All circular reasoning which is sound is tautological and cannot justify shifting expectation.
Does your perspective on this also imply that mathematical proofs should never shift one’s beliefs? It sounds like you are assuming logical omniscience.
Also, it is possible for a circular argument like “A; A → B; so, B; and also, B → A; therefore, A” to be sound without being tautological. The implications can be contingently true rather than tautologically. The premise A can be contingently true rather than tautologically.
One trusts proofs contextually, as a product of the trusts of the assumptions that led to it in the relevant context. Insofar as Bayesianism requires justification, it can be justified as a dependency in EV calculations.
We’re not going to find a set of axioms which just seem obvious to all humans once articulated.
People understand EV intuitively as a justification for believing things, so this doesn’t ring true to me.
The premise A can be contingently true rather than tautologically.
True, I should have indicated I was rejecting it on the basis of repetition. One could reject any repetition of what is already a given in a proof and not lose access to any conclusions. Repetitions contains tautologies (edit: more importantly, repetitions contains sound circular arguments), and I’m ruling out repetitions with EV as the justification. Anything updateful about an argument with circular reasoning is contained in the tree(s) formed by disallowing repetition.
Does your perspective on this also imply that mathematical proofs should never shift one’s beliefs? It sounds like you are assuming logical omniscience.
Also, it is possible for a circular argument like “A; A → B; so, B; and also, B → A; therefore, A” to be sound without being tautological. The implications can be contingently true rather than tautologically. The premise A can be contingently true rather than tautologically.
One trusts proofs contextually, as a product of the trusts of the assumptions that led to it in the relevant context. Insofar as Bayesianism requires justification, it can be justified as a dependency in EV calculations.
People understand EV intuitively as a justification for believing things, so this doesn’t ring true to me.
True, I should have indicated I was rejecting it on the basis of repetition. One could reject any repetition of what is already a given in a proof and not lose access to any conclusions. Repetitions contains tautologies (edit: more importantly, repetitions contains sound circular arguments), and I’m ruling out repetitions with EV as the justification. Anything updateful about an argument with circular reasoning is contained in the tree(s) formed by disallowing repetition.