This section is absolutely crucial. I don’t think you can read the Treatise properly if you haven’t grasped Hume’s concept of relation. Relations are the building blocks of Hume’s system. This is where we can see why Deleuze aligns Hume with the “minor philosophers” of becoming, rather than the major philosophers of being: the building blocks of Hume’s system is a list of the kinds of relations that obtain between beings, as opposed to, say, Aristotle’s books on logic, which begin in the Categories with a list of the kinds of beings that there are. This conceptual strategy provides Hume a set of first principles stable enough to build on, but flexible enough to avoid many pitfalls of classical metaphysics. This move is a key part of the Treatise’s brilliance. In fact, as Deleuze points out repeatedly, the most crucial thing to understand about Hume’s concept of relation is that a relation is always outside the two entities it relates. This doesn’t mean that relations don’t have being or aren’t entities. It means, basically, that when we have two related ideas, we are dealing, conceptually, with four entities: each of the two ideas separately, the relation between them, and the assemblage or complex of both ideas plus their relation, which forms a fourth distinct entity.
A relation is basically the connection or relationship between any two ideas in the mind. Hume notes that his “philosophical” sense of relation is different than that of “common language,” which considers two things “related” only if they have some kind of natural or inherent proximity or connection. Thus in philosophical terms even to say “these two ideas are [relatively] unrelated” is itself to describe a kind of conceptual relation (more on this below; note that this distinction between the common and the philosophical sense of a word is typical of Hume’s consistently sharp attention to usage and language).
According to Hume, all operations of the mind (and thus all concepts of philosophy) are rooted in seven basic kinds of relation: resemblance, identity, space+time, quantity, quality, contrariety, and cause & effect. Hume also adds that “It might naturally be expected, that I should join difference to the other relations.” But here two more astounding similarities to Bergson emerge. First, Hume notes that difference is not a form of relation but the absence of a relation: it’s the idea of a relation between two concepts, plus the idea of their not having that relation (in other words, Hume, like Spinoza, Bergson, and Deleuze, has a purely positive theory of difference that does not require negation in the Hegelian sense). Second, like Bergson, Hume distinguishes between two kinds of difference: ”The first is call’d a difference of number; the other of kind" (what Bergson calls "difference in degree" and "difference in kind," respectively, or, if we were disciples of Duns Scotus, what we could call "numerical distinction" and "formal distinction").
Two more points bear explaining here, which are closely related. The first is the difference between “resemblance” and “identity,” which, in the wake of 20th-century philosophy, we might be inclined to regard as the same thing. The simplest way to grasp this is to think of “resemblance” as a relation between two or more entities (closer to our English sense of “similarity”), while identity is a relation of a thing to itself: identity is the persistence of a thing in duration, since, as Hume notes elsewhere, we only have an idea of duration or continued existence insofar as we have sequential perceptions of the same entity and connect these in our mind into a belief that these perceptions present us with the same entity, which remains unchanged in the interval. This belief is precisely the relation of identity.
The second point, which might seem counter-intuitive, is the reason that relations are graphed as a bell curve rather than a simple upward line. After all, earlier in the TreatiseHume describes relations as a question of intensity: the more intense the connection of ideas, the more consistent the relation; identity and relation might be expect to be in direct proportion, since no relation is more consistent than between a thing and itself. But as we’ve repeatedly noted, Hume is not building a typologybut rather a conceptual plane of immanence. To understand a given concept, we have to understand it in relation to all the relevant distinctions, and in I.I.V Hume introduces another distinction, which is the distinction between resemblance and association: “tho’ resemblance be necessary to all philosophical relation, it does not follow, that it always produces a connexion or association of ideas.” We can tentatively say, then, that a relation or resemblance is, broadly speaking, the probability or likelihood that two ideas will be connected in the mind, while an association or “connexion” is anactual connection between two ideas (the former is general or abstract, the latter particular or specific). Think of it this way: when you think of a can of Coke, what’s your first association? Maybe it’s “soda” as a general idea; maybe it’s the refreshing sensation of a cool drink; maybe it’s that sugary aftertaste on your teeth; maybe your first association to “can of Coke” is “bottle of Coke.” But statistically speaking, it’s pretty unlikely that your first association when you hear “can of Coke” is “another can of Coke.”
In other words, an association marks a middle ground between similarity and difference. If two ideas are too different, the chance of an association forming between them is small, because their association would serve no practical use. But similarly, if two ideas are too alike, there’s no reason for the mind to call them up together, since the idea of one is basically contained in the idea of the other; furthermore, if an idea was most intensely associated with another thing of exactly the same kind, the mind would end up stuck in a loop: all you’d think about all day was one can of Coke after another. That’s why relation in Hume is a bell curve.