Hume's Fork
Overview
An account of Hume's fork and its significance for his philosophy.
ALL the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact.
Though not explicit, Hume's fork identifies the dichotomies we now talk about as analytic/synthetic, necessary/contingent, a priori/a posteriori.
The importance of Hume's fork lies not only in its clear presentation, but in its central place in Hume's philosophy. It is the seed of Hume's scepticism, which provides a more precise delimitation of the scope of deductive reason than had hitherto appeared.
A bigger picture with Hume's fork at its epicentre.
The Fork
ALL the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact.
When David Hume's Treatise on Human Nature "fell dead from the press", he concluded that his exposition was at fault and set about writing a shorter and more accessible account of the most important parts of his philosophy. In An Enquiry Concerning Human Understanding, Hume's own distillation of what mattered most in his philosophy, at the very epicentre (Section IV Part I) we find the following oft quoted passage:

"ALL the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic; and in short, every affirmation which is either intuitively or demonstratively certain. That the square of the hypothenuse is equal to the square of the two sides, is a proposition which expresses a relation between these figures. That three times five is equal to the half of thirty, expresses a relation between these numbers. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence.

Objects of Enquiry
Hume's fork is concerned with a single classification of the "objects of enquiry". He does not here tell us what kind of thing an "object of enquiry" might be.but it sounds like the kinds of thing of which we might have knowledge, so judgements or propositions are contenders, or possibly sentences in context or statements. Hume does talk about propositions here, and for Hume a relation between ideas is a kind of thing which might be expressed by a proposition. This usage is similar that of Russell and corresponds to treating propositions as sentences (in context) "up to" equivalence in meaning or as equivalence classes of synonymous sentences. If however, we consider propositions to be the kind of thing expressed by sentences (without going into exactly what they might be), i.e. we take them as meanings rather than as things which have meanings, then in this sense of the term proposition a relation between ideas would be some kind of proposition rather than something expressed by a proposition. A further possibility is that the objects of enquiry are the things which propositions are about, i.e. in the terminology of first order logic, an interpretation, model or structure, or in mathematical terminology, some mathematical structure, such as a group. To further refine Hume's fork we will need to look more closely at this question.

Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. That the sun will not rise to-morrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood. Were it demonstratively false, it would imply a contradiction, and could never be distinctly conceived by the mind."

Relations of Ideas
This might be taken psychologically, an idea might be the same kind of thing as a thought, or it might be some kind of thing which could be entertained in a thought but which is not itself psychological. The examples cited by Hume make it clear that he intends the latter. In fact he here cites entire branches of mathematics as examples of objects of human reason which concern relations of ideas. He gives no other specific examples but then provides a second characterisation of this class of "objects of reason", viz. "every affirmation which is either intuitively or demonstratively certain". So we now know that these objects are "affirmations".
Matters of Fact
Though Hume does not talk explicitly of necessity when he talks about relations between ideas, he here talks about possibilities in his characterisation of "matters of fact", and from this we might infer that he believes that true propositions about relations between ideas are necessary. Matters of fact are then what we would call contingent.
Three Dichotomies in Hume's Fork
Though not explicit, Hume's fork identifies the dichotomies we now talk about as analytic/synthetic, necessary/contingent, a priori/a posteriori.
Introduction
I'm going to point here to the evidence in Hume's description of his fork for the features which correspond to three separate distinctions which have been important in analytic philosophy ever since (two of the originate long before Hume, the third is sometimes held to have begun with Kant).
Analytic/Synthetic

The analytic/synthetic distinction is usually considered to be a semantic distinction, but is sometimes also described in what we would today call "proof theoretic" terms, i.e. in terms of how the propositions can be demonstrated. Hume's primary characterisation is in terms of subject matter, and may therefore be considered semantic, but he also provides a proof theoretic characterisation using the phrase "intuitively or demonstratively" certain.

There are therefore reasonable grounds for considering Hume to have identified here, in all but name, the analytic/synthetic dichotomy. Hume's method here may be thought superior to the characterisation appearing later in Kant, since it depends less upon the incomplete understanding of logic which both Hume and Kant inherited from Aristotle. Hume's characterisation in terms of subject matter depends less on logic, but goes to the underlying essential features of the dichotomy.

Necessary/Contingent
Again Hume does not talk explicitly of logical necessity or contingency. He does say the negation of a matter of fact is possibly, and from this we can infer that (if this is a dichotomy) that relations between ideas are necessary. More importantly, he talks about relations between ideas as being "intuitively or demonstratively certain" and we find later that he talks extensively in relation to matters of fact of the lack of necessary connections. So it does seem plausible to regard Hume as having encompassed the necessary/contingent distinction in his fork.
A Priori/A Posteriori
Again, without actually using these terms, Hume invokes this kind of distinction. Talking of relations between ideas he says that:
"Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe."
and talking of matters of fact
"are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing"
and in particular, are not demonstrable.
A Fundamental Dichotomy

Hume does not consider himself here to be describing multiple dichotomies. He is giving a characterisation of a single fundamental dichotomy which is central to his philosophy, in mixed terms from which we can reasonably infer that he would have considered the three separate characterisations coincident if he had considered them separately..

Subsequent philosophers, starting (so far as I know) with Kant separated out the three dichotomies and pulled them apart. Other philosophers put them back together again. The debate goes on.

Its Place in Hume's Philosophy
The importance of Hume's fork lies not only in its clear presentation, but in its central place in Hume's philosophy. It is the seed of Hume's scepticism, which provides a more precise delimitation of the scope of deductive reason than had hitherto appeared.
Some Context

To a reader unaquainted with the historical context Hume's Enquiry begins with a criticism of sceptical philosophy and then presents a philosophy which was subsequently regarded as of the deepest scepticism, as a radical opposite to the dogmatic rationalism of Descartes, and as virtually constituting a reductio ad absurdum of empiricist philosophy.

Both Descartes and Hume were however responding philosophically to a period in which Phyrrhonean scepticism had been revived for use in religious controversy, and its implications outside religion demanded a philosophical response.

Descartes provided a response to Pyrrhonism which despite a pretence at methodological scepticism ends in a dogmatism diametrically opposed to Pyrrhonism. By contrast Hume's philosophy strikes a compromise by accepting deduction as delivering true and certain knowledge, but contrasting that with the more tenuous character of empirical knowledge.

The Plan

Hume's reasoning forward from the fork is well structured. Having asserted that our evidence for matters of fact is quite distinct from that we have for relations between ideas, he then notes that our conclusions about matters of fact are obtained from their evidence by causal reasoning, argues that causal reasoning is what we would now call deductively unsound, and from therefore that none of our conclusions about matters of fact are justified.

His more detailed examinations of various kinds of knowledge of matters of fact, even if we do not accept his scepticism, provides a better characterisation of the limits of deductive reasoning than had hitherto been known.

This constitutes a more detailed account of what lies on the two sides of this fundamental dichotomy, and what Hume provides here is far better than any previous account.


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