Pyrrhonian skeptics are known to (allegedly) suspend judgement on ALL matters, thereby being completely free of all presuppositions.
But could such a skeptic suspend judgment about their own omniscience? Omniscience here being defined as: "The state of knowing everything there is to know."
Given this definition, I'm not sure a pyrrhonian skeptic can actually suspend judgment about their own omniscience. Either:
They actually know everything there is to know, in which case they are omniscient by definition. But a genuine skeptic would be unlikely to make such a claim lest they ceased to be a skeptic.
They do not know everything there is to know, in which case they are not omniscient by definition. But a skeptic would be hard pressed to assert that they lack omniscience, since doing so would require them to judge themselves to be not omniscient. Suspending judgement seems to entail asserting one's own status as not being omniscient.
So in summary, the pyrrhonian skeptic can:
a) Refrain from positively asserting their own omniscience, due to the immodesty of such a claim. But they cannot meaningfully suspend judgment on this question, since either they are omniscient (by virtue of knowing everything) or they are not (by virtue of not knowing everything).
b) Remain agnostic about omniscience as a general conceptual possibility for human beings. But when it comes to their own cognitive state, a skeptic either does or does not meet the definition of omniscience, leaving no meaningful "middle ground" of suspended judgment.
Maybe I'm missing something here. It would strike me as odd that no one ever conceived of that argument against pyrrhonian skepticism - at least I've found nothing about it.
Your thoughts are much appreciated!