Even though Nietzsche's Eternal Return is going to be the most important part of this section on the history of univocity (pg. 39-42) I did spend a little time inconclusively thinking about what Deleuze says regarding Scotus and Spinoza.
Particularly the part about Spinoza, since I've at least read the Ethics. I think I get the basic idea -- for Spinoza, everything is a modification or expression of God in a particular way; God is Nature, or the universe conceived as substance. Nature always speaks with the single voice of God. But I've always found myself a little puzzled by why Spinoza felt the need to add another layer to the equation -- he has God (substance) and the modes (things) but also attributes. What are the attributes? Well, in the Ethics he only discusses thought and extension, though he states that there are actually an infinite number of attributes (God being absolutely infinite and all; I've always wondered what the other attributes are). They are like categories that all the modes have in common, but that they also share with substance as well, since God has the same attributes. Here's how Deleuze puts it:
Spinoza organises a remarkable division into substance, attributes and modes. From the opening pages of the Ethics, he shows that real distinctions are never numerical but only formal - that is, qualitative or essential (essential attributes of the unique substance); and conversely, that numerical distinctions are never real, but only modal (intrinsic modes of the unique substance and its attributes). The attributes behave like real qualitatively different senses which relate to substance as if to a single and same designated; and substance in turn behaves like an ontologically unique sense in relation to the modes which express it, and inhabit it like individuating factors or intrinsic and intense degrees. From this follows a determination of modes as degrees of power, and a single 'obligation' for such modes: to deploy all their power or their being within the limit itself. Attributes are thus absolutely common to substance and the modes, even though modes and substance do not have the same essence.
This idea that various modes (which is Spinoza's name for all the stuff around us) have the attributes in common struck me as vaguely related to the idea of repetition, or at least of recognition, since these attributes seem to reappear in every mode. I don't really think of the attributes as "objects", but somehow this commonality put me in mind of Whitehead's equally puzzling idea of "Eternal Objects". It would take way too long to try and adequately explain what Whitehead had in mind by eternal objects, and in any case I've never felt I completely understood it. My general impression would be that eternal objects are what allow for the possibility of the repetitions from time T to time T+1 in the atomic scheme I attributed to Whitehead last time. These are called "eternal" because they are not in time in the same way as the temporal atoms that compose that scheme, but somehow kind of persist, or maybe reincarnate, across time, outside the pure and undivided flux. When you ask Whitehead for an example of an eternal object, he is most likely to come back with something like "the color blue", or "a particular type of sound" -- ie. what these days people would call "qualia", or types of qualitative experience. At first, this might suggest that these eternal objects could be Spinoza's missing attributes. Maybe, but then why are we calling these attributes (extended, blue, etc ...) "objects" now?
A few years ago I read Isabelle Stengers' book Thinking with Whitehead. This improved my understanding of his philosophy by leaps and bounds, especially since it is not an exposition of Whitehead's complete and final philosophical scheme (which in any case doesn't exist) but a historical journey through the problems that led him from mathematics to metaphysics, and the concepts he came up with to address them. So I looked back through that book in an attempt to get a better handle on why Whitehead created the concept of an eternal object. And it's feakin' complicated. However, I did find a relatively straightforward discussion of why Whitehead created the concept of "objects" before he started calling them eternal. Here are some of the relevant quotes from TwW; remember to situate yourself in a temporally atomized, post-endo-cannabinoid-phase-transition, world without forms before you read these:
Stengers quoting Whitehead:
I use recognition for the non-intellectual sense-awareness which connects the mind with a factor in nature without passage ... I am quite willing to believe ... that there is in fact no recognition without intellectual accompaniments of comparison and judgement. But recognition is that relation of the mind to nature which provides the material for the intellectual activity.
Things which we thus recognize I call objects.
Objects are the elements in nature which can "be again".
Day by day and hour by hour we can find a certain chunk in the transitory life of nature and of that chunk say, "There is Cleopatra's Needle." If we define the needle in a sufficiently abstract manner we can say that it never changes. But a physicist who looks at that part of the life of nature as a dance of electrons, will tell you that daily it has lost some molecules and gained others, and even the plain man can see that it gets dirtier and is occasionally washed ... The more abstract the definition, the more permanent the Needle.
Recognition and abstraction essentially involve each other. Each of them exhibits an entity for knowledge which is less than the concrete fact, but is a real factor in that fact. The most concrete fact capable of separate discrimination is the event. We cannot abstract without recognition and we cannot recognize without abstraction.
Note: Cleopatra's Needle is some mini-Washington monument type thing, and every colonial power seems to have pilfered one from Egypt.
Stengers herself:
"Say, there it is again." Cleopatra's Needle, for instance, which rises in downtown London. What we are aware of in the perception of the Needle, a fortiriori because we can designate it by a name, certainly implies those intellectual faculties known as memory and judgement. No matter what those terms refer to, moreover, knowledge is ultimate, that which the concept of nature must refrain from explaining. But if nature is not to bifurcate, with the mind being held responsible for everything that "is again," for everything that acts as a landmark, it must offer a foothold for memory and judgement. The concept of nature must include what is required by the experience of "recognizing Cleopatra's Needle." "Object" is the name Whitehead gives to this requisite, which is presupposed by knowledge but does not explain it.
Some background might help here. Stengers construes Whitehead's early philosophy as focused on the problem of how to avoid a "bifurcation of nature" that would leave the natural world as this colorless, odorless collection of atoms whizzing about, and pack all qualitative experience (including the experience of any identity) away as a construct of the human mind. He is targeting the sort of "apples aren't really red; they are just a collection of molecules that happen to reflect a certain wavelength of light" type of naive materialism that scientist's tend to resort to when backed into a philosophical corner. This means that if you have the experience of seeing Cleopatra's Needle "again", even if we grant your mind wonderful and unexplainable powers of recognition and memory, unless your mind is just completely fabricating this identity wholesale, there must be some aspect of reality that allows you to recognize the thing. You aren't necessarily recognizing the identity of the "thing itself" -- in fact, you are explicitly recognizing just some abstract aspect of the identity-less flux -- but if you're not just to be making the whole thing up as a brain in the vat type illusion, something about that flux must really lend itself to that recognition, even though it seems like this implicates something beyond the flux itself.
Here's Whitehead later on:
The explanatory purpose of philosophy is often misunderstood. Its business is to explain the emergence of more abstract things from the more concrete things. It is a complete mistake to ask how concrete particular fact can be built up out of universals. The answer is, "In no way." The true philosophic question is, How can concrete fact exhibit entities abstract from itself and yet participated in by its own nature? In other words, philosophy is explanatory of abstraction, and not of concreteness.
Now, all this is interesting, you might say, but we've gone a long ways from the original question, which was: can we use Whitehead's idea of eternal objects to help us illuminate what Deleuze is saying about Spinoza, and hence better understand his concept of univocity or difference? And the answer so far seems to be, "In no way". But, and this is the punchline it turns out, the very next paragraph in Stengers book does do something to help us understand Duns Scotus a little better, and can even add something to our earlier discussion of signs.
Here's Stengers again:
Indeed, in The Concept of Nature, Whitehead seems to me to come close to the man his contemporaries named the "doctor subtilis," Duns Scotus. Subtle indeed was the position of Duns Scotus, who, faced by the alternative that either "universals" are relative to knowledge or else they belong to reality, refused to choose. For Scotus, all abstract features that fit a multitude of different individuals, all the distinct "quiddities" that allow me to describe them at different levels of abstraction, do indeed belong to what is described. Yet when I enumerate them and define them qua attributes of this individual, I treat them as if they were actually, that is, numerically, distinct (a horse is an animal, a mammal, a herbivore, an ungulate ...) whereas ontologically they are only "formally" distinct, composing the individual as a unique concrete being. The same is true of Whiteheadian objects: like the subtle doctor's plurality of "forms," they are the "respondents" of "that which" we recognize, name, judge, and compare: that is, what these operations answer to and also what can eventually answer for them. Yet, although they exhibit themselves as abstract or permanent, they cannot be isolated from the concrete event, which, for its part, passes without return.
The Whiteheadian object may also make one think of the signs of Charles Saunders Peirce, which is rather appropriate since Peirce placed his undertaking under the banner of Duns Scotus. Indeed, Peirce's sign is real, although its meaning requires an interpreter to make it signify. It is real because the person who interprets does not fashion signs in a mute or "insignificant" world: she requires signs in the way Whiteheadian recognition requires objects. Signification is ours, no doubt, but the fact that there is a sign liable to signify is not the product of a "psychic addition" alien to what we call reality.
Now this is interesting. Apparently Scotus was saying that the attributes of existing things are really distinct aspects of the thing, but that they do not thereby amount to properties of the thing, in the sense that a property belongs to some substantial subject. It's as if the thing nomadically inhabits the attribute, or partakes in it, without converting it into a "property". In fact, everyone can share in the common property, even God, just to different degrees. The attributes or forms that we're talking about in the case of Scotus and (so far) with Whitehead may at first still seem a lot like the specific differences that were the underlying forms of Aristotle's theory. After all, Whitehead is calling them "objects" and Stengers is reaching for taxonomic examples to illustrate Scotus. And in some sense I think they are still like that, and await transformation into attributes by Spinoza and eternal objects later in Whitehead's philosophy. But there has actually already been a major shift here. Because the direction of abstraction, so to speak, has been reversed. With Aristotle, the real and essential stuff was just the form, the identity, and from that you could knock off as many numerically distinct copies as you like. This idea left us completely unequipped to deal with the world we actually experience directly, and in particular with why there should be more than one copy of any of these forms, and any difference between these copies. With Scotus or early Whitehead, we can already see that the concrete individual beings (or atoms or occasions as Whitehead likes to say) are the fundamental stuff of experience, and that the forms we use to link them together into identities, while still real things in their own right, not just magically invented by the human mind, are the abstract bit. In other words, we've taken the first step towards making the difference fundamental, and the identity derivative.
Later on with Whitehead, this mistaken direction of abstraction will acquire a specific name -- the fallacy of misplaced concreteness. I've found over the past decade or so that this has become one of my go to phrases, because once you understand it, you see it everywhere. For example, when the physicist tells you that the world is "really" made out of protons and electrons. See, there they are, under the scanning electron microscope. "Really"? The world is made out of incredibly abstract mathematical concepts invented by some hairless chimps? Well, sure, those electrons are real, objective, whatever you like to call it -- not just "subjective" and in the heads of scientists. But they are just an aspect of reality, doubtless a useful way to describe it for many purposes. An electron cannot be "right there" because it's an abstraction, not a stone, lying about with a certain spatial position. Naive materialism confers on the electron a concreteness that is completely misplaced.
Finally, there's this intriguing bit about signs that helps me understand Peirce (whom I have also not read) a little better. A sign is not something that we arbitrarily attach to the world to transmit meaning, like the way "tree" as a set of symbols arbitrarily makes us think of leafy greens to which it has no inherent relation. There may be a "psychic arbitrariness" that our human minds add to the world via language, but the world gave us some material to work with first. That material was a sign. The tree stood out, in certain aspects, to us chimps, who have a certain constitution for noticing these things. It was individuated, for one. Spatially located, for another. The tree was a sign waiting to happen. Or maybe it's better to say that the "tree process" has aspects or singularities that can mean various things as they are taken up by other parts of the world. I can't claim to fully understand this line of thought yet. For one, I think I'm in danger of mixing up aspect or attribute which things have in common and singular mode which differentiates them. But I like this idea -- the world is full of real, objective signs ... that only mean something when a properly attuned interpreter comes along to pick them up. An interpreter cannot add meaning to the world without there being some order in it to begin with.
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