The second half of this section on univocity is taken up with Deleuze's whirlwind tour of the three most important figures in the philosophical history of the concept. Unfortunately, I haven't read any Duns Scotus. And dealing with Spinoza is tough and would take us very far afield. So I think I'll focus on the way Nietzsche's Eternal Return illustrates univocity, especially since this is clearly going to be the most important concept in a book about difference and repetition.
Let me start with an image that I attribute to Whitehead. Whitehead always called himself an atomist. Normally the concept of atomism refers to spacial atoms. The state of the world at any given time T involves the position of these atoms in space, and the state at some later time T+1 involves the same atoms at different positions. Mostly we don't think about it, but this type of description of the state of the world obviously presupposes the identity of the atoms between T and T+1. It's not like the curtains drop, everything winks out of existence, and when they come back up, it's a whole new set of atoms, just in different places. We presume a continuity of identity of the spatially located atoms across time -- ie. we say that the same atoms simply moved.
We don't have to look at it that way though. We could remove the assumption that the world was naturally divided up into atoms that have a stable identity over time. In which case we would come up with a different type of atom, a temporal atom. Each atom would consist of the state of the entire world considered as an undivided whole at a given time. This atom obviously can't move. It appears, and then it disappears in the next instant. Each atom in this case is completely unique. If there are similarities between two of these atoms, it can't be because they have components with stable identities throughout time because time itself has been atomized in this scheme. Those similarities, say some overlap in the spatial patterns at a particular location, can only be called repetitions. The paperweight sitting on my desk at time T is not "the same" paperweight that sits there at time T+1, it merely reflects a world at time T+1 that repeats the paperweight aspect the world at time T. What we usually think of as identity across time, is really repetition, or propagation from one time atom to another. That repetition can't taken for granted, because what we're really given are just different time atoms, but it can happen sometimes.
If you really want to bake your noodle, now try imagining that both space and time are independently atomized.
All this is just backdrop to help us imagine the world that fits with the idea of the Eternal Return.
Eternal return cannot mean the return of the Identical because it presupposes a world (that of the will to power) in which all previous identities have been abolished and dissolved. Returning is being, but only the being of becoming. The eternal return does not bring back 'the same', but returning constitutes the only Same of that which becomes. Returning is the becoming-identical of becoming itself. Returning is thus the only identity, but identity as a secondary power; the identity of difference, the identical which belongs to the different, or turns around the different. Such an identity, produced by difference, is determined as 'repetition'. Repetition in the eternal return, therefore, consists in conceiving the same on the basis of the different.
This world of the will to power is clearly the same one we were discussing last time in the context of squirreldom. In order of explain the actual world with a particular set of squirrels in it, we need to lose the idea that there was any such thing as "squirrel form" that you could just pour Being into to manufacture a real squirrel. Instead, univocal Being encouraged us to see the world as a pure flow of becoming, a proverbial Heraclitean river, where real squirrels weren't manufactured from pre-existing squirrel-molds, but were individuated from the flux, each squirrel absolutely unique, a singular eddy of sorts.
How do you know when something is individuated enough to exist as a "thing"? When is has the power to come back, to repeat, even though this "repetition" really means that it is a different thing every time. It's less repetition, than reproduction -- or better yet, production, again, of something capable of producing itself, again. This is actually the same fractal infinite series we saw in the introduction in the context of festivals. The power of a singularity is the ability to repeat as an infinite series, which in mathematics actually even goes by the name of a "power series". Infinite expansion is a weird sort of "identity" though, because each time you come "back" you've actually changed into something else. The only "you" here will be in the process of coming back, each time going beyond your original self to be transformed into something different. In fact, univocal Being says that's the only way to "be" at all.
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