I see no reason to assume that question is beyond the reach of empiricism, which has been (both by its own standard and by naive common sense) effective in a way that alternatives have not. Non-empirical approaches may be able to construct self-consistent theories, but there is an infinitude of self-consistent theories, the overwhelming majority of which are useless under naive common sense. I trust empiricism because I was able to get there in Neurath's boat fashion from the everyday naive common sense that we all live by in practice.
> You are implicitly making the strong claim that knowledge can only be attained through empiricism. This is clearly not the case. I know that I am conscious and I assume that you are, but I cannot use empiricism to test this hypothesis, not can you use it to verify that I am, indeed, conscious.
I don't accept your claim. To the extent that "consciousness" refers to something meaningful, it refers to something empirical. (At least, my experience - under formal empiricism, naive common sense, and along the path between them - is that theories that involved entities detached from empirical consequences were misleading, and less effective than theories that did without such entities).