Is Hume's Fork self-refuting?

Question

David Hume wrote:

If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.

An Enquiry Concerning Human Understanding

This is known as Hume's Fork. By his own criterion, shouldn't we reject his own work? It's not any abstract reasoning concerning quantity or number, nor is it any experimental reasoning concerning matter of fact and existence. It seems as if Hume's Fork is self-refuting. It would surprise me that he didn't notice this himself.

Did Hume address this issue?

Answer 1

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.

Answer 2

It would seem that Hume considered his own philosophical enquiries to fall squarely on the side of "experimental reasoning concerning matter of fact and existence". This is spelled out in the introduction to A Treatise of Human Nature. Hume situates his book within the new Science of Human Nature, i.e. psychology:

Here then is the only expedient, from which we can hope for success in our philosophical researches, to leave the tedious lingering method, which we have hitherto followed, and instead of taking now and then a castle or village on the frontier, to march up directly to the capital or center of these sciences, to human nature itself; which being once masters of, we may every where else hope for an easy victory.

Hume is clear that the Science of Human Nature is experimental:

And as the science of man is the-only solid foundation for the other sciences, so the only solid foundation we can give to this science itself must be laid on experience and observation.

He follows by calling the related philosophy "experimental philosophy":

It is no astonishing reflection to consider, that the application of experimental philosophy to moral subjects should come after that to natural at the distance of above a whole century . . .

Where he counts Bacon, Locke and others as "experimental philosophers".