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.
I said earlier that I believe that rationally speaking, skepticism proves itself correct and ordinary ideas of rationalism prove themselves self-refuting. However, I believe on faith (in the religious sense) that skepticism is false, and have beliefs on faith accordingly.
Therefore, I sort of believe in a double truth, but in a coherent fashion.