I've raised arguments for philosophical scepticism before, which have mostly been argued against in a Popper-esque manner of arguing that even if we don't know anything with certainty, we can have legitimate knowledge on probabilities.
The problem with this, however, is how you answer a sceptic about the notion of probability having a correlation with reality. Probability depends upon axioms of probability- how are said axioms to be justified? It can't be by definition, or it has no correlation to reality.
Complete elimination of error would logically imply knowing the truth.
Something like empirical positivism is like a castle on air- it makes assumptions with no basis in reality.
Given that it happens within physical brains it obviously does have at least some basis in reality.
Genuine deep skepticism doesn't happen in real brains and therefore has no basis in reality.