Lev Shestov ( All Things are Possible 
, 64) observes that it is a “school axiom” that “logical skepticism refutes itself, since the denial of the possibility of positive knowledge is already an affirmation.”
Shestov doesn’t think this works: For starters, “skepticism is not bound to be logical, for it has no desire whatever to gratify that dogma which raises logic to the position of law.” Besides, “where is the philosophical theory which, if carried to its extreme, would not destroy itself? Therefore, why is more demanded from skepticism than from other systems? especially from skepticis, which honestly avows that it cannot give that which all other theories claim to give.”
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