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A Conflation of Spinoza Diagrams

How Spinoza Thought of the Eye, the Lens and The Modes

Perhaps this is an irresponsible and trite comparison, but sometimes the mind indeed works visually, even in authors as exacting and deductive as Spinoza attempts to be. It is striking that Spinoza uses two very similar diagrams to illustrate on the hand, the powers of spherical lenses to most ideally focus rays across an infinity of axes, (the manifestation of which is subject to the properties of real lenses):

Text not available

Letter 39 to Jelles, March 3rd 1667
Benedicti de Spinoza opera quotquot reperta sunt quotquot reperta sunt By Benedictus de Spinoza, Baruch Spinoza, Johannes van Vloten, Jan Pieter Nicolaas Land

Depicted above are the hypothetical intersection of rays, in two sets taken to be parallel, as they arrive at the surface of a spherical lens. Such rays are taken to be then focused at the back of the circumfrance, as the would be at the back of the eye, or as part of the refractions of a lens.

 

In this diagram, Spinoza illustrates how each contingently expressive mode – what is usually taken to have come into existence and then will pass away – are implied by, that is caused by as immanent to, the Idea of an infinity of points that make up a circle. In this way, the rectangles that are immanent to a circle’s circumfence are by analogy seen to be dependent upon that circle. The rectangles come and go, the circle remains eternal. As explained in Ethics IIp8s:

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.

There is the simple coincidence of using a circle to diagram both physical effects, and metaphysical effects (which for Spinoza are of course commensurate). But if one allows a conflation, one that may have occurred within Spinoza’s thinking, in the first we have the effects what occur within the eye, as it interacts with events outside of it, and in the second, we have the effects (modes) as expressed immanent to the circle that contains them.

Because Adequate Ideas are understood by Spinoza to be Ideas uncaused by something external to them, I don’t think it is too big of a leap to understand that when Spinoza is diagramming the effects of light with the eye (and for a lens, post-angle of incidence), he is thinkingof the second diagram. It is perhaps for this reason that Spinoza is not obsessed with the crystality of vision that occupied Descartes in his quest for the hyperbolic lens. The sharpness of an image is but a part played in an assemblage of knowledge. However clearly one’s eye, or lenses work, this simply is not clear thinking. Of course Descartes understood this as well, but there is something to how Descartes and Spinoza each responded to spherical aberration which reveals a difference of emphasis in the very project of mental and physical liberation. I believe in this co-incidence of diagrams, a profound conflation is being accomplished in Spinoza’s process of thinking.

I see hear as well an interesting graphic subsumption of the scattering of rays that occur with spherical aberration, as in being focused they tend about a “mechanical point” [Johannes Hudde]. Much as rays are never entirely focused to a mathematical point (even with real, hyperbolic lenses), so too we never possess wholly adequate ideas. The focus rays as seen in the first diagram (again, if we allow an analogical thought), appear to enact indices found in the second diagram. Is Spinoza at some level conceiving of rays of focus as being parallel to the adequacy of ideas? And is Spinoza’s theoretical acceptance of spherical aberration [a la Hudde] a product of his acceptance of the fundamentally inadequate nature of ideas we hold? Is his mechanical project of lens focusing analogous to a mechanical – that is, pragmatic, rational and crafted – construction of human freedom? These are large and obscured questions.

This certainly does not make up an argument either for Spinoza’s position, or for an interpretation of Spinoza’s position. It is really more an intuition into the kinds of thought processes Spinoza may have been engaged in, in part elicited by the diagrams he used to make things clear. Meant is a direction for future analysis.

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Pythagorian Spinoza?

Leibniz’s Summation

Of some significance, here I post a summation of Spinoza’s philosophy, as passed through the mouth of a loyal friend, Tschirnhaus, and as relayed to Leibniz in 1675, originally published in English by Wim Klever. It draws out some curious Klever might say esoteric aspects of Spinoza’s thinking. Most distinct about it is the notion that Spinoza held a Pythagorian idea of a transmigration of the Mind. Besides the obvious distortions that can be brought about through one man telling another man what someone else believes, there remains the possibility that the account is somehow intentionally colored in details, either to couch Spinoza, or to put him in a personally favorable light:

As Klever relates:

“In spite of Spinoza’s warning that Tschirnhaus should be reluctant in communicating what he had received for private use, we know that Tschirnhaus nonetheless revealed many secrets to the inquisitive Leibniz. This appears from a note written by Leibniz which he must have made shortly after a meeting. I think it worthwhile to quote this note here in full because it enables us to see how Spinoza’s doctrine was perceived, understood, and explained by his friends and followers in or around 1675. A second reason is that this note which is not known by many scholars and iis not yet available otherwise in English contains several interesting points which cannot be found elsewhere and is also for that reason relevant:

Sir Tischirnhaus told me many things about the handwritten book of Spinoza. There is a merchant in Amsterdam, called Gerrit Gilles [Jarig Jelles] I think who supports Spinoza. Spinoza’s book will be about God, mind, happiness or the idea of the perfect man, the recovery of the mind and the recovery of the body. He asserts the demonstration of a number of things about God. The he alone is free. He supposes that freedom exists when the action or determination originates not from an external impact, but only from the nature of the actor. In this sense he justly ascribes freedom to God alone.

According to him the mind itself is in a certain sense a part of God. He thinks that there is a sense in all things to the degrees of their existence. God is defined by him as an absolutely infinite Being, which contains all perfections, i.e. affirmations or realities or what may be conceived. Likewise only God would be substance or a Being which exists in itself, or which can be understood by itself; all creatures are nothing else other than modes. Man is free insofar as he is not determined by any external things. But because this is never the case, man is not free at all, though he participates more in freedom than the bodies.

The mind would be nothing but the idea of the body. He thinks that the unity of the bodies is caused by a certain pressure. Most people’s philosophy starts with creatures, Des Cartes started with the mind, he [Spinoza] starts with God. Extension does not imply divisibility as was unduly supposed by Descartes; although he supposed to see this also clearly, he fell into the error that the mind acts on the body or is acted upon by the body.

He thinks that we will forget most things when we die and retain only those things that we know with the kind of knowledge that he calls intuitive, of which of which only a few are conscious. Because knowledge is either sensual, imaginative, or intuitive. He believes a sort of Pythagorical transmigration, namely that the mind goes from body to body. He says that Christ is the very best philosopher. He thinks that apart from thought and extension there are an infinity of other positive attributes, but that in all of them there is thought like here in extension. How they are constituted cannot be conceived by us but every one is infinite like space here (“Spinoza’s life and works” Cambridge Companion to Spinoza, 46-47)

 

I posted below some rough thoughts I had some time ago, and their related Spinoza texts. Klever’s evidence of a kind of at least percieved Pythagorian transmigration adds an esoteric meaning to Spinoza’s mathematization. And while I cannot conceive how such a transformation could be understood within the propositions of the Ethics [on what account is the preservation of identity maintained], it does give conceptual context for some of the more difficult to interpret passages on this issue.

Notable as well is the summation’s deviation from Spinoza’s theory of the three knowledges as found in the Ethics. Here, the trinity of “imaginary, rational, intuitive” has become “sensual, imaginary, intuitive”. Assuming an accurate translation of the passage, this may give some clue to the differences of Spinoza’s treatment of the Imaginary and Order (spoken about here, in Spinoza’s Two Concepts of Order). Professor Della Rocca in correspondence had affirmed his belief that Spinoza is somewhat inconsistent in his treatment of “order” in the various parts of the Ethics. What is suggested by the Leibniz summation, perhaps, is that even the rational, propositional conception of true and free in Spinoza is still imaginary; this may be linked to Spinoza’s variation on whether we can or cannot ever have wholly Adequate Ideas.

John Donne’s Material Monism of Love, and Spinoza’s Eternity of the Mind

John Donne’s “Valediction Forbidding Mourning” articulates a metaphysics which makes of a death an anchor point, upon which a living being can compass itself, creating a death-defying eternity of affection. He speaks in seemingly dualist terms of a sublunary love “whose soul is sense” contrasted with a love “inter-assurèd of the mind”. In this he seems to compose a rarification of affects such that when stretched materially, thinly enough, become etherialized, though substantial:

Dull sublunary lovers’ love
-Whose soul is sense- cannot admit
Of absence, ’cause it doth remove
The thing which elemented it.

But we by a love so much refined,
That ourselves know not what it is,
Inter-assurèd of the mind,
Care less, eyes, lips and hands to miss.

Our two souls therefore, which are one,
Though I must go, endure not yet
A breach, but an expansion,
Like gold to aery thinness beat.

If they be two, they are two so
As stiff twin compasses are two ;
Thy soul, the fix’d foot, makes no show
To move, but doth, if th’ other do.

And though it in the centre sit,
Yet, when the other far doth roam,
It leans, and hearkens after it,
And grows erect, as that comes home.

Such wilt thou be to me, who must,
Like th’ other foot, obliquely run;
Thy firmness makes my circle just,
And makes me end where I begun.

But here is a certain monist clue in the description of sublunary love. The love whose soul is sense “cannot admit of absence”, since the very elements of its composition, if absent, destroy the very love which might do such perceiving. Much as in Spinoza, the idea cannot be torn completely away from its object (knowledge is merely a privation, and there is nothing positive in knowing, which is false). In just a few lines Donne sums up a physicalist argument of a sort, the very recognition of absence is itself the testament of the physical preservation of that love’s elements. In a certain sense, there can be no such missing (or missing is merely a misconception, as Spinoza puts it, it has no Being). The elements which preserve a state prove to its perseverance. Instead Donne proposes an “inter-assured” love of the mind, a presencing in which any separation is necessarily an expansion, and not “a breach”. The transformation of “breach” into expansion is the view of a monist assemblage, and not of a dualism; “mind” is still composed. Despite the abstraction of such a love, its spiritualization (compared to gold beat thin) by the same reasoning of compositional elements, is a material endurance, made clear by mind.

 

Though the love after death is not of “eyes, lips and hands”, it seems it must still be physical (just as beat gold is still gold, just as the mind has the body for its object), made of the elements of which it is an expression. In fact, instead of anatomical body parts, it is made now in part by text, in part by bodily afffections, and the relational compositions which preserve. Donne here, in the compassry of two legs, the geometry of a circle, makes an argument against Time (as breach), as the material going out is subsumed in a deeper circle. Like Spinoza he proposes a world where absence has no basis, sub specie aeternitatis, which is experienced through memory, trace, but also the material expansion of those traces in Time, as understanding.

Place Donne’s notion along side what some have taken to be controversial and inconsistent, declaration of the eternity of the Mind:

5p23: The human mind cannot be absolutely destroyed with the Body, but something of it remains which is eternal.

Scholia: There is, as we have said, this idea, which expresses the essence of the Body under a species of eternity, a certain mode of thinking, which pertains to the essence of the Mind, and which is necessarily eternal. And though it is impossible that we should recollect that we existed before the existence of the Body-since there cannot be any traces of this in the body, and eternity can neither be defined by time nor have any relation to time-still, we feel and know by experience that we are eternal. For the Mind feels [sentit, senses] those things that it conceives in understanding no less than those it has in the memory. For the eyes of the Mind, by which it sees and observes things, are the demonstrations themselves.

Whereas Spinoza wants to make a distinction between memory trace, and “the eyes of the Mind,” Donne’s point seems a bit more refined, as he speaks of the experience of circular and timeless inscription, as compositional trace, the way that when one “foot” stops moving in time, the physicality that binds foot to foot moves it still, drawing it out, as it stretches so thin as to reveal a tremendous arc, the experience of ending where one has begun. There no absolute dichotomy of existence and Mind, memory and mental seeing. I believe that Donne captures something of Spinoza’s argument, that Spinoza himself is not here capable of.

To add to this account see Spinoza’s Letter 17 to Peter Balling (July 20, 1664):

…a father so loves his son that he and his beloved are, as it were, one and the same. According to what I have demonstrated on another occasion, there must be in thought an idea of the son’s essence, its affections, and its consequences. Because of this, the father, by the union he has with his son, is a part of the said son, the father’s soul must necessarily participate in the son’s ideal essence, its affections, and consequences…

 

Closely Related Post: Anselm’s Proof of God, Wittgenstein’s Lion, Davidson’s Belief