Full Idea
Even skepticism contains a belief: the belief in logic. The most extreme position is hence the abandoning of logic.
Gist of Idea
The most extreme scepticism is when you even give up logic
Source
Friedrich Nietzsche (Unpublished Notebooks 1872-74 [1873], 29 [008])
Book Reference
Nietzsche,Friedrich: 'Unpublished of 'Unfashionable Obs' period (v 11)', ed/tr. Gray,Richard T. [Stanford 1995], p.191
A Reaction
Some might say that flirting with non-classical logic (as in Graham Priest) is precisely travelling down this road. You could also be sceptical about meaning in language, so you couldn't articulate your abandonment of logic.