I’m not sure you’re characterizing deductive and inductive reasoning right here in Bayesian terms. Bayes factors come from metaphysical assumptions and concept groupings, neither of which seems meaningfully described as “inductive reasoning” here
I find it useful to think in terms of failure modes: inductive reasoning is the sort of reasoning that tends to fail because you overestimated the strength of the existing evidence, abductive reasoning is the sort of reasoning that tends to fail because you didn’t evaluate the direction of the existing evidence well (maybe you over-weighted something, maybe you’re missing a possible hypothesis and hence a direction in possibility space, etc.) Of course if you’re simultaneously thinking about all priors and all pieces of evidence these are the same type of error, and a perfect Bayesian update avoids both problems. Indeed a perfect Bayesian doesn’t recognize a distinction between these at all. The problem is that a perfect Bayesian needs perfect Bayesian metaphysics for concept formation and identifying reference classes—metaphysics is already very hard, but it’s much harder if you also want to be a Bayesian with it. The upshot is that members of this community should probably not worry about this distinction, because the accepted approach around here obviates it (as you oberve here) and gives you very different (but equally hard!) things to think about instead.
I’m not sure you’re characterizing deductive and inductive reasoning right here in Bayesian terms. Bayes factors come from metaphysical assumptions and concept groupings, neither of which seems meaningfully described as “inductive reasoning” here
I find it useful to think in terms of failure modes: inductive reasoning is the sort of reasoning that tends to fail because you overestimated the strength of the existing evidence, abductive reasoning is the sort of reasoning that tends to fail because you didn’t evaluate the direction of the existing evidence well (maybe you over-weighted something, maybe you’re missing a possible hypothesis and hence a direction in possibility space, etc.) Of course if you’re simultaneously thinking about all priors and all pieces of evidence these are the same type of error, and a perfect Bayesian update avoids both problems. Indeed a perfect Bayesian doesn’t recognize a distinction between these at all. The problem is that a perfect Bayesian needs perfect Bayesian metaphysics for concept formation and identifying reference classes—metaphysics is already very hard, but it’s much harder if you also want to be a Bayesian with it. The upshot is that members of this community should probably not worry about this distinction, because the accepted approach around here obviates it (as you oberve here) and gives you very different (but equally hard!) things to think about instead.