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Category Archives: Badiou

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.

The Emperor’s Clothes: Adieu/Badiou?

Been away for a day or so, and it seems that the flare-up over the effrontery  of not to be thrilled by Badiou apparently has died down, for whatever it is worth. Sewing the button I posted a comment  over at “Daily Humiliation,” attempting to second Ben’s affirmation of my characterization of a general dissatisfaction with the apparent recovery of the Truth at the hands of Badiou. Good to post it here as well…

Yes, elephant in the room, methinks. Perhaps this comes from a decided and articulate force of pro-Badiou expositors on the web, the ever-hovering threat that Set-Theory could descend upon you, like some kind of (n+1) dimensional philosophical object if you dared abstain from the enthusiasm, and the ever-present, softly Maoist reproach that you were merely reactionary (called Neo-liberal these days), not truly radical or nor thoughtfully caring enough, not loyal to the “name”/event of revolution, now called “Badiou”, if chills did not run at the sound of its name…all of this pushing the not-so-inspired-ones  silently into the relative corners of the handful of blogs we seem to imagine compose the “blogosphere” (more like a blogo-cul-de-sac). Someone finally mentioned, “Hey, he really isn’t that interesting or profound” and all those in the corners looked up and said “the others see the elephant in the room”. This is not, was not, a wave or a throng of hatred. It is merely a kind of shrugging off, with a sigh of a kind of relief.

I have read few writers not so much retract, but be careful to in addition to their criticism also stake-out a small piece of real estate in the Badiou revolutionary empire, who knows, there very well be a spike in the Communist Housing Market. For me though it is simply the fact that there are more interesting, more vital thinkers out there (both living and dead), as my francophile and social justice philosophical impulse remains as strong as ever. Its not that we disaffected ones begrudge the enthusiasm of others over their thinker of choice, as reserve the right to be less excited than they without having to incur the accusation of disloyalty, (or enmity), or even adolescence. Not all flight is Icarian. Not every maze Daedaled.

The Banality of Badiou…


Splintering Bone Ashes puts it this way,

Whilst his ontological position has a certain minimalist elegance about it, everything he builds atop it is little more than a ridiculous hyper-structure of nonsense piled upon nonsense, an unsteady philosophical folly whose absurd (yet po-faced) architecture has only been exacerbated by (what I have read thus far of) Logics of Worlds.

And Naught Thought collects the pieces of a disaffected sense of betrayal (a betrayal that isn’t even dramatic enough to be betrayal).

For me it was never the case that I was enchanted with Badiou, only savoring his study of Paul, often just seeing him as something of a One-ups-man of his much more influential and preceding, Deleuze. Who is going to inherit the shared crown of the Dioskouroi, Derrida and Deleuze, so as to enthrall today’s students, and convince them that real philosophy is being done somewhere, now? Continental Philosophy’s need for a frontman.

Yet really it comes back down to this “mimimalist elegance”. The austerity would be austere if it were only intense. If things are to be abstracted, honed, rarified, condensed, they must vibrate, burn in all their mimimal character. Instead it all comes off as a sketch in a student’s notebook, some essential diagram dreamed up, and then written on without end. It is like Plotinus without the Vision. It is a mathematical analogy taken too literally, nicely clever, so as to self-convince. Its like seeing a magician who fails at magic, the transformative performance of that which magic is, and turning illusion into mere trick, someone who forgot the Prestige. After you make the world disappear, you have to bring it back.

[Spoiler: Do not watch if you haven't seen the film, The Prestige]

The Fantasm of the Point: Vico, Plotinus, Campanella and even Badiou

(ca. 204-270 AD) 

To return to the diagram of my last post on Plotinus I want to think along with a confluence of ideas that condense upon the very center of it, the infintesmal locus of “matter” which exists merely as a private, yet also which alternately can be considered as a radiating center (under a different analogy).

The direction I want to go in this is a rumination that first starts from Badiouian notion that Being is not of the One, or “the One is not,” and that mathematics in a sense speaks Being,  pronouncing what is expressible of being-qua-being. The principle that the non-numerical One is beyond Being is of course one that Plotinus holds at the pinacle of his Ontology, for Being starts with the varigated particularization of the Nous. It is there that the predication of Being takes hold. The way that Plotinus tells it, the Nous is produced by the plentitude/emptiness of The One, and necessarily breaks it apart into a kind of representation which divides it into parts. The reason that Plotinus gives for this division into likenesses is interesting. It is that the Nous struggles with the fact that it has no control over that upon which it ultimately depends, a control which expresses itself in the desire to preserve:

The hypostasis of the Intellect [Nous] cannot maintain its vision of the One in primal unity, but “being being unable to preserve the power which it was procuring, it broke it up and made the one [power] that it might bear it part by part [katà méros]” (6.7 [38] 15.20-22). In so doing, Intellect constitutes itself as an imitation of the Good, as a many-hued and varigated Good (agathòn poíkilon).

F.M. Schroeder, citing Plotinus in Form and Transformation

Now there is a great and dissatisfying danger of simply reading these particularizations as mere abstractions of an esoteric philosophy, the most gripless of metaphysics, but Plotinus’s reasoning as to why the Nous indeed breaks up the One has strong affective, phenomenological correlates. It is the very dependency of the unity of the Nous upon what lies beyond it, and inclusive of it, that generates a corresponding particularization. In drawing power from what is outside, the inside distinguishes itself. If we turn to the simple figure of a circle (for millenia a favorite of philosophers, and think in terms of systems theory, we understand that whatever system there is, it necessarily is less complex than its environment. This is to say, as all systems (the inside) depends upon a more complex outside, the very inside/outside boundary issue of dependency drives the very divisions of the inside in regard to what lies beyond it. If we allow the observations of evolutary theory, life has moved from less to more complex, and with this increase of internal divisions (differences that make differences) it has relatively gained a greater role in the preservation of the power upon which it depends (and, notably, which it is also an expression). Plotinus’s story of the Nous serves as a metaphysical directionality which prescribes how any person (organism) might orient themselves to conditions which are beyond it, like the Nous with totalizes these relations, the move is towards a complexification of differences that make differences.

For Plotinus, this process of particularization comes from what he calls “beholding” or “witnessing”. Whereas the first particularization beholds the One/the Expressed, those of Soul and Sensation are even more narrow in what they behold, all the way down to matter, which simply exists as a non-existent privation. A speck of darkness.

A Retreat to Vico’s Conception of Mathematics: the ficta of points (1668 – 1744)

I find this speck of nothingness interesting because its very non-divisibilty division reflects something of mathematics, the way in which points or numbers are non-existent distinctions that operate as a kind of limit. What I have in mind is Giambattista Vico’s interpretation of mathematics as the most divine of human acts, because in the invention of the point and the unit human beings act just a God did, creating something out of nothing in imitation of divinity, scientia humana divinae sit imitatrix. For Vico, a forerunner to some themes found in Kant, human beings cannot truly know things that they have not created. Only God truly knows what is created. The reason why human beings can have perfect knowledge of mathematics is that its creation is wholely their own. In a sense, mathematics operates “within” the circle of human articulation.

To quote some Vico, and then a commentator, to give perspective on his position:

…man defines the names themselves, and on the model of God with no underlying thing he creates (creat) the point, line and surface as if from nothing, as if they were things…to establish (condidit) for himself a certain world of forms and numbers, which he embraces within himself: and by producing, shortening, or composing lines, by adding, substracting, or reckoning numbers, he effects infinite works because he knows infinite truths within himself

But the point of the human imagination is not the point we draw with a pencil: “the point, when you draw it, is not a point: the one, when you multiply it, is no longer fully one.”

“man, containing within himself an imaginary world of lines and numbers, operates in it with his abstractions, just as God does in the universe with reality.”

With something of Plotinus’s reasoning, the very imaginary abstraction that human beings creates is a coping mechanism for that which lies beyond them and upon which they depend. Here Robert Miner provides a good overview of Vico’s approach to the knowing of human understanding:

Abstraction is the mind’s way of coping with its estrangement from things. Because he cannot possess ‘the elementa rerum by which things themselves exist with certainty,’ he resorts to the fabrication (confingere) of elementa verborum, elements which, despite their unreality, are able to ‘stimulate ideas with no controversy.’”

Vico has described human truth as a factum that is arrived at through a synthesis of elements that are only partially grasped, because they exist outside the mind which grasps them. If the human mind is essentially outside the elementa rerum, how does it manage to grasp even their outside edges? Vico proceeds to answer this question: “God knows everything, because he contains within himself the elements from which all things are composed; man seeks to know these elements by a process of dividing (dividendo).”

What is the relation of “dividing” to making? Is dividendo creative or destructive? Vico’s answer is “both.” De antiquissima 1.2 begins with an homage to the fecundity of dissection. The “anatomy of nature’s works” gives birth to a range of human scientiae. It does so by inventing their objects. One can divide man into body and spirit. From body, human science has “picked out (excerpsit) or, as men say, abstracted figure and motion, and from these, as well as from all other things, it has extracted (extulit) being and unity.” The objects obtained through abstraction give rise to the human scientiae metaphysics (whose proper object is ens), arithmetic (unum), geometry (figura), mechanics (motus from the edge), physics (motion from the center), medicine (corpus), logic (ratio), and ethics (voluntas).

The fecundity of dissection comes at a cost. Man creates the human scientiae by fragmenting, and therefore destroying, the whole…The entities created by abstraction – being, unity, figure, motion, shape, intellect, will – are “one thing in God, in whom they are one, and another thing in man, in whom they are divided.” Ripped from the whole in which they have life, humanly obtained elements are disiecta membra. “In God they live, in man they perish.” Our efforts to understand nature by cutting it up supplies us with theories rather than works: “in nobis sunt ratiocina, in Deo sunt opera.” All that man acquires through dividing the whole, is like man himself, nihil prae Deo; all finite and created beings are nothing but disposita entis infiniti ac aeterni. Etymology confirms the connection between division and diminution: Vico asserts that minuere means both “to lessen” and “to separate.”

The limitations of abstraction ensure that we have access only to the extrema of the elementa rerum. In what is likely to be an illusion to Lucretius, Vico declares that when man starts to investigate the nature of things (naturam rerum vestigabundus), he finds that “he does not have within himself the elements from which composite things exist.” This lack (brevitas) is not a morally neutral feature of the human condition, but a “vice of the mind” (mentis vicium). It is an effect of fallenness, a decline from a primordeal state in which mind and nature where integrated. (Vico uses nefas to characterize physicists who think they can provide real defintions of things.) Man responds to this condition by turning the mentis vicium to good use, by performing an operation that relies solely upon the mind and bypasses, as it were, the material world. “By abstraction, as they say, he fabricates (configit) two things for himself: the point that can be drawn and the unit that can be multiplied.” The association of abstractio and configere suggests that abstraction is creative. The suggestion is confirmed in the Prima Riposta, where Vico writes that mathematics [move to quotes on mathematics].

Truth in Making, Robert Miner

The Terminus Point of Nonbeing: Campanella (1568 – 1639 )


There is another evocative figure of radiating being, that which Campanella uses to characterize how each thing is but a point from which non-Being radiates, a kind of photographic negative of Plotinus’s conception:

 What we are concerned with is something that has an actual bearing on the existential order [not "relative nothingnesss" (nihilum secundum quid), the essence of a thing prior to existence], i.e., the composition of an infinite nonbeing with a finite being in existing realities. This is the point at issue, and this Campanella tries to illustrate by means of an analogy. Just as we can conceive a line stretching from the center of the earth beyond the circumfrence of the sky in infinitum, so, he says, man, like any other creature, is but a little dot where infinite nonbeing is terminated. Man is in effect the negation of an infinite number of other things and of God himself, being surrounded, as he is, by an infinite nonbeing (Bonansea, Tommaso Campanella, citing Met, II, 6, 3, 7)

In this Campanella presents something very close to Spinoza’s letter 21 claim that “all determination is negation,” something that Hegel made quite a bit of. Only in Spinoza any particular determination/negation is not a negation of God/Substance, but rather its Substance (Campanella always heretically veering towards collapsing God and Creation into one panpsychic whole, like Spinoza, but careful to walk the line).

What I am inspired to say about these circular analogies for Being and coherence of action, with their distinct and performative inside/outside designations, is that somehow mathematics in coming out of the pure fictiveness of human creation, in inventing the Non-Being of the immaterial point, somehow grasps whole the entire matrix of radiating conceptions, and is able to map out with great fecundity the very Oneness which is beyond Being (in a Plotinian sense). Weaving out the very absence, the infintesmal (as my wife tells me, what is the decimal point which divides the infinitely large from the infinitely small, made of?), we get a glimpse of the very varigatedness that Plotinus attributes to Nous likeness taking.  The whole thing is sutured closed, or at least remotely closed, for one imagines that there are many kinds of mappings that can be woven from the nothingness of the point.

Further though, even in its appropriation of the infinite nothingness, mathematics owes Alfred Korzybski’s adage “The map is not the territory,” while keeping in mind that mapping, and map-following is itself part of the territory (one hunts through the map, as one hunts through the territory). All organisms seem to in some form follow Plotinus’s thoughts on why the Nous mirrored the One, being unable to preserve that upon which they depend. The semiotic relations that make up an organisms internal relations, and then thus relations to other organisms, are not only performances, but also are duplications (not necessarily representations), “picking out” (intelligere, to choose out) certain aspects of the world, and it is always a tension between picking out the most important, valued features, and sheer numericity, since these two are intimately related. In a certain sense, mathematics too needs to be seen as a vast material organism/organization, as material as any map, appendage to the human species.

Hearing Alain Badiou on Hardtalk: The Bashful Maoist

I’m sorry, I had never had the pleasureof hearing Badiou speak on contemporary politics, or even speak on anything. A funny thing happens when you see the person. Ideas, tones, the very specular sense of a person invades the writing, filling it out. Here in Hardtalk, originally posted by Infinite Thought, Badiou attempts to make himself clear. I can’t say that in presence this is a man bristling with intellectual acuity. Perhaps it is that he is speaking in English, but my sense of him as a thinker is diminished even from the sense that I already had that his ideas were somewhat inflated. Here Badiou’s ideas filtered down to everyday language and deprived of their technical, interlocking workmanship, appear pale and disorganized thought-themes.

Infinite Thought regretfully admits that this is not the most “successful” interview, something she chalks up to the interviewer’s “pure crystallised Anglo intello-Franco-phobia” (my goodness, PURE?). I have to say as someone who is rather intello-Franco-philic, I found Badiou alternately filled with sopping facializations or staid retreats into ambiguities and prevarication. Perhaps one feels that it was the interviewer’s job to try to draw out what is unique and gemlike in Badiou, a showcase…only though if one is a cheerleader, a true believer, it would seem. Badiou brings almost nothing on his own. We must believe that Communism is the “right hypothesis” despite (brutal) 20th century failures, why…because “faith” is sometimes a good thing.  If you have read Badiou you understand why he says this, but without all the terminology, concept-architecture and whatnot, this is pretty much how it all boils down. If intellectuals can’t do better than this, they are to remain essentially what they are, text-producers for a highly selective, and privileged readership.


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