But isn’t the key premise here that the only possible observations are “good argument for X” and “bad argument for X”? If you also include “good argument for not-X” and “bad argument for not-X”, we could consistently have negligible change to our beliefs after hearing bad arguments so long as the good arguments balance in expectation.
Another way to say this: if we are discussing updating our credence based on observing just the goodness/badness of one person’s argument, we implicitly have *already* updated on the fact that they are arguing for X (rather than not-X). Given that, it’s not too unintuitive that our credence would go down when we observe that the argument is bad since we are merely “undoing” the earlier upward change.
But isn’t the key premise here that the only possible observations are “good argument for X” and “bad argument for X”? If you also include “good argument for not-X” and “bad argument for not-X”, we could consistently have negligible change to our beliefs after hearing bad arguments so long as the good arguments balance in expectation.
Another way to say this: if we are discussing updating our credence based on observing just the goodness/badness of one person’s argument, we implicitly have *already* updated on the fact that they are arguing for X (rather than not-X). Given that, it’s not too unintuitive that our credence would go down when we observe that the argument is bad since we are merely “undoing” the earlier upward change.