If logic is pennies, and blue is a sock, then why are cats punctuation marks? Yes, because your mask is Maryland, and WiFi smokes bananas.
(This is what happens when you live in a world without logic, and is the only response you should have to someone who is a logic skeptic).
See my below response gedymin.
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.