In practice, to say that a belief refutes its own justification is usually not to say it's inconsistent, but rather, the alternative was.
So "x refutes its own justification" doesn't seem like an argument against x, rather, an argument against the position which the justification assumed - which will usually be an anti-x position, if the pyrrhonian example is typical. So, favourable sign for x.
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Hard to say if the update has to be favorable for x on the whole, since this seems to be a logical-uncertainty update rather than a Bayesian update.
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Thank you
End of conversation
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