Hume's basic premise is that worthwhile information must contain:
- abstract reasoning concerning quantity or number
- experimental reasoning concerning matter of fact and existence
When we're talking about abstract reasoning as to quantity or number, we're talking about words and symbols that represent things. The abstraction of a thing is not an actual thing, only an interpretation by which we are better able to understand the actual thing.
All of language is abstraction. This is true of spoken/written languages such as English, as well as mathematical languages, programming languages, etc.
We can only use language to understand what we already know a priori, based on our pre-existing knowledge and experience of the world around us. Our experience, language, and reasoning are all subjective as a result.
According to a strict interpretation of his criteria, perhaps we would have to throw out his own reasoning, which presents a paradox. However, the paradox can be resolved by an interpretation that factors in what we mean by worthwhile information, as in, what empirical truths are we attempting to arrive at, and does the information present reliable, repeatable data, or a reliable method by which to produce reliable data.
I think what Hume is presenting is an empirical method to produce data. How we interpret the data and use it to arrive at experiential truth is another matter.
EDIT: I'm leaning upon Kant's response (1781 Critique of Pure Reason) to Hume's Fork, where one of his points is that analytic reasoning cannot tell us anything that is not already self-evident, which I would interpret as, anything that is our justified belief.