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Spinoza’s Circle and the Interior

Some Ruminations on Spinoza’s “Simplest” Thought

A single figure keeps returning to me as I contemplate Spinoza’s optical concepts and metaphysics, in view of the prevailing Cartesian science of the age, that elementary figure that Spinoza provides to help explain how he conceives of the reality of the modes, even the modes of ideas for non-existent things, in relationship to the ultimate reality of Substance, God or Nature. As Spinoza explains, the figure stands for something that has not parallel, not example, because it is a fundamental relationship which is unique and totalizing.

Ethics part 2, prop 8 schol. — The nature of a circle is such that if any number of straight lines intersect within it, the rectangles formed by their segments will be equal to one another; thus, infinite equal rectangles are contained in a circle. Yet none of these rectangles can be said to exist, except in so far as the circle exists; nor can the idea of any of these rectangles be said to exist, except in so far as they are comprehended in the idea of the circle. Let us grant that, from this infinite number of rectangles, two only exist. The ideas of these two not only exist, in so far as they are contained in the idea of the circle, but also as they involve the existence of those rectangles; wherefore they are distinguished from the remaining ideas of the remaining rectangles. (Elwes trans)

This has always been a convenient image for the explanation how the modes dependently are an expression of the totality which is all of what there is. One practically sees how the modes, while causally interacting with each other to produce current states of being, immanently rely upon a larger comprehesivity. And if one wants to even leave off from the narrowness of Spinoza’s explicit thought, the chords D and E could be read as vectors which produce an intersecting point (unlabeled), the modal expression of two lines of force, a point of focus, this seems at least arguable when considering much of the rest of Spinoza’s view.

But two other realizations come to me as well. The first is that the rectilinearitythat Spinoza presents within the borders of the circle very well may for Spinoza have represented the linear analyses of motion provided by Descartes. Part of the challenge presented to Spinoza, as he tried to heal a perceived breech between Body and Soul, Thought and Extension, was how to bridge mathematical descriptions with affective realities. In a certain sense the rectilinearity with the circle of Substance for Spinoza represents the ideational crispness of mathematical description understood as a partial, yet sufficient expression of substance. The mathematics is to some degree subsumed. Just as Huygens and others struggled to assume the advantages of the Perspectiva  tradition in optics, yet still fully explain the properties of light’s propagation (which Huygens would show to be that of a wave or a pulse), Spinoza too sought to preserve the mechanized sureties of Descartes mathematizations, yet with a view that could account for the affective propagations living bodies (as early as Kepler’s Paralipomena light is described as an “affectus”).

Secondly though is the realization that the circle does not only represent Substance as a whole, but also any conatus expression of Body (defined by Spinoza as a preservation of a ratio of motion and rest over time). The circle above can also be read as the recursive coherence of a body, and the internal causal relationships of which it is composed, immanent to its essence. 

In other words, a body, in the ordinary as well as in the Cartesian sense, preserves its physical integrity in just the same way the whole universe preserves it: they differ only with regard to the degree of probability that each can ‘survive’ externally caused modifications. Only the unique individual of level-ω can be modified in infinite ways without giving up its identity.

The Physics of Spinoza’s Ethics, David Lachterman

What level-ω is in Lachterman’s nicely conceived reduction is the last border of an entire body. Level-2 is the most elementary kind of body for Spinoza, a hypothetical composition of what one supposes is at least two of the most simple bodies “corpora simplicissima”. The human body, and all such bodies we regularly recognize as such are what Lachterman regards as level-k bodies (2 < k < ω). Following these descriptions, the circle above from the Ethics could be read not only as the schema of the level-ω Body, but also of any typical level-k Body. It is only the degree of power, freedom and being that preserves such a circle (ratio) that distinguishes it from the ultimate whole. Spinoza world can be seen as one of circles within such circles. The modal causal interactions are immanent expressions not only the totality of Substance or Nature, but also are expressions of the ratio of motion and rest of which a said body (level-k) is composed. The existential modality of ideas and extensions which is interior to the circle (level-k) can be read as contingent to the essence of that Body taken as a whole, as it is determined to exist.

While it is fair and best to understand the diagram exactly in the way that Spinoza meant it, I think it is important to realize that in a figure such as this, representing something for which Spinoza says there is no parallel, the image is likely overdetermined by several other Spinoza concerns and conceptions. The circle and its interior floats through Spinoza’s thinking process (additionally). The diagram can be read across at least these two layers: the affective subsumption of Cartesian mathematicization of Nature in terms of propogating, interacting bodies; and, the immanence of constituent modes of bodies under gradations of Being and power. And I would end that the suggestive recursivity of this body (level-k) opens itself perhaps to Autopoietic descriptions, at least for those bodies considered to be alive, and Autopoiesis itself to Spinozist re-description.

Spinoza and Plotinus, some morning thoughts

I ran across a LiveJournal entry that touched on something I have always found of interest, the relationship of Spinoza to Plotinus:

It’s amazing how much Spinoza resembles Plotinus.

Plotinus said that, instead of creation ex nihilo, existence emanated from God.

Emanation ex deo (out of God), confirms the absolute transcendence of the One, making the unfolding of the cosmos purely a consequence of its existence; the One is in no way affected or diminished by these emanations.

This mirrors Spinoza’s idea that “creation” (so to speak) was necessary because God exists; and that the world is the way it is, and could be no other way, because of the nature of God. And though physical things are contingent (limited by things outside of themselves), God/substance is the only non-contingent, necessary thing, because God is not acted upon by outside agents (there is nothing outside of God). Existence necessarily exists, because of the nature of God, but the modes of existence are contingent.

In Plotinus’ view, it’s the ulimate destiny of contingent things to reunite with the One. I haven’t read anything about ultimate ends in Spinoza’s Ethics, but if I remember correctly, he agrees (kinda) with Plotinus. Not only is it our fate to disappear into God (to become one with the Force!)–a fate which we have no choice about–we should actively assent to it, in order to increase our happiness.

The conceptual parallels between Spinoza and Plotinus have always appeared to me to be significant, as it seems that somehow through Plotinus Spinoza had an inheritance of the “degrees of Being” interpretation of power and truth. One does not know if he received this Neo-Platonic inheritance through Augustine or through an early youth exposure to Kabbalistic thinking that was rife in the religious community at the time, but very few interpreters seem to give it much weight, preferring instead the Cartesian root-stem. But Spinoza vectorial treatment of knowledge and his General defintion of the affects surely demands such an additional analysis. That I know of, only Deleuze (EiP:S, pp 170 -178) gives substantive consideration to this continuance, as he touchily tries to parse out Spinoza’s immanencefrom Plotinus’s emanation, a perhaps vital distinction (dictionary bending, one that always gets me flipping the pages to re-familiarize myself with these two words).

Such a connection proves significant because it bears on “ladyelaine’s” final paragraph here the path to freedom, for Hegel too thought that Spinoza’s position ultimately lead to an acomism, the collapse of all that exists into an non-distinct whole, a Blob of Being, without reflection. Hegel’s view was likely held because reflection was the gem-stone of his personal brilliant crown, the manner by which he pulled himself free, and originally from Spinoza gravity, the analytic that distinguished himself. Spinoza was missing the Reality of the “negation”, but was he? Hegel’s saving of the “soul”, the surety that the human soul was special, made of a distinction that was different in kind from the manner of distinctions that made rocks, and lakes and even sun’s light distinct somehow fails to grasp the grandeur of Spinoza’s treatment of the negation. The negation is indeed Real, but real as a comprehensive expression of the whole, wholeness against which the vectors of knowledge and power leverage themselves as completing. My own conceptions are composed of illusionary negations (distinctions of separation) only insofar as they limit my ability to act. Following Augustine in some way, they are composed of a relative poverty, degrees of privation. And this privation is only resolved through addition, an addition that is both bodily and relatively clear (insofar as).

I believe that a subtle key is that the “active assent” that ladyelaine intuits to be missing from Spinoza, only at first blush only seems absent, because it is everywhere. Every thought Spinoza asserts is an assertion. This is only retarded by imagining that a “person” is at the center of this assertion, instead of being composed by it. ladyelaine elsewhere touches on the difficulty she has in accepting that mind can be ascribed to something that is not a person (here). This of course is an ultimate question. Is it coherent to think of a rock having “mind”? Or, perhaps more tempting, is it coherent to think that a rock has “information”? It seems to me is that Spinoza proposes a unique monist (and material) solution, one that allows us to see that as minds we much necessarily combine with other minds, and (a very signficant “and”) as bodies we must combine with other bodies, forming compositional, thinking and affective wholes (however fleetingly). And, our freedom depends on it.

Related: Becoming Intense and Longitude: Deleuze and Guattari , Deleuze Lecture on Spinoza

The Reality of the Affects: Spinoza’s Plotinian Real

In counterbalance to the points made in the post below, I have the following thoughts which stem from Lilli Alanen’s response to Della Rocca:

In reading Alanen’s response to Della Rocca’s “Rationalism Run Amok” I have a few questions. In particular it is her trouble with the idea that all affects are illusionary.

Here is the germ of it:

So existence is not an all or nothing affair but comes in more and less. But then the conclusion that we with our passive affects exist to a much lesser degree than the eternal and infinite God does not seem very startling. It becomes so only if one, as Della Rocca seems to do, sides with idealist Spinoza commentators in thinking that anything less than full intelligibility, and with it full perfection or being, lacks reality.

Do we really need to draw such drastic conclusions? More to the point: do we need to draw these drastic conclusions?

Here’s a worry: There is, Della Rocca argues, a sense in which passive affects are real and fully intelligible, namely qua ideas in God’s mind. The very same ideas which are confused in my mind are distinct and adequate in God’s. This is just a manifestation of what he calls the mind-relativity of content (p. 19). Does this mean affects are fully real in God’s mind? Hardly qua affects, since God’s mind contains only adequate ideas. So are they unreal after all? I’m troubled by mind-relativity here and have a hard time seeing how adequate ideas in God’s mind could be the same as the confused one in ours?

This is the difficulty that I have. Alanen seems to argue that because our intuition tells us that if something exists to some degree, it can be said to exist completely so. That is, because Spinoza grants that affects are idea-expressions of degrees of being, these affects themselves must be said to exist, fully. But isn’t it Spinoza’s entire point that such ideas and affects in so far as they have being, are already perfect (in the mind of God), and in so far as they don’t have being, are imperfect and inadequate? Because Spinoza makes being itself the vector of inadequacy, I don’t see how one can say that affects actually are (despite our intuition, and experience that they are). The way that Spinoza has set it up seems to be that the predicate of being is entirely linked to the degree of adequacy. By insisting that affects are “real” Alanen is insisting something of the order that “degrees of being are real” has full being, and I am not sure how in Spinoza’s system on could do that.

If I put my question a different way, Spinoza in a famous letter to Jellis, denies the being of “negation”:

As to the doctrine that figure is negation and not anything positive, it is plain that the whole of matter considered indefinitely can have no figure, and that figure can only exist in finite and determinate bodies. For he who says, that he perceives a figure, merely indicates thereby, that he conceives a determinate thing, and how it is determinate. This determination, therefore, does not appertain to the thing according to its being, but, on the contrary, is its non-being. As then figure is nothing else than determination, and determination is negation, figure, as has been said, can be nothing but negation.

Letter 50 to Jellis, June 2, 1674

The negation of which a particular figure is composed, pertains only to its non-being. Would one say then that “negation” for Spinoza must have being? Or even that “non-being” for Spinoza, must have “being”? This seems like a similar kind of assertion to the one that Alanen proposes, and it appears to undercut what Spinoza is attempting to say.

A similar problem occurs in the assessment of the Blind Man in his letter to Blijenbergh (Letter 21, Jan 28, 1665). Here Spinoza wants to tell us that a blind man is no less perfect than a stone is perfect:

“I proceed further to the explanation of the terms “Negation” and “Privation”…I say, therefore, that Privation is, not the act of depriving, but only the pure and simple lack, which is itself nothing. Indeed it is only a Being of reason, or mode of thinking, which we form when we compare things with one another. We say, for example, that a blind man is deprived of sight because we easily imagine him as seeing…But when we consider God’s decree, and his nature, we can no more affirm that of man than of a Stone, that he is deprived of vision…God is no more the cause of his not seeing than of the stone’s not seeing, which is pure Negation”

If one replaces “seeing” with “affect” we see that having an affect is only a negation, a negation which is nothing (has no Being). If we connect up any affective being with the Totality of which it is an expression (that is, remove all its negations and border), the affect disappears, because there is no transition in power or degree of being. That is Spinoza’s point, is it not?

The same thing seems to register on the level of epistemology:

E4p1dem: Falsity consists only in the privation of knowledge…”

What Alanen seems to be want to say is that the “privation of knowledge” is real, the “negation of sight” in a blind man (and a stone) is real, that non-being is real. But this seems to undercut a primary embrace of Being, the idea that Being is a plentitude and that negation is an illusion of perspective, comparison, projected ideas and inadequate ideas. Although she critique’s Della Rocca for accepting an Idealist-type conclusion, one that makes the changes in the world to be mere illusions, she seems accept the very thing that Hegel critiqued Spinoza for failing to see, the Reality of the Negation. Rather it seems, Spinoza has to be taken at his word, that degrees of being are exactly that, degrees of being.

I wonder how she would square her interpretation with the clear comments on Negation and Privation taken above?

Closely Related Post: Negation and the Unseeing Stone