> In order to see HOOO EP as a provability notion, you have to interpret the axioms as a theory about provability.
A notion can generally be prior to a particular formalization. If you have an alternative notion of probability in mind, you should be able to express it.
> Now, I can only suggest a formal theory, but the interpretation is up to users of that theory.
Ok, well, it has no users other than yourself, so if you want to communicate how it could be useful, I recommend you find a way of expressing/communicating an interpretation of it.
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Also, I think your idea of a “bias towards consistency” is unclearly described at best.
A notion can generally be prior to a particular formalization. If you have an alternative notion of probability in mind, you should be able to express it.
> Now, I can only suggest a formal theory, but the interpretation is up to users of that theory.
Ok, well, it has no users other than yourself, so if you want to communicate how it could be useful, I recommend you find a way of expressing/communicating an interpretation of it.
—- Also, I think your idea of a “bias towards consistency” is unclearly described at best.