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Tag Archives: Infinity

Infinitely Narrow: How Spinoza Corrects Descartes’ Lenses

Corry Shores has another nice post up in his series on my study of Spinoza’s optical theories and practices. He is the only person, as far as I know, who has made an attempt to read through the whole of my study and it is with great appreciation to find my thoughts reflected there. Here, 6: Seeing Differences between Descartes and Spinoza. Some Observations on Spinoza’s Sight. [The Kvond Spinoza’s Foci Summary Series], he points out a power conceptual, and pictorial difference between Descartes and Spinoza. In my understanding it is hard to over estimate just how pervasive Descartes’ optical metaphor for consciousness and methodology for clarity became, in particular when it was grafted onto by Idealist notions of fundamental intentionality, self-hood, and subject/object duality. Spinoza’s correction to the hyperbolic lens, the lens that Descartes felt would unlock all the powers of clear, nearly unlimited vision to man, stands at a fundamental cross-roads in the history of philosophy, noting the turn-out where modernity could not branched off from the Idealism it followed.

This contrast between the narrowly clear and self-evident, and the broad spectrum, comprehensive intuition of a whole makes an interesting contact point to a discussion Carl Dyke and I have been having over at his blog, on the Infinity Standard (something he regards as an unhealthy societal influence), Existential infinity. Descartes envisioned an infinity as well, an infinite power developed upon the tunnel vision of narrow band precision of clarity, ultimately founded upon the notion of the “self” as indubitable. While Spinoza wanted to say of lenses, of eyes, and ultimately of consciousness, whenever we are perceiving something clearly it is always because we are already perceiving the vista of what lies beyond it. There is no narrow clarity that supersedes and establishes the role of the margin. In fact, as is the case in criticisms of philosophies of Presence, it is always the margin, the ground, that allows the narrow, bright center to have importance, or even substance at all. As I have mentioned before, recent concerns about objects and their centrality are grown out of the image of clear centrality itself, something that comes out of Descartes’ optics, and as I tried to show, Kepler before him.

We do not realize how much our folk and philosophical conception of consciousness and the world is governed by a metaphor of tunnel vision.

A related post: The Hole at the “Center of Vision”


What is “Passing through Infinities”?

Corry Shores has another beautiful, traveling meditation and analysis of some thoughts that I raised (I certainly enjoy seeing my thoughts reflected in that mirror, as I discover things that I must have been thinking however dimly, or should be thinking). Here he takes on the trope of “passing through infinities” that I found in von Kleist’s “On the Marionette Theatre”  and the appeal I made to Leibniz’s triangle. He does such an excellent job of explicating Kleist’s story, I recommend his post if only for this. There is a certain openness and journeying that marks Corry’s analysis of things, as he works his way forward, a real pleasure. And Corry does a wonderful job of bringing out the illustration of the concave mirror, and the reversal/vanishing of the image that occurs as the object approaches the focal point (passing onto Deleuze and Bergson). Again, Spinoza’s optics, his experiences with the building of telescopes (and perhaps likely use of mirrors and/or camera obscuras), is something no one has considered when weighing the meanings of Spinoza’s take on infinities. What Corry brings out, though not explicitly, is that Spinoza’s own position upon infinities was itself shaped by his work with lenses and mirrors.

Transverse Condensation

But I want to think to myself about what it means for us to “pass through an infinity” as Kleist claims that a conscious person must in order to attain grace. What I strongly suspect is that this is what Spinoza has in mind when he talks of the three tiers of knowledge, with emphasis on the latter two of these: the imaginary, the rational and the intuitional. Intuitional knowledge is that which is produced when rule-following, rational description is suddenly acceded, surpassed with a kind of accelerated leap of clarity, a clarity which is necessarily comprehensive and not apparitional: Spinoza uses the example of how we can do mathematics without having to move consciously through all our steps. As we journey down into the details of anything in the world, including ourselves, any rational ordering of “what is” not only employs imaginary separation of things from all else (their causes included), but there is a certain density that is achieved in any contemplation wherein one crosses through to the other side, having absorbed the orderings of our body. The confusions and conflations that mark out our imaginary engagements, bringing together under a certain mode of intensity, are first separated out into rational descriptions of causation, but then these delimitations are transcended. The world itself is not transcended. Only our imaginary/rational structurings of it are. And in this way Spinoza’s “intuition” bears a certain condensive similarity to “imagination” such that the two work to prepare and then exonerate the rational which lies inbetween.

I want to say that it is not enough to be analogical here, or more loosely, metaphorical. It is not that we cross through infinities like passing through the focal point of a curved mirror, or like a line crossing over another. Instead infinities are literally gathered up in bounded limitations, and pursued together along certain lines of traverse, and that then these infinities are passed through, onto the other side so to speak, unto a certain comprehensiveness, the kind of comprehensiveness that Spinoza (contrary to Decartes) urges us to start with.

Spinoza, Infinite Substance, and Kabbalah Influence

Math Unto Infinities of Different Sizes and Badiou

I’ve been looking into the status of mathematical knowledge in Spinoza’s ontology and epistemology, and been having some discussion with Eric Schliesser with whom I agree: Spinoza is a skeptic in terms of a stable, mathematical knowledge of nature via mathematical thought and operation. This of course is rather counter intuitive considering the heavily rationalistic interpretation of Spinoza in the last century, and the rather strong circumstantial evidence of his more geometrico form of his Ethics, which seems to announce the primacy of mathematical knowledge.

There is also a timely subject matter to these questions, at least in these circles of blogged conversation, as Badiou’s Cantor-inspired Set Theory framing of Being runs right up against and perhaps turning upon the onto-epistemic standing of maths in Spinoza’s philosophy. Aside from any critique that Spinoza might offer Badiou’s Being a la maths, there is the provocative historical fact that Cantor’s Set Theory was heavily influenced by early study of Spinoza, in particular his position on kinds of Infinity and questions of divisibility. Spinoza represents a kind of Ur-figure in the concepts Badiou make central, so getting a firm grasp of Spinoza’s differences seems contemporaneously a significant thing to have.

The Door of Heaven and Spinoza’s Early Influences

But in this post, given my personal context, I simply want to post a significant passage on the connection between some of Spinoza’s most elementary ideas, and the thesis that Spinoza was strongly influenced by concepts found in the Kabbalah and the Zohar. Long have I noticed the similarities, and have even come upon other sources outlining them, but it seems that it is a fact/thesis that often get forgotten – some of Spinoza’s most significant contributions to philosophy, not to mention his involute and sometimes sublated Neoplatonism, are best reflected in the ideas found  in this religious thinking. It is good to provide a googable link and easy reference for those who have not thought about it much.

The best Spinoza interpreters continued to link the great philosopher with the doctrines of the authentic Kabbalah, especially those of the Zohar. One of the most important among them was Stanislaus von Dunin-Borkowski, a German Jesuit whose book Der Junge de Spinoza/ is still a classic hardly ever matched by more recent publications. Dunin-Borkowski has a full chapter called “Kabbalistische Wanderfahrten” (Kabbalist travels). A subdivision of it reads (pp. 176-90): “Der Ursprung der Mysticism-Kabbalah und die Urkeime des Spinozismus” (The origin of Mystericism-Kabbalah and the first germs of budding Spinozism). The author stresses that “a higher form of cognition of all finite things, a cognition of God and the light of eternity in the Kabbalah as well as in De Spinoza appears as the highlight of Ethics“. According to him, there was a highly developed older and intermediary type of Jewish mysticism prevailing beside the Kabbalahin the thirteenth century, and the Talmudists had already conceived the existence of mediators between God and the Universe. From these mystics, he concludes, an infinitely long and slow but almost straight evolution leads, through the ideas of the (kabbalistic) sephiroth and the neoplatonic emanations, directly to the basic concepts of the natura naturans and the first links of the natura naturata  in Spinoza’s system. Dunin-Borkowski, in contrast to Heinrich Grätz, the well-known historian of Jews in Germany, calls the sephiroth in the Sepher Jetzirah (Book of Creation) of the Zohara “highly advanced evolution of the secret philosophy of the Talmud, a groping for a link with secular science, an important transitional work pointing to the speculation of the oldest gaonitic religious philosophers. The concept of the En Sof, the Endless or Boundless one, Dunin-Borkowski continues, dominates the Zoharto the same extent as it will later be prevalent in Spinoza’s mind. And here we encounter exactly the same determinations which by so many thinkers and scholars consider a fundamental clevage between Judiasm and Spinozism. God (the En Sof) cannot be designated by any known attributes. He is best called Ayin (the undeterminable). Hence, in order to make His existence known to all, the Diety was obliged (or, what amounts to the same thing, wishes) to reveal Himself at least to a certain extent. But the En Sof, being boundless, cannot become the direct creator, for he has neither will, intention, desire, thought, language nor action, attributes which belong only to finite beings. The En Sof, therefore, made His existence known in the creation of the world by the ten sephiroth, which flowing directly from Him, partake of His perfection and infinity.

These substances or emanations are parts of one another, as sparks are part of the same flame; yet they are, at the same time, distinguished from one another, as are different colours of the same light…The pantheistic suggestions of the first and third book of the Zohar  have become of the highest significance for Spinoza. For there the sephirah “wisdom” forms a perfect unity with the crown and the En Sof. “They are like three heads which, actually, form only one. Everything is connected and linked together in the one whole (the universe). Between the Universe and the Ancient One (God) there is no distinction at all. All is One, and He is all – without distinction and separation.He who describes the sephiroth as separated from one another, destroys God’s unity’.

But Dunin-Borkowski has made another important discovery. The concepts of the Kabbalah were first transmitted to young Spinoza in a rather palatable contemporary version, i.e. Abraham (Alonzo) Herrera’s famous book Door of Heaven. It was written in Spanish and translated into Hebrew by Isaac Aboab. This work, which dealt with Kabbalistic philosophy, was a favorite sourcebook of Baruch’s noted Talmud teachers, Saul Levi Morteira and Manasseh ben Israel. In 1678 (one year after Spinoza’s death), a Latin version appeared under the title Sha’ar Hashomayim  class=”hiddenSpellError” pre=”Hashomayim “>seu Porta Coelorum. In quo Dogmata Cabbalistica Philosophorum proponuntur et cum philosophiae Platonis conferuntur.

Herrera himself had already died in 1639, and young Baruch absorbed the contents of Door of Heaven just during those most decisive years of mental development when the imprint of new ideas of strongest and everlasting in every budding intellectual. He read, of course, the book in its Hebrew version, the language he mastered best up to his death (despite his somewhat clumsy Latin publications and Dutch letters).

According to Herrera, there is on original substance with an infinite extension. Outside it, there are only divine modiwhich are all encompassed in that original substance, the En Sof, even in the potentialities. Thus, there is a created (finite) and a non-created (infinite) State of God, i.e. both God in His proper sense and the Universe; but God is and remains the immanent cause of all things, and the “Universe is actually nothing but the revealed and unveiled God”. Therefore, we find in the “Lexicon Cabbalisticum” (a chapter of the Door of Heaven) the unequivoked statement: “the acceptance of this unity is part and parcel of the faith of every genuine Israelite; we must believe that the Infinite manifests Himself in all His modi through the unity” (my italics). There is one substance, Herrera stresses, with infinite properites. It is determining itself by a multitude of infinite beings which are, however, nothing but its modifications. God is One and Many at the same time – one in so far as He is infinite; many in so far as He determines Himself in His attributes and modi. These modi cannot exist nor be understood without the Divine One inherent and indwelling in them. Everything is one in God(my italics). Dunin-Borkowski reaches the following conclusion: “Especially the first five treatises of the book [Herrera’s Door of Heaven] explain that only blind prejudice can overlook this source of Spinoza’s.

“Spinoza and Kabbalah” by Henry Walter Brann,  in Spinoza: Context, sources, and the early writings (2001), edited by Genevieve Lloyd

If Spinoza had read The Door of Heaven  it was likely before the age of 15, but really the Kabbalah was a prevalent conceptual touch-stone at this time due to messianic stirrings in the political realm. In any case, as I see it, Spinoza’s Kabbalistic influence seems likely, and it is noteworthy that Brann reads the Kabbalistic impulse, along with its mathematical preoccupations, as part of the attempt of mysticism to come to grips with the power of science. In a certain sense Spinoza’s system can be seen as an extremely rigorous, scientific and literal radicalization of both the religious impulse of the Kabbalah, but also its political force (an immanent unity towards a freedom through communication, an offspring of Renaissance revolutionary conceptions of civil transformation). In a more particular view towards the question of the status of mathematical knowledge in Spinoza’s system, the Kabbalistic influence of an insistently Infinite and unbroken Substance helps interpret the power of Spinoza’s seemingly anti-mathematical stance in his letter 12 to Meyer, wherein he declared mathematics imaginary in origin. Perhaps we get a glimpse of just how Spinoza conceived that it is through the Intellect that we see any quantity as infinite and undividable into finite parts, despite our ability through mathematics to divide quantities with incredible facility and clarity.  Additionally, Spinoza’s pantheism, (the issue under which the Catholic Cantor most firmly staked his objection of Spinoza), understood as a position taken upon mathematical infinity and set=making itself, may help provide the most robust correction to Badiou’s mathematical ontologies.