On scientific knowledge

I was watching this very interesting debate between some great thinkers of our time. And of course I was thinking: "no, that have to be wrong"!
The question at hand is: is all knowledge empirical? Kruass is strongly advocating thing line. Dennet and Pigliucci is a bit more vague, but at the end seem to lean to the same conclusion. I would claim that this is wrong. There is knowledge (if we even can define the term!) that is not empirical. My example of this is basically mathematical knowledge. Krauss is claiming also mathematical knowledge is empirical since the basis (the axioms) is empirical to their nature is not correct. There can be many axioms not at all connected to any empirical facts - in fact ZF is an excellent example of this. Even the designers of the damn thing did not like it since it was counter intuitive with all these axioms. Nevertheless we would all agree that "the integral of 1/x is ln(x)" is knowledge. Or an even better example, the properties of the monster group constitute knowledge.

I think I would rather go further actually and say that all knowledge is of non-empirical nature. Empirical stuff is what can be observed. However observations can never be trusted. Never. However, deductions (which might be based on observations) can be trusted and render knowledge. But all that knowledge is of the for "if a the b". If a is observed, that b can be deduced. Thus, the knowledge does not depend on the empirical fact, but is only claims something about logical consequences given the empirical fact.