Excellent post by Edward Feser on this topic, but full of enough careful reasoning that excerpting it defeats the purpose. You’ll need to just go read it. Here’s a bit from the opening section to get the flavor:
Modern empiricism hoped sharply to delimit the boundaries of speculative reason in a way that would decisively undermine (what empiricists regarded as) the excesses of Scholastic and rationalist metaphysics. Principles like Hume’s Fork — the thesis that any meaningful proposition must concern either “relations of ideas” or “matters of fact” — seemed at first glance formidable weapons in the empiricist arsenal. The key theses of Scholastic and rationalist metaphysics appear to be neither true by virtue of the relations of the ideas they express, nor knowable the way ordinary empirical matters of fact are. Thus we may as well “commit them to the flames,” as Hume recommended. A crisp and clear refutation of traditional metaphysics, yes?
Well, no, actually, for there are several serious problems with Hume’s Fork. First, why should anyone find the principle remotely plausible in the first place who isn’t already committed to the background empiricist picture of human knowledge that informs it — as, of course, Scholastics and rationalists are not? From the point of view of those against whom the principle was directed, then, it seems manifestly a question-begging non-starter. Second, there are areas of knowledge affirmed by both empiricists and their enemies for which Hume’s Fork cannot plausibly account. In particular, truths of logic and mathematics are notoriously difficult to make sense of in terms of either Hume’s “relations of ideas” or “matters of fact.” Third, taken at face value the principle is obviously self-refuting. For Hume’s Fork is not itself either true by virtue of the relations of the ideas it expresses, nor knowable the way ordinary empirical matters of fact are. Hence, by its own standard, it would have to be rejected as meaningless. Or if it is not meaningless, that can only be because it presupposes precisely the third, metaphysical sort of perspective that it purports to rule out.
What I see here is that unbreakable thread that leads from what passes for thought in the modern world through Hegel, Fichte and Kant, on through Hume and Descartes, and back to Luther and Calvin: the idea, contra the Thomists, that Truth can be got outside, somehow, the workings of the mind in the world, in such a way that nothing in the world can challenge it. If you do not agree with Calvin or Luther (or Hegel or Marx), the problem is YOU. You are unenlightened, lack insight, are on the wrong side of history, in every way unworthy of rebuttal – you are trying to reason about things that are simply beyond reason UNTIL you accept the premises laid down. Which is to concede the whole game, as the rational questions are about exactly those premises.
Anyway, check it out.