Hume distinguishes matters of fact from relations of ideas. To take the division as exhaustive leads to a very familiar account of metaphysics.
A relation of ideas has two properties 1.) a truth that can be known by demonstration or intuition, 2.) a claim where the truth of the statement does not depend on the existence of the subject. Mathematical objects serve as proofs for (2), for example, it’s true that all Euclidean circles are round or that points have no parts, and this remains true even if there are no such things as Euclidean circles or points. It follows from (2) that matters of fact are only true if the subject exists, and we have many examples of this e.g. it cannot be true that the sun rose this morning if the sun did not exist this morning. So far, so good but matters of fact also have to be non-demonstrative and non-intuitive. Both properties are crucial, and if we take them as exhaustive it follows that any inquiry into things that actually exist must be purely a posteriori and inductive. Metaphysics (the inquiry into existence) is identified with an inductive, tentative, and even experimental method – that is, with science, or, what amounts to the same thing, metaphysics is impossible.
It is inarguable that there are matters of fact and relations of ideas, but a critique of this would be to treat the distinction as not absolute or non-exhaustive. One approach would turn on finding truths that were both demonstrative or self-evident and yet which would not be true if the subject did not exist. Cartesians might volunteer the the claim “I exist”; Aristotelians would point to large and significant sections of the Physics and Metaphysics.