I've been working on this Univocity section (35-42) for a while now and a straightforward translation continues to elude me, so I think we'll just have to wade in at random and see how it goes. The concept of Univocity is a tough one because of how abstract and metaphysical it sounds. Beyond even that though, Univocity exhibits a particularly gnarly form of ontological feedback that makes it especially tough. In other contexts, Deleuze will discuss this concept as the question of immanence (as opposed to transcendence) and describe it as "the very vertigo of philosophy". To succinctly state the problem: the idea of immanence really bakes your noodle because if everything comes from within, then so does your theory that everything comes from within. In other words, your thought about things is another thing; there's no way to represent the world without adding to it. If that recursive structure sounds like it's going to be as navel-gazingly simple as thinking about thinking ad infinitum, try watching some video feedback.
Anyhow, so, I think the first thing to notice about the concept of Univocity, at least as presented in this context, is that it is not Equivocity. It is explicitly opposed to construing the unity of Being as analogy, which was how Aristotle understood it in the last section.
The unity of analogy rested on some capacity for third party judgement -- a subject who could judge that two concepts were linked by analogy even though they "really" had nothing to do with one another (in fact, had so little connection that at first we weren't even able to call them "different " but simply "other"). I think my understanding of this point would improve a lot if I read more Kant. But let's pass over the idea of judgement for now, because anyways Deleuze is about to replace it with a different idea, that of the expressive proposition. According to Deleuze an expressive proposition has three parts: 1) a thing or mode or designator that does some pointing, 2) something designated or pointed at by those pointers, which, in the reverse directions is expressing itself through the pointers, and 3) the sense or meaning that is expressed by the proposition as a whole. It's not completely clear to me why Deleuze chooses to introduce propositions and expressions here, other than the connection to Spinoza, who we'll see also believed in Univocity and considered everything an expression of God. Maybe it also has something to do with the way that this concept of expression forms a circle where the designators point at the designated while the designated expresses itself through the designators, which would seem to obviate the need for a third party judgement.
Or maybe, to return to our starting point, the whole idea is just to set up the contrast with analogy. With propositions, we get a model of how different things could designate something in common in the same way, as opposed to analogous but different ways.
What is important is that we can conceive of several formally distinct senses which none the less refer to being as if to a single designated entity, ontologically one. It is true that such a point of view is not sufficient to prevent us from considering these senses as analogues and this unity of being as an analogy. We must add that being, this common designated, in so far as it expresses itself, is said in turn in a single and same sense of all the numerically distinct designators and expressors. In the ontological proposition, not only is that which is designated ontologically the same for qualitatively distinct senses, but also the sense is ontologically the same for individuating modes, for numerically distinct designators or expressors: the ontological proposition involves a circulation of this kind (expression as a whole).
There's something really odd going on in this quote. We've become accustomed to thinking of Being as a sort of ontological substance. So the idea that many designators point to the same substance probably isn't too surprising to us. This would be another version of the idea that there is one underlying principle behind reality, one type of "stuff" from which it is built (whether you think this is mathematical forms or Absolute Spirit or electrons depends on what age you were born into). Everything we see is really just a manifestation of this stuff, which is the only stuff that really, ontologically, IS. Other stuff is just illusion and mere appearance, not real reality. But in the quote above, we're told that "the sense is ontologically the same" for the appearances that indicated this underlying reality. "Sense" doesn't seem like an ontological substance though. It seems like the reality of "sense" would be in the process by which a designated expresses itself through designators that in turn designate it. Sorry for the mouthful there, but I'm trying to draw the circle I mentioned before that I think he means by the circulation of "expression as a whole". That a process can be said to be, that it could be an "ontological thing" (see how our everyday language is biased?), is already a pretty strange idea in a Western metaphysics that worships stasis and despises motion.
But in fact this quote gets even weirder when you realize that this whole discussion started with the name of Duns Scotus. Now, I don't know spit about medieval theology, but I have gathered that for Scotus, the major point of the univocity of Being was to counteract Aquinas' idea that we only know God through analogy. When I say that my dog is good and that my neighbor is good I mean to use "good" in the same sense. But, for Aquinas, when I then say that God is good, I don't mean that in the exact same sense that I meant with my dog or neighbor, I mean it in a merely analogous sense. Scotus was explicitly denying this and claiming that if we're going to genuinely know God at all, the qualities we attribute to him have to be in the same sense as we attribute them to everything else.
In effect, the essential in univocity is not that Being is said in a single and same sense, but that it is said, in a single and same sense, of all its individuating differences or intrinsic modalities. Being is the same for all these modalities, but these modalities are not the same. It is 'equal' for all, but they themselves are not equal. It is said of all in a single sense, but they themselves do not have the same sense.
If we translate this reference to Scotus to our current context, I think we end up with three distinct senses of "being" that the doctrine of Univocity is claiming are all the same. First, there's the "Being of Being", as it were. Surely Being is, right? This is familiar ontological substance sense we employ when we say talk about the unity of what "really exists" (God, electrons, whatever). Second, there's the "Being of beings". Normally, we think that these mere appearances are just there to point at the underlying Being, and aren't "really real" durable substances in and of themselves. Following Duns and Deleuze though, we're now claiming that beings are in the exact same sense that Being is. I exist and my dog exists and god exists, and while we are all different, in so far as we exist, we all exist in the same way. Appearance now becomes as real as reality. Third, I think there's an implication here that the sense itself in which Being is said of everything is an ontological "thing" of its own -- as if there were also a "Being of sense", which could only be a sort of process of the circulation of expression where Being expresses itself through beings that designate it. And of course, this final sense of Being is the same sense as the first two. Or perhaps it's better to say that this final ontological sense is the most fundamental one that gives meaning to the first two, which would lead you to a formula like: Being is process, the process of the expression of Being.
To me though this is all getting a bit too academic. I don't really love the term Being in the first place. If you want to talk about God, talk about God. Being seems a thin veneer. And either way, they are both so abstract that it's hard to be sure you're actually saying anything and not just tossing word salad. I think I learned something here, but the final formula seems a bit like something a geriatric Heidegger would be saying to his golf buddy.
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