Philip Dodds' objections are common ones, and I don't think that they are too difficult to answer. Now to begin the substantive critique.
Intuition is no more arbitrary than any other sort of knowledge.
Well, introspect at how you perform a mathematical proof. You will notice that at some point, you do not produce a proof of a step, but simply see that the step is valid and make it. Now suppose that a deduction skeptic came along and demanded a proof of that last step. I don't see any re-definition of knowledge at all, but rather a synthetic claim about our means of acquiring knowledge. He seemed perfectly sober to me.