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.
Implicit assumptions- not just the senses, but the reliability of memory and the reliability of rules of induction.
I already mentioned that I believe in the world, not because I think it rational, but as an act of religious-style faith. I think it irrational to believe the world exists because it makes so many assumptions that can't be defended in a rational argument.