Deleuze on Repetition vs. Generality

One might think of repetition as some kind of generalization: you see something repeat itself because there's some underlying law that makes the same thing happen, or you repeat an experiment to see the average outcome that everything is some small deviation from, or perhaps anything being repeated suggests they're all manifestations of the same thing in general. The idea goes all the way back to Plato, who posited that there might be differences between instantiations of a given form but that there was some form that they all came from; something in common that makes all chairs chairs first and different types of chairs second (in later times this philosophy would come to be known as Essentialism.)

In order to lay down a clear break from this thinking, Gilles Deleuze starts Difference and Repetition with the statement that "repetition is not generality." What does he mean by this? Consider the following scenario: you need to replace a worn-out gear in a conveyor belt. You can find two replacement gears, both of which are made of the exact same material and are of the same size and shape, but one of them is painted red and one of them is painted blue. By any reasonable definition of the word, these are clearly different gears, their color is different. But to the machine, they are exactly the same: both would function exactly the same way.

In this context, there is a generality that makes the two gears identical because they are completely interchangeable. To the machine, therefore, they both have the same identity, which is determined by the role they play in the larger environment that they're part of. But of course, when one zooms out further from this system, one can find things that clearly make them different. Identity is therefore something that's relative, and speciifcally a matter of function.

One can similarly apply this logic to the repetition of "something". Repetition, by definition, is doing the same thing over and over, but the same thing according to whom or what? The identity of something is always a question of its relationships to other things, but that in turn means that identity is never absolute but always relative. Outside of any such system of relationships, any enactment exists in its own right insofar that without a system of relationships, there exists no criteria at all to say whether they are actually the same.

Category theory captures this idea of generality and identity via the Yoneda Lemma, which states that any "properties" of a given object are equivalent to its relationships to other objects, which means that while there is technically a difference between two isomorphic objects (there are two of them), the difference cannot be found in some kind of ostensible hidden structure but only in the presence of two distinct objects. Technically, this means you could simply draw the "same" object twice, with all the same relationships, and it would be no different than drawing an isomorphic object*. But even if one can do nothing more than impotently insist that one object "is" the set {1, 2, 3} and the other the set {"one,", "two", "three"}, it remains the case that on the physical diagram these two objects are different, the act of drawing them an irreducible repetition elided only by the syntactic relationships they share with the formal rules constraining but not fully dictating how the diagram can be drawn.

* Note to mathematicians: if I'm wrong about this specific part, feel free to contact and correct me, I'm just going with what's apparent to me.