The Third Circuit

ॐ पूर्णमदः पूर्णमिदं पूर्णात्पूर्णमुदच्यते ।

पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते ॥^[1]

—Invocation to the Iśāvāsya Upanishad

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The “third.” Is it a third like the holy trinity, “God, the Son, and the Holy Spirit”? Is it a third like “reality,” which, at first, appears to be just some authorizing chip that Kant needs to have when constructing what some have called an “intracategorial” system? Perhaps the third is just a simple circle, which connects a plate with the concept of round. Though, we should be careful in passing over the circle so quickly…

But regardless, Kant himself passes over the circle with rapidity, and moves onto a more “theoretical” notion of Schematism, and says that, the categories, since they are a-priori, and since they operate without need to appear to us, since they are the basis of our understanding (and therefore the very Reason which engenders the operations of discourse), must be made sensible, and this making-sensible of categories is the “Schematism,” via “time-determinations.” Time, of course, being the pure intuition of the inner sense; the inner sense which, in absolute time, draws sense-impressions into a synthesis through the imagination. The categories, though themselves a-priori and cannot appear to us, are pointed towards via discursive objects, allowing for the writing-out of the discursive, reflective, critical text.

If only it were so easy. As Kant says, “The schema is, properly, only the phenomenon or sensible concept, of an object in agreement with the category” (A146/B186). This particularly troublesome quote could lead us astray in that basic formulation which Kant wishes us to accept. What does it even mean, to make concepts sensible? Either concepts are always already sensible, and therefore they are only able to appear to the senses insofar as they have come to appear at the correct time determination, or—as that formulation itself suggests, verlan—the sensible is already intelligible. Time, stretched to infinity, becomes the stable concept through which such intelligibility, as sensible, appears in these time determinations; that is to say, in history. This is a Hegelian reading, it is animated, it has a dynamic quality. But Kant is not a Hegelian. As Hegel always says, Kant reduces everything to a “lifeless schema.” Schematism is replaced by Spirit, this active, dynamic, absolutely free productive historical power that turns god into Man, and man into God. But even with all that practical Freedom entails for Kant, God is not the God of Freedom, Kant just gives humans the power of the moral world, a power before held in the hands of the lord, now, with the correct discipline, given to Man. God, for Kant, is far more illusive, excessive. God is something so mysterious and wonderful no discourse could capture him, and only human action can reach toward him through an inescapable teleological world order that always sees God at the end—but Kant says, no, see Man at the end, because God has no ends. See Man as man had seen God, but know that he is not. That is the name of practical freedom.

We return to the cold, lifeless schema. The schema which, in fact, was neither sensible intelligibility—as it was for Schopenhauer—nor intelligible sensibility—like for Hegel. But the former held a closer, in my view, position to Kant, as the Schema transcends, and grounds, both the intelligible and sensible worlds, it is the ultimate privileged object—the schematism is, in fact, the architectonic, the architecture of discipline, of practical reason; and don’t misunderstand my genitive: practical reason only operates insofar as it is a schematism.

A border must be previous to the thing which the bifurcated action of bordering acts upon; that is, a border, in its construction, is always a priori—yet such priority is always derived retroactively. The conditions under which what is a prior is established always already as the concrete expression of the intelligible in or as a system by which it is received as sensible. That would be, thereby, the Schematism.

The text lives in its dynamism, it takes the wild, the untamed, and schematizes it, bounds and gags it, disciplines it, and drives it forward in chains. Practical reason is the border of a territory, an island, which has been sailed to on the boat of dynamism, and upon which Freedom has planted its flag, where Freedom produces, draws, and demarcates the habitable territory. A bordering is always vanishingly thin, a sensibly quality whose intensive degree is always approaching 0, but remains the limit, the threshold, which must be breached for anything to appear. In fact it is the case that, the more intensive something stimulates, the higher its degree, the more totalizing and absolute the sensation becomes—approaching 1, we approach an absolute unity where all borders fade away. But at 0, or rather, just above it, there is a vast multiplicity of difference engendered by the increasingly complex determinations of borders which, the more complex, the more they threaten to dissolve entirely the more feint each becomes—which is also a drive towards a unity beyond structure. All human life exists within these bounds, the absolute circle of the 0, a zero which is constantly under assault by whatever might exceed it. Recall that the 0 in the analogy of experience already requires a-priori reason, that makes the 0 the perfect border, equidistant as a circle on all sides. Why wouldn’t the ancient Indians^[2], to whom the nature of शून्य^[3] first came to light, think any different, as even that which is empty always already contains an immense fullness. The very characteristic of the full, is that it is bordered by that which yet becomes full once again. A sensible concept requires this bordering operation at its basis.^[4]

As Kant clearly describes in the Method, the bound and disciplined Reason operates with an exploratory function, once it’s internal wars are resolved—resolved by being elucidated in the sensible world, from which before Kant wrote the Critique of Pure Reason, such conflicts were never able to find their sensible bearings, and after which the Critique of Pure Reason operates as the primary event where Reason begins to author itself into the sensible world, and defines in that exploratory moment the architecture (the architectonic structure, whereby the Critique appears to us) which explodes onto the scene, and gives a regulative trajectory for its outbuilding. But that every moment of that conflict which Reason wages in the sensible by the sensible is a moment that practical reason captures^[5], and that capture becomes for practical reason a new origin point, a radical originary movement, where it reinstates its absolute primacy in the negative, its absolute freedom, and from that point now grasps all other originary moments as already being born from this moment, so at once the whole dynamic movement of Freedom begins again with every word, and every word is comprehended as the totality in the structure which it pulls forth.

        This schematic function of practical freedom, that is, it’s structural positioning which at once establishes in every originary moment, in every word, a negative border, occurs when the totality of time determinations, which are brought forth at every word, necessarily at every moment delineate that which stands in the negative, the intelligible sphere, but it is the power of their architecture which describes the practical freedom and not the negative itself, in freedom, which drives the structure forward. This is why I said, the Schematism has far more primacy than Spirit for Hegel, and more primacy than Freedom itself, since it is the schema which always already exceeds itself and through this excess, this structuring excess, expands, since every originary moment is always already negative towards all other moments which are never moments for the originary moment, but always vast imbrications that find a dynamic arrangement. Every word of the Critique of Pure Reason is the first word, and that word always has the privileged point of a schema, which always already marks the very absolute time which it must function within at a higher level, the levels of the sensible and the intelligible, demarcated precisely by the schematisms that must pull forth the structures which define them, and which retroactively conceal the originary moment in every moment—the schematism is always turned towards the structure, and never stands above it as that moment which practical freedom has originated. We never see the pure sensibility, the pure intelligibility, we see the words, and the words point to what they are not—that is, the totality erected by the very word itself. It hides, I say, in the power of Freedom; Freedom is that empty concept in which all schematization, at every word, stands forth.

        The war machine of practical reason is thus itself an intelligible outgrowth of the violent convulsions of the schematic architecture, the architecture which is always already new and originary at every moment.

That what we call sensation, does not seem to be ordered within those words, but the words, instead, appear as a net for the sensible, is itself a πρόληψις. The element of reality comes before it’s pure (b)ordering under the 0, but that 0, and it’s intensive magnitudes of degrees, always stand a priori, as I note above—but we must not take a priori to be given in this rudimentary form; we must see the a priori as the delimitation of the schematism which gives shape and structure to it. So what, in fact, appears as a limit, is already a shape. In that shape, the 0, the empty circle, what would later be named the empty set, we have the most basic formulation of all structure: and isn’t the definition of any ordinal, according to set theory, the union of the empty set with another empty set, such that 0 = {},  1= {{}}, 2={{{}}}... endlessly, as Derrida would say, invaginating, folding into itself as it expands. So that at every level of Von Neumann ordination, that is, at the level of the 0 which is given as the ground and most basic unit of elaboration, we have an emptiness which is coming onto the scene as emptiness—but ordering emptiness, where every moment finds its unity in the originary 0, and the expansion of the empty set is the architecture of that moment, the architecture structured in terms of degrees. Such degrees we could simply name as ordinals themselves, as the ordering which the schematic architecture enacts.

This architectural framework would seem to be split between what Kant calls the transcendental imagination (unity of the inner sense) and the transcendental unity of apperception (formal unity). The former the unifying force of the analytic, the latter in the dialectic, both defined in the Deduction as having a necessary relation, one always articulated through the other. We might see that the border which Kant creates at the beginning of the dialectic, the aforementioned island, is an attempt to separate the former from the latter—if not also the Schematism, the Amphiboly; in fact, throughout the whole Critique of Pure Reason Kant stresses the need for a dichotomy between the inner sense and formal unity. But only in those respective moments does it appear to be purely formal or purely empirical. For the imagination, it is the 0 which takes primacy. For Reason, as outlined in the Paralogisms and the Ideal of Pure Reason, it is Pure Reason (Reason which gives the names “I” and “architecture,” in the Paralogisms and the Ideal, respectively)^[6]. Though the difference, as I’ve said, between this interpretation and Hegel’s, is that for Hegel, that second moment, the rational moment, which necessarily follows in the development of spirit upon the movement of bare structure, is the more Absolute in the revelation of Spirit. The “this” here and now, of the Introduction (of the Phenomenology) though already taking on spirituality, in the fact that they participate in that social-structural unity, cannot be the final word of the Phenomenology^[7]—and that former spirituality only becomes apparent at the end, which has no end, but only a frozen circle. For me, the primacy is given to the structure itself, a structure which generates at every moment its absolute rationality via its intelligibility, but which itself, in a truly Kantian fashion, cannot be described (or rather, circumscribed) but through the negative which is already given by that structure. But this is not a negative that somehow moves towards a positive, or was already positive. It is a negative that is negative only insofar as the inside of a circle is negatively defined with regard to the outside, and each is the negative of the other. That an absolute difference^[8] must stand as a permanent excess for each towards the other, and that this difference stands as the difference of the shape itself at the level of its shapeness, the zero at its zeroness, or the ego at its ego-ness.

The meaning of transcendentality, then, is not a sheer excess which has solid ground on the one hand, and a feminine delirium of the in itself, as Schopenhauer names his Will. Nor is it the necessarily rational order of sensibility, with the transcendent, the Absolute, infecting the whole analytic and making it, as Hegel says, spiritual. The Transcendental lies far closer to the topological concept of the closed and open sets, in that a closed set is merely the complement of an open set; they are trapped in a relation where one is defined via the other, but within nothing but permanent, and absolute difference. A difference which gives no heed, nor reference, to the nominality of Reason—that is, like recursion, which only seeks to define the logical operation which allow formal mathematics to occur, yet a recursive proof requires within its negatively defined logic regular language which—supposedly—would follow that very same logic within its own operations. In this space of difference, there is no time, but only an ever increasing system of complexity growing out from such a simple set of rules.^[9] This machinic capacity of logic after it has been grounded in the materiality of schematism becomes the very network of signification, or even imbrication, whose definitions then grow out of its structure—but the very structure itself, in its density, its complexity, it's auto-poeisis, begins to overtake the very nominals that have come out, and those nominals become like spires on Prague’s skyline; even as the architecture, like the Centre Pompidou, continuously expands out of itself.

This architecture is what binds us, what builds us, and what has been only intensified by Kant. We are dealing with, then, a historical a priori—what is added to experience are these very words and names that come prior, but not just words in a purely transcendental sense, but words as architecture, the very schematics that structure and order—it is an imbrication, an “insistent previousness” of textuality, as Moten might say, quoting Nathaniel Mackey. And it was this architecture that is situated most densely in subject formation, in the negativity of the relationship between the inner sense and the formal I. So although this essay is about the schematism, what became the object of attention was the means by which the schematism becomes the absolutely privileged term in the Kantian system, and we found that it was in fact via this difference which is most clearly elucidated in the Deduction, where Kant describes the three fold unity—synopsis, representation, and formal unity. Though it is in the beginning (of the A edition), I say, at the level of the synopsis, or even before it, where Kant is most clear: any unity requires the gathering up of all moments into one^[10]: and it is this operation which turns out, in the discursive, structural, architectural system of the transcendental, to be the most revealing, and what solves this equation of the split between the synthesis of the imagination, and the transcendental unity of apperception.

The subject, then, is itself historically mediated; a product of that which has been built before, and every positionality within subjectivity, from the person to the sign, is, to quote Pink Floyd, just “another brick in the wall,” a brick towards the building of something other than, something marvelous and stretching towards, constructing itself out of what has been called ἄνθρωπος. What is this but the creation of the living embodiment of excess itself, the thing, the thing which we strive to create. God is beyond us, but Kant has abandoned the lord in heaven, and wants us to intensify the creation of a new God from below, a God who breathes his concepts “through nature,” who drives reason to the brink of insanity, who appears as an abomination, a “sublime” entity beyond the bounds of intuition. The Great Ought, the great tyrannical overlord of the Ought—like a slave driver—the chthonic entity Kant brings into the world.

Having said all that with a Lovecraftian flourish, I will conclude this essay with a more moderate tone. Even this ever expanding indefiniteness of the architecture, building up to itself, which only count insofar as that which lays beyond it is always count-able, where the operation, stretched to regulative infinity in its practical course—that is, in the productivity of the very demarcations themselves—suggests a rather brittle set of bones. I wonder if the whole building will fall apart before we finish making it.

Works Cited:

Ishavasya Upanishad, Shri Shankara’s Introduction. https://www.wisdomlib.org/hinduism/book/ishavasya-bhashya-by-sitarama/d/doc145017.html. Accessed 1 Jan. 2024.^[11]

Kant, Immanuel, and Norman Kemp Smith. Immanuel Kant’s Critique of Pure Reason.     Macmillan, 1933.

Land, N., Mackay, R., & Brassier, R. (2011). Fanged noumena : collected writings 1987-2007. Urbanomic.

Smithsonian Institution. Annual Report of the Board of Regents of the Smithsonian Institution: Showing the Operations, Expenditures, and Condition of the Institution. U.S. Government Printing Office, 1903, https://books.google.com/books?id=0_UyAQAAMAAJ.

Bibliography:

Chomsky, Noam. Language and Mind. (1968). https://www.marxists.org/reference/subject/philosophy/works/us/chomsky.htm. Accessed 1 Jan. 2024.

Foucault, Michel, and Roberto Nigro. Introduction to Kant’s Anthropology. Semiotexte, 2008.

Kant, Immanuel, and Norman Kemp Smith. Immanuel Kant’s Critique of Pure Reason.     Macmillan, 1933.

Kant, Immanuel, and Ingeborg Heidemann. Kritik der reinen Vernunft = [Critique of pure reason]. Studienausgabe, Reclam, 2002.

Kant, Immanuel, and Paul Guyer. Critique of the Power of Judgment. Cambridge University Press, 2000.

Land, N., Mackay, R., & Brassier, R. (2011). Fanged noumena : collected writings 1987-2007. Urbanomic.

Moten, Fred. In the Break : The Aesthetics of Black Radical Tradition. University of Minnesota Press, 2003.

Munkres, James R. Topology. 2nd ed., Prentice Hall, Inc., 2000.

Pinkard, Terry P., editor. Georg Wilhelm Friedrich Hegel : The Phenomenology of Spirit. First edition., Cambridge University Press, 2018.

Pinter, Charles. A Book of Abstract Algebra. 2nd ed., Dover Publications, 2010.^[12]

Schopenhauer, Arthur. The World as Will and Representation. Dover Publications, 1969.

 

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[1] “Om. That is full, this is full; from the full, the full is arisen. Having taken the full from the full, the full still remains.” My translation.

[2] I know. Would you have preferred I said “Ancient Aryan”?

[3] The word zero (“shunya”) in Sanskrit, from which is derived the word शून्यता (“shunyatā”), zeroness. And, apparently, a doublet of the word cipher, calqued from the Arabic ṣifr which is itself a calque of शून्य: “We shall therefore have to accept the old explanation that Arabic sifr in the meaning of zero is a translation of the corresponding Indian sunya.” Smithsonian Institution (518).

[4] A most appropriate quote from Schopenhauer on this matter, taken, even more fittingly, from the esteemed Land: “The genuine symbol of nature is universally and everywhere the circle, because it is the schema or form of recurrence; in fact, this is the most general form in nature. She carries it through in everything from the course of the constellations down to the death and birth of organic beings. In this way alone, in the restless stream of time and its content, a continued existence, i.e., a nature, becomes possible.” (162). The editors of Fanged Noumena say it is from World & Will as Representation, Vol. 2 pg. 477.

[5] We say in archaic English, to fang, as in the German Anfang (“to begin,” but, in archaic usage, “to grip”). Perhaps it is this issue of translation, where ἀρχή—which means, in Greek, quite famously, to begin and to rule—takes on the additional valence of capture when translated into German Anfang; and this mistranslation, or imbrication of meanings, is what gives rise to Kant’s philosophy when it mixes German into the realm of Greco-Latin. This conforms to my quasi-foucauldian reading, I suppose.

[6] I think I should also note the importance of the difference between words and names. A word would be that which stands in a relation to other words, or occupies a certain place in a structure (well, for me, obscures its order and enacts that structure). A name, on the other hand, stands in an order of identity and unity for itself, and stands within that identity as absolutely different from other names—names, which grow out of the imbricative structure like the fruiting body of mushrooms sprouting out of a vast mycelial network. The difference between the unity of the inner sense, and the formal unity, then, is precisely this difference: between the structural and nominal.

[7] The final word, of course, being Golgotha, the crucifixion of Jesus which is also already the relinquishment of Spirit and also the moment, just before, of the beginning of the rational understanding of the intuitions.

[8] I first heard this notion of absolute difference vis-a-vis Hegel from Peter Hallward, who said it was from Deleuze.

[9] In the Chomskian sense. See in the bibliography.

[10] The problematics of subject formation and the tension between the unity of imagination and the formal unity certainly appear in the Transcendental Aesthetic, but the Deduction deals with it more explicitly. It would be valuable to produce a further study of this architecturalitly entirely from within the scope of the transcendental aesthetic, but unfortunately there is neither space nor time here for that sort of work.

[11] Ignore all the commentary and the translation provided here, it’s highly sectarian and practically irrelevant to my reading. I just listed it as a place to find the referenced text.

[12] Pinter and Munkres above are the references for mathematical topics in this essay. Books, I might add, which I should study more closely before referencing authoritatively. But I mostly used them as touchstones, since I was reading them at the same time as when I first read the Critique of Pure Reason, so some of these thoughts occurred to me back then. I feel Kant is more original, and these works merely derivative, attempting to mold what still stands as an enigmatic and radical philosophy into the paltry discipline of pure math.