Fair point. The ambiguity is already included in the original formulation of the thought experiment. The first formulation is compatible with lowering the posterior expected strength of evidence of other books after reading one of them, but it is also compatible with being not convinced by the evidence at all. Assuming the first interpretation the problem is underspecified and no apparent paradox is present.
The second interpretation can have several subinterpretations:
2a) For each book x, reading x convinces ordinary human about the particular proposition argued for in x (possibly using biases and imperfections of human mind).
2b) For each book x, reading x convinces ideal Bayesian reasoner (IBR) about the particular proposition.
2a was probably closest to the meaning intended in the OP. It is a paradox only if we assume that ordinary human resoning is consistent, which we don’t assume, so there is no problem. 2b depends on what IBR exactly means. If it has no limitations on processing speed and memory the thought experiment becomes impossible, since the IBR has already considered all possible arguments and can’t be swayed by rhetorical trickery. If, on the other hand, the IBR has some physical limitations, 2b can be used to show that its thinking leads to inconsistencies, but it is not much more surprising than the same conclusion from the case 2a.
Fair point. The ambiguity is already included in the original formulation of the thought experiment. The first formulation is compatible with lowering the posterior expected strength of evidence of other books after reading one of them, but it is also compatible with being not convinced by the evidence at all. Assuming the first interpretation the problem is underspecified and no apparent paradox is present.
The second interpretation can have several subinterpretations:
2a) For each book x, reading x convinces ordinary human about the particular proposition argued for in x (possibly using biases and imperfections of human mind).
2b) For each book x, reading x convinces ideal Bayesian reasoner (IBR) about the particular proposition.
2a was probably closest to the meaning intended in the OP. It is a paradox only if we assume that ordinary human resoning is consistent, which we don’t assume, so there is no problem. 2b depends on what IBR exactly means. If it has no limitations on processing speed and memory the thought experiment becomes impossible, since the IBR has already considered all possible arguments and can’t be swayed by rhetorical trickery. If, on the other hand, the IBR has some physical limitations, 2b can be used to show that its thinking leads to inconsistencies, but it is not much more surprising than the same conclusion from the case 2a.