Think about it for a while. Even though Hume himself uses this principle in his argument, we could never justify it on his principles. The denial is not a contradiction. But at the same time, this principle is not a mere matter of fact. I think that these two claims are convincing counter- arguments to Hume's conception of reason.
Reason does more than merely discover the presence of absence of contradictions.
It just turns out that Hume underestimates the power of reason when he limits it to locating the presence or absence of contradictions. I probably won't convince anyone in so brief a presentation. But at least let me raise some doubts in the minds of convinced Humeans. I think that it plainly does. Conclusion Hume assumes that reasoning can do nothing except locate the presence or absence of contradictions.