed-out story where the LI eventually has self-trust and can also come to believe probabilities produced by other LI processes. And, logical induction can come to trust outputs of other processes too. For LI, a “virtuous process” is basically one that satisfies the LI criterion, though of course it wouldn’t switch to the new set of beliefs unless they were known products of a longer amount of thought, or had proven themselves superior in some other way.
For LI, a “virtuous process” is basically one that satisfies the LI criterion,
I don’t think this is true. Two different logical inductors need not trust each other in general, even if one has had vastly longer to think, and so has developed “better” beliefs. They do have reason to trust each other eventually on empirical matters, IE, matters for which they get sufficient feedback. (I’m unfortunately relying an an unpublished theorem to assert that.) However, for undecidable sentences, I think there is no reason why one logical inductor should consider another to have “virtuous reasoning”, even if the other has thought for much longer.
What we can say is that a logical inductor eventually sees itself as reasoning virtuously. And, furthermore, that “itself” means as mathematically defined—it does not similarly trust “whatever the computer I’m running on happens to believe tomorrow”, since the computational process could be corrupted by e.g. a cosmic ray.
But for both a human and for a logical inductor, the epistemic process involves an interaction with the environment. Humans engage in discussion, read literature, observe nature. Logical inductors get information from the deductive process, which it trusts to be a source of truth. What distinguishes corrupt environmental influences from non-corrupt ones?
It’s worth noting that in the case of logical induction, there’s a more fleshed-out story where the LI eventually has self-trust and can also come to believe probabilities produced by other LI processes. And, logical induction can come to trust outputs of other processes too. For LI, a “virtuous process” is basically one that satisfies the LI criterion, though of course it wouldn’t switch to the new set of beliefs unless they were known products of a longer amount of thought, or had proven themselves superior in some other way.
I don’t think this is true. Two different logical inductors need not trust each other in general, even if one has had vastly longer to think, and so has developed “better” beliefs. They do have reason to trust each other eventually on empirical matters, IE, matters for which they get sufficient feedback. (I’m unfortunately relying an an unpublished theorem to assert that.) However, for undecidable sentences, I think there is no reason why one logical inductor should consider another to have “virtuous reasoning”, even if the other has thought for much longer.
What we can say is that a logical inductor eventually sees itself as reasoning virtuously. And, furthermore, that “itself” means as mathematically defined—it does not similarly trust “whatever the computer I’m running on happens to believe tomorrow”, since the computational process could be corrupted by e.g. a cosmic ray.
But for both a human and for a logical inductor, the epistemic process involves an interaction with the environment. Humans engage in discussion, read literature, observe nature. Logical inductors get information from the deductive process, which it trusts to be a source of truth. What distinguishes corrupt environmental influences from non-corrupt ones?