3.1 the sordid boon of freedom

For hundreds of years it has been thought by some philosophers, and not by others, that determinism in the natural world is incompatible with freedom of the will. If everything that happens in the world is causally determined by what went on before, then one’s actions, in particular, being events in the world, are causally determined from time immemorial, and there is no scope for freedom of action. I count myself among the others. One is free, in the ordinary sense of the term, when one does as one likes or sees fit; and this is not altered by the fact, if fact it be, that what one likes or sees fit has had its causes. The notion that determinism precludes freedom is easily accounted for. If one’s choices are determined by prior events, and ultimately by forces outside oneself, then how can one choose otherwise? Very well, one cannot. But freedom to choose to do otherwise than one likes or sees fit would be a sordid boon.

—W. V. Quine, 1986

In order to update Quine’s “freedom of the will” in empirical terms as an evolutionary (not to say “emergent”) byproduct, Daniel Dennett sounds an argument by etymology in his Freedom Evolves (2003)—namely, that ‘determinism’ ought not be conflated with ‘inevitability’ inasmuch as we require strictly determinate environmental cues if we are to “evit” (Lat. evitare ‘to avoid’) that rock, for instance, hurtling along its auspicious arc towards our frangible nutshell. Duck! From this reduces one law with two faces: insofar as harm-avoidance equals pain-aversion (as the engine of adaptation), Dennett renders an excellent, strictly negative argument which, by recourse to the mechanics of rudimentary organism, stands on par with early Freud. Not too shabby.

But here is the trouble with ‘law.’ If any and every truth counts as a law, or even any and every general truth, then this version of determinism can be shown to boil down to the empty ‘What will be will be’. If on the other hand some distinctive concept of law is intended, failure has long since attended the efforts to define it.

—W. V. Quine, 1986

Despite said failure, the perennial parade of philosophers, physicists, psychoanalysts, politicians, psycholinguists, patriarchs, psychologists, pedants, pundits, poets, and posers—from the postulator to the pontificator—shows no sign of flagging. One may wonder just how much theory is left to theorize—if not how much there was to begin with. Nonetheless, as a matter of methodology, or theory put to praxis, we should like to recap and redefine the previously posed problematical tactics for investigation and interrogation, namely:

“enormous leaps over the internal history of things”

Can we restrict and refocus the problem, from (Leibniz’s “Sufficient Reason” as recapped for revocation by Wittgenstein as) discerning (P) “the net” from (Q) “what the net describes” to discerning the net, as (P2) a propositional framework composed of discrete elements—from itself, as (P1) a conceptual framework composed of continuous manifolds? Again, we would accomplish this by revoking the linguistic constraints that (we presume, or presuppose to) have been superimposed upon whichever underlying fundamental conceptual schemas or topological primitives that we (surmise, or retroduce to have been) inherited as vestiges of pre-human cognitive constraints.

If indeed we were able to effect such procedures, we could thus recast the net from (P) the semiological substrate of “thinking” to (Q) the substrate question of “being” by exceeding what we have (via recursive hypethetico-deductive, empirico-rational retroduction) speculatively surmised to be (P1) these same evolved conceptual boundaries, a vantage point from which we could retrace (P2) the revolving contours of their linguistic constraints. (This, in effect, is what Plato naïvely termed anamnesis, or ‘unforgetting’). To that end, we can briefly compare two examples of methodological schematism, the texts of which should prove illustrative despite their lack of visual supplements. Moreover, to subtract points for style, compare Bergson’s flowery prose to Bruno’s economy of phrase:

In short, try first to connect together the discontinuous objects of daily experience; then, resolve the motionless continuity of their qualities into vibrations on the spot; finally, fix your attention on these movements, by abstracting from the divisible space which underlies them and considering only their mobility (that undivided act which our consciousness becomes aware of in our own movements): you will thus obtain a vision of matter, perhaps fatiguing for your imagination, but pure and freed from all that the exigencies of life compel you to add to it in external perception. Now bring back consciousness, and with it the exigencies of life: at long, very long intervals, and by as many leaps over enormous periods of the internal history of things, quasi-instantaneous views will be taken, views which this time are pictorial, of which the more vivid colors will condense an infinitude of elementary repetitions and changes.

—Henri Bergson, 1896

To advance, you must regularly progress through four cognitive faculties: first, by perceiving what physically surrounds you; second, by mental visualization in which images are whirled around you; third, moving by purposive imagination among intentionally positioned images; thenceforth, by precise meditation, you may comprehend individual thoughts as they are formed.

—Giordano Bruno, 1583

Insofar as they concern in-vestig-ation, contrast the actantial motives and parabolic arcs retraced in (A) Bergson’s “leaps over enormous periods of the internal history of things” and in (B) Bruno’s “comprehend individual thoughts as they are formed.” Both authors worked over time to develop reciprocal reformulations of “contraction” as derived from Plotinus; while interpretations are legion, we may circumscribe a constrained snapshot: in these particular examples, Bergson emphasizes exoteric movement—of extension, or expansion (or, cf. Bergson’s Fr. détante to Eng. neologism “detension” as in Deleuze’s 1966 Bergsonism, 1991 Zone translation) by which phenomena exceed the range of intellective discretion, whereas Bruno emphasizes esoteric movement—of intension (via introjection/introspection), by which intellection recaptures the mechanisms of phenomenal rearrangement.

That may be a mouthful, but even in brief excerpt, we can see how Bergson’s interrelation with (purveyors of) Modernism and Impressionism (in literature and in painting) stand in contradistinction to Bruno’s reliance on combinatorial diagrams to provide geometric (topological, graph-theoretic) constraints. Both thinkers strove to explicate methodologies for reciprocating concepts and percepts by way of terms and schemas; if Bergson erred on the side of aestheticization, Bruno erred on the side of mechanization. For example, we might compare Bruno’s “purposive imagination” and “precise meditation” to Kant’s Einbildungskraft and Apperzeption—moreover, the tireless Hegelian dialectician (if none other) will have noted that Bruno enumerates “four faculties” as three-plus-“thenceforth.”

But what of the reversible provisos that would bar self-knowledge from investigation and interrogation, particularly as they are applied to those counter-arguments with which we must contend (if not with which we should like to dispense)? In contrast to Eco, who works his way around problematical topics from every exploitable angle, and in contrast to Metzinger, who blocks all the exits before he shouts “fire!” in the Cartesian theater, these provisos are invoked, by and large, either while feigning—or less insidiously, demonstrating an ignorance of the (psychical) consequences and (logical) implications of the redoubled fideist/fallibilist parallel. What does this mean in practice?

to shrink extensions without a point

For the crucial example—that is, the presupposition that spans the ultra-mega-discourse-domain of Cognitive-Science-&-Philosophy-of-Mind—on one hand, theorists one and all take it as trivial (as an “uncontroversial” given—or, we might say, as an axiom of givenness) that we, each and every, neither ‘are’ nor ‘have’ one unit personage (‘immortal soul’ etc.) who shuffles off this mortal coil only to surf clouds with erstwhile house-pets or drown in lava with least-favorite uncles for ‘eternity’—which is taken as an interminable temporal period, or quantity—that is, taken as commensurable with linear duration as we live it (often called, in a bit of a dodge, “finitude”). On the other hand, how we manhandle the topic discursively is another matter. For an inelegantly interleaved instance, despite the denotative continuity of their arguments, the connotative disjoint between Wittgenstein’s liminal hysterics and Dennett’s offhand bons mot could not be more evident:

[LW 1927:] The philosophical self is not the human being, not the human body, or the human soul, with which psychology deals, but rather the metaphysical subject, the limit of the world—not a part of it.

[DD 2008:] Each one of us is trapped within a point of view. I can’t ever get inside your head and you can’t ever get inside mine.

[LW:] There is no such thing as the subject that thinks or entertains ideas. The subject does not belong to the world: rather, it is a limit of the world.

[DD:] You’ve got to leave the first person out of your final theory. You won’t have a theory of consciousness if you still have the first person in there, because that was what it was your job to explain. [...] So the Cartesian materialist is the one who describes large parts of the machine, but it’s still inhabited.

[LW:] Where
in the world is a metaphysical subject to be found? You will say that this is exactly like the case of the eye and the visual field. But you do not really see the eye. And nothing in the visual field allows you to infer that it is seen by an eye.

[DD:] If you make yourself really small, you can externalize virtually everything. [...] So the imagery keeps shrinking back to a singularity; a point, a sort of intersection of two lines and that’s where I am.

[LW:] Here it can be seen that solipsism, when its implications are followed out strictly, coincides with pure realism. The self of solipsism shrinks to a point without extension, and there remains the reality co-ordinated with it.

[DD:] That’s the deadly error, to retreat into the punctuate self. You’ve got to make yourself big; really big.

[LW:] If we take eternity to mean not infinite temporal duration but timelessness, then eternal life belongs to those who live in the present. Our life has no end in just the way in which our visual field has no limits.

[DD:] The undeniable fact that we have these perspectives is not closely paralleled with anything else we know about anything else.

Now there is, without nit-picking it to bits, something “in the visual field [that] allows you to infer that it is seen by an eye”—namely, another eye—the de facto inter-subjectivity by which—yes, on one hand, as “trapped” subjects, “I can’t ever get inside your head and you can’t ever get inside mine”—but on the other hand, by which the fact that “our visual field has no limits” reciprocates into trans-subjectivity of the type we previously strove to explicate—while neither invoking nor revoking “eternity [as] timelessness”—from the reflexive topology of Wildgen’s centrifugal/centripetal schema, and from the ‘absolute relativity’ of Cusanus’ Learned Ignorance. So here we are, then.

Susan Blackmore:   I often feel that I’m falling again and again into some kind of dualism between inner and outer, or subjective and objective, or me in here and the world out there.

Patricia Churchland:   There is a real dualism here, but not one involving spooky stuff. One of the things the brain does is build a model, and within that model it marks the difference between what’s inner and what’s outer. In my brain’s distinction between inner and outer I always have an efference copy of a command to make a movement. So I always know the movement is mine, and I can’t tickle myself. But schizophrenics can. Something is wrong with their system for efference copy.

Paul Churchland:   They don’t know where their self leaves off and the independent world begins. (2008)

And there you have it—the return of the repressed realism vis-à-vis “the independent world”—a surmise which, while (nominally) dualistic and (surreptitiously) dogmatic, cannot be accused of succumbing to precritical naïvety—or cannot, at least, without some sophistical chops. Should we lob aloft such a third-order deixis as “they don’t know where their self leaves off and the independent world begins”—being in no wise apodeictic, might we venture to strike it towards a categorical bucket of assertoric or problematic proposition?

Theoretical egotism can never be demonstrably refuted, yet in philosophy it has never been used otherwise than as a skeptical sophism, i.e., a pretense. As a serious conviction, on the other hand, it could only be found in a madhouse, and as such it stands in need of a cure rather than a refutation.

—Arthur Schopenhauer

That being said, what we face here may be less a line of argumentation in need of counterpoint than a cluster of symptoms in need of diagnosis. The key questions are subtle, but we may best address them in terms of the collectivized (or if you prefer, ‘contractual’ or ‘customary’) brokerage of subjectivity under which one’s individual self (or personage) is provisionally demarcated from other selves (or persons)—subtracted from the mass, as it were, while preserving manifold interoperability—that is, not merely propping up ‘intersubjectivity’ but coordinating movement towards cross-modal cohesion of goal-directed actions (hunting, gathering, ritual sacrifice and so forth). To turn internal purgatories to external purgatives, compare Quine on coherent correspondence to Lacan on anticipated assertion:

The coherence theory [seems to rest] on the absurd idea that the infinite totality of possible statements admits of only one overall distribution of yesses and noes that is logically consistent. Moreover, the theory makes no visible demands on observation and experiment. [...] On the other hand the correspondence theory [seems] vague or vacuous. What on the part of true sentences is meant to correspond to what on the part of reality? [...] The significant contrast between the correspondence theory and the coherence theory, when we set the untenable details aside, is that correspondence looks to the relation of the true sentence to what it is about, such as the white snow, while coherence looks to the relations of the true sentences to other sentences. Some sentences, to begin with, we accept as true directly on the strength of observations; the essential mechanism here is a conditioning of strings of words to sensory stimulations.

—W. V. Quine, 1986

But temporal objectification is more difficult to conceptualize as the collectivity grows, seeming to pose an obstacle to a collective logic with which one could complete classical logic. I will nevertheless show what such a logic would have to furnish, faced with the inadequacy one senses in an assertion such as “I am a man,” couched in whatever form of classical logic and derived as the conclusion from whatever premises one likes (for example, “man is a rational animal,” etc.) This assertion assuredly appears closer to its true value when presented as the conclusion of the form here demonstrated of anticipating subjective assertion:

(1) A man knows what is not a man;

(2) Men recognize themselves among themselves as men;

(3) I declare myself to be a man for fear of being convinced by men that I am not a man.

This movement provides the logical form of all “human” assimilation, precisely insofar as it posits itself as assimilative of a barbarism, but it nonetheless reserves the essential determination of the

—Jacques Lacan, 1945

By juxtaposing the two thinkers, what we glean at a glance is a relatively concise formula for self-accounting (not to say ‘self-cause’) in which “the I” collectively verifies its (‘own’) individual subjectivities on the basis of correspondence to (‘Other’) individual objectivities—more particularly, we re-form and re-con-figure a graph-theoretic (or matrixial) correspondence which is warranted by anticipated certainty of inter-sentential coherence.

Moreover, we should be able to extract the determinating conditions (the net-net, as it were,) in reverse: inasmuch as “the essential mechanism here is a conditioning of strings of words to sensory stimulations”, assertoric proclamations of nominal self-substance, or continuity of form by way of accident or actancy (e.g., “I am a man”, “I am Ralph”, “I am the mower of lawns”) can only reserve “the essential determination of the ‘I’” so long as “we accept [the assertions] as true directly on the strength of observations”—ping, pong; repeat.

We have thus, in effect, retraced the wake of Descartes’ retraction (to simplify matters, in English) from the deductive fallacy of “I think therefore I am” to the abductive stale-mate of “I think. I am.” Should we attempt to explicate the parties implicated by this pairwise reduplication, we should not be the least surprised to find that while the post-Kantian philosopher holds the parallelism of the latter sacrosanct, our never-will-have-been-postmodern subject clings to the reification of the former as surely as the anxious toddler clings to a threadbare scrap of blanket—and with as little hope for substantive coverage.

jargon automat or juggernaught a mort

That philosophy must be ontology means first of all that it is not anthropology [... which] assumes, as such, the empirical discourse on man, in which the one who speaks and that of which one speaks are separated. Reflection is on one side and being on the other. Knowledge understood in this way is a movement which is not a movement of the thing. It remains outside the object. Knowledge is then a power of abstraction, and reflection is an external and formal reflection. Thus empiricism refers to a formalism, just as formalism refers to an empiricism.

—Gilles Deleuze (review of Jean Hyppolite’s Logique et Existence, 1954)

[E]mpiricism and formalism have no other function here besides that of being the terms of the couple they form. What constitutes bourgeois epistemology is neither empiricism, nor formalism, but rather the set of notions through which one designates first their difference, then their correlation.

—Alain Badiou (trans. Ray Brassier; The Concept of Model, 1969)

Quine’s naturalization of epistemology and subversion of the analytic/synthetic distinction reveals one way of overcoming this formal/empirical dichotomy without relinquishing empiricism: by grounding the formal modeling of the empirical in an empirical modeling of the formal. In other words, by proposing as ultimate horizon for naturalized epistemology the construction of a scientific model of science’s model-constructing capacity in general.

—Ray Brassier (Badiou’s Materialist Epistemology of Mathematics, 2005)

Through the course of editing The Model Mind, our ‘Good Cop’ will continue to aim for just such a construction, despite that our ‘Bad Cop’ is unwilling to recapitulate Quine’s cake-eating disavowal vis-à-vis the sordid boon of freedom. What to do? If nothing else, we may ask how such disavowals are manifest in practice. For example, when one (e.g., scientist, philosopher, psychologist) is faced with a demand for axiomatic justification of Law as such to undergird particular laws—or more generally (if less rigorously), when requested a compact rationale for ethical or moral customs or behaviors—the default cata-phatic (affirmative) response will doubtless harmonize in perpetuity to the tune of “Because my Black Box said so” (insofar as Law is Law be the One True Black Box Invariant). Conversely, we are unlikely to find as typical such apo-phatic (negative) responses as “there are no such grounds for justification” (for in fear, if none other, that Oprah et aliae will not invite you back for a redemptive second chat). Here pragmatism trumps rigor, does it not?

or, “what constitutes bourgeois epistemology”

It would seem, in brief, that rather than formally staking an empirical fiat (that is, an epistemic equivalent to the axiom of choice) that can be ontically undergirded (or ontologically overdetermined) by, say, (cataphatic) vitalism, or (apophatic) nihilism (or some Nietzschean short-circuit thereof)—or otherwise, by (anarchic) panpsychism, or (hierarchic) pantheism (or some Spinozistic short-circuit thereof), we are apt to find (1) generally speaking, the popular Anglo-American recourse (e.g., Dennett 2006), is to purport for refutation (1A), the “ontological proof”—in token, of the existence “of God” but in type, of the existence of anything whatsoever—as per the go-to straw-man, Anselm of Canterbury. Despite being cataphatic (in positing the existence of “a Being than which none greater” etc.), this argument is mistakenly (more to the point, irrelevantly) refuted as if it were apophatic.

Intentionally or not (so to speak), the apparent oversight of (1A) elides the properly apophatic argument of (1B), the denial of ostensive attributes—nominally, as would be predicated “of God”—but formally, as would be predicated of anything whatsoever—e.g., as per the no-go monstro Nicolas of Cusa. (While this would be a particularly hard-line ‘nominalism’, this term’s own varieties and vicissitudes are for all intents innumerable.) By contrast, compare (2) the perpetual ping-pong of (largely) Franco-German philosophers (e.g., from Descartes to Leibniz to Kant) who have kept the (apophatic-)cataphatic (non-)ball in (non-)play the better to levy (2B) preemptory subtractions from (2A) presumptive scientisms—but without relinquishing rationalism. Game, set, match, and

The first point is Badiou’s: Kant’s (and later Wittgenstein’s) finitism is at variance with the specifically modern discovery of the immanence of the infinite with Cusanus, the primacy of the infinite (over the finite) with Descartes, the calculability of infinite quantities with Leibniz and finally the plurality and non-totality of the infinite with Cantor (who, as Badiou points out, was in many ways a Thomistic philosopher and theologian). For this reason, it is not that a speculative use of mathematics by philosophy is arbitrary; it is rather that mathematics has itself made a controlled speculation about the infinite newly possible. (One can agree with Badiou about the primacy of the infinite while still insisting that Nicholas of Cusa’s more ‘negative’ understanding of this priority—the infinite is projected by us as in-finite, is preferable to the Scotist-Cartesian tendency to say that we can grasp infinity ‘clearly and distinctly’ as a ‘positive’ notion, even if we cannot fully comprehend it.)

—John Milbank, 2010

neo-neuro-neutro-platonism for nitwits

Let us ask, in as finite a foray as feasible, what follows from such surmise as that “mathematics has itself made a controlled speculation about the infinite newly possible.” In particular, while this would typically be labeled as “Platonism”—such a label presupposes (not only Plotinus et al., but) Plato to have granted ideal (virtual, transcendent, a priori ) mathematical structures a real existence in excess of their immanent instantiation (manifestation, concretion, actuality)—but this would be an arguable interpretation of Plato—and moreover, of Platonism, given its many and varied historical forms—or rather, its periodic re-formulations. To wit, for a two-minute bout of platonic endoxa-boxing, compare “Mad” Max Tegmark’s radical heterodoxy to Alain Badiou’s radical orthodoxy. ¡Ding!

I believe consciousness is the way information feels when being processed. Since matter can be arranged to process information in numerous ways of vastly varying complexity, this implies a rich variety of levels and types of consciousness.

—Max Tegmark, 2008

Thus does the manic metaphysicist of massively manifold multiverse manipulation characterize himself as a “radical Platonist” (on the model of Gödel, with props to Bruno). However, Tegmark’s autonomic label is backed by the cognitivist framework of Computationalism within which, although nominally opposed to Constructivism, such terms as “computation” and “processing” stand in for any and every event—i.e., every entropic erosion of energy in accord with the second law of thermodynamics—and so ring as hollow as “there are laws of nature” or “what will be will be.” Tegmark, like the (ahem) VAST number of physicists, mathematicians, and philosophers who presuppose a pre-extant transfinite combinatoire (of Babel, Mendel, or otherwise), is more surely a Pythagorean.

This criterion of the exteriority (or transcendence) of mathematical structures (or objects) results in a diagnosis of ‘Platonism’ for almost all works belonging to the ‘philosophy of science.’ But this diagnosis is undoubtably wrong. It is wrong because it presupposes that the ‘Platonist’ espouses a distinction between internal and external, knowing subject and known ‘object’; a distinction which is utterly foreign to the genuine Platonic framework. However firmly established this distinction may be in contemporary epistemology, however fundamental the theme of the objectivity of the object and the subjectivity of the subject may be for it, one cannot but entirely fail to grasp the thought-process at work in Plato on the basis of such presuppositions.

—Alain Badiou, 2005

To warrant our assertions as to whole objects and their constituent parts, we need not presuppose—unless individually predisposed or collectively obliged thereto—that their mathematical specifications enjoy an eternal transcendence over or against their measurable manifestations, only that the parts preceded the wholes—that is, until the vanishingly small parts of parts depart across the infinitesimal horizon of specificity—at which point, all of our pong paddles ping as hollow as “a thing is identical with itself” or “A = A.” Thus, for our money, the “Arche” in Archemind need not be taken as a deixis to an Ideal Archeo-Logos, only to an archeological index of ideas. If this strikes you as 40lbs of metaphysics in a 4lb bag, what can we say? Other than: evidently, you’re not on the metric system. ¡Ding!

Two men, two minutes. While the sacrosanct “second rule of fight club” secures the first rule as unspeakable, the two rules do not resolve to an identity by disquotation (rule 1: “you do not talk about fight club”; rule 2: “you do not talk about fight club”)—rather, contextual repetition secures their ineliminable difference. In consequence, you can lock them up in Quine’s paradox, “Yields falsehood when preceded by its quotation” yields falsehood when preceded by its quotation, or unchain them unto Derrida’s différance. Before we strike the bell for round 2, in place of an interstitial bikini-clad ‘ring card girl’ (lest the Derridean post-feminist presume we propound “phallogocentric” pugilism to secure patriarchal privilege), may we submit for your consideration the interstitial musing of a recording artist:

If you’re gonna be creative, you know, you’re ultimately offering yourself as a sacrifice—a sacrifice of channeling something bigger than yourself and existing here at the same time. You know—being measured upon your word when you’re channeling something higher than your state is a pretty serious job to take on. So, if they’re truly about—the word—poetry, singing, writing it drawing it painting it, however it is, then you know one has to realize that we’re here to record—ripples of divinity, you know—ripples of mathematics, that’s really what you’re dealing with.

—Natalie Stewart (Blackalicious, The Craft, 2005)

Stewart delivers her explicative surmise quite matter-of-factly—that is, while it may come across as ‘offhand’ it is certainly not naïve. In any event, it makes no difference whether we reframe her univocal supposition as a redoubled self-abjection (from “higher than yourself ... higher than your state” to “ripples of divinity ... ripples of mathematics”) or a multiplex pronominal hypostatization (“you’re ... they’re ... one ... we’re”) or a Badiouan “truth procedure”—for she evidently speaks from the same (Pythagorean? Platonist? Porphyrian?) position of combinatorial commutation as that from which so many write, but minus the sophistical showboating. “Cause there’s nothing as sad,” croons Alan Sparhawk, preeminent post-punk-mormon-minimalist, “as a man on his back counting stars.” ¡Ding!

Even so, there is a link between idealism and the Platonic mystical traditions that requires clarification. [...] First, there is the kind of theory that simply defends the claim that there is a second, deeper source of insight [...] in the divine dimension, where we have direct contact with God; in morality, where we are in direct contact with the spirit of the community; or even in epistemology, there the spirit of the world reveals itself to us (the Stoic heritage). This is the kind of mysticism Kant embraced briefly in 1768. Second, there is a theory that tries to show that [...] the foundations of knowledge are not accessible to ordinary knowledge. So a special insight is required, and this is said to be demonstrable [...] entailing a continuity between philosophical argument and ensuing mystical practice, which pursues the direction philosophical arguments intimate.

—Dieter Henrich, 1973

towards a definition of “by the fact, if fact it be, that”

It is of the utmost importance to observe—in the experience of the unconscious Other where Freud is our guide—that the question does not find its outlines in protomorphic proliferations of the image, in vegetative intumescences, or in animastic halos radiating from the palpitations of life. This is the whole difference between Freud’s orientation and that of Jung’s school, which latches onto such forms: Wandlungen der libido. These forms may be brought to the fore in a mantic, for they can be produced using the proper techniques (promoting imaginary creations such as reveries, drawings, etc.) in a suitable site. [...] If Freud rejected this mantic, it was at the point at which it neglects the guiding function of a signifying articulation, which operates on the basis of its internal law and of material subjected to the poverty that is essential to it. [...] For if the Other is removed from its place, man can no longer even sustain himself in the position of Narcissus.

—Jacques Lacan, 1955

“Transformations of the libido” indeed. While we may have front-loaded the above illustrations as a gag, they illustrate (if perhaps obliquely) Lacan’s argument on “the guiding function of a signifying articulation” at the level of repetition automatism (Freud: Wiederholungszwang, ‘compulsion-to-repeat’—or more literally, ‘hauling-back-over-constraint’). More particularly, they index the extent to which schematic (or, ‘schematistic’ or, ‘schematismic’ or, ‘schematological’) thinking recapitulates itself automatically, irrespective of the matter under consideration—be it psychopathology, epistemology, informatics, you name it.

While we ‘self-identify’ neither as Freudians, nor as Jungians, nor as Lacanians, we shan’t hesitate to utilize each where appropriate. Having learned our own upside-down card tricks by schematically reshuffling Bruno’s systematically blackened decks, the rest is rifled trifles. Put to a grotesque—if you want to Post Structuralist sausage, simply inculcate Freud’s libidinal Cerberus through Saussure’s cerebral chiasmus, and out c-c-c-concatenates Lalacan’s lalangue and D-d-d-derrida’s grammatographical arche-wready-to-broil bratwurst: one Brunian blagueur brags as black as the next—or, who needs Hegel when you’ve got Joyce? (for “got” read “contain” where “A ≠ A”)

or, how high must a Lacanian learn to count?

On one hand, Lacan most likely did not intend to situate those three colorful compounds (“protomorphic proliferations ... vegetative intumescences ... animastic halos”) quite so, amid the three-ring circus of (the Symbolic, the Real, and the Imaginary) Orders that co-constitute his contortional Symptom (or his Sinthome—1955 being avant la lettre if for no other reason). On the other hand, in reading mid-to-late Lacan, as often as not you can mark out the metrics of his monologues as so many iterations of the “four-corners game”—whether or not he advertises (or even intends) them as such.

The same is true, e.g., of Cusanus, Bruno, Kant, Hegel, and Peirce—as all were surely, to borrow Eco’s phrase, “harboring systematic ambitions”—and moreover, deployed their systems by way of the same tightly constrained set of topological formulae for reciprocating difference and repetition. To take the mystery out of it (in keeping with our present task), we can explicate these formulae in brief (for we further disentangle this rat’s nest in The Model Mind) by supplementing our prior knot/rings/sieve example. To spare the reader excess Franco-Anglo-Teutonico contortions, we will take Quine as our narrator:

Semiotic or the theory of signs, according to Charles Sanders Peirce, was concerned with a three-way relation. [...] He trichotomized the signs into qualisigns, sinsigns, and legisigns according to what sorts of things they were in their own right (no questions, please), and into [three more] according to how they were represented to their interpretant, and into [three more] according to how they signified their objects. Symbols, in particular, he classified into terms, propositions, and arguments; and arguments in turn he classified into deductions, inductions, and abductions.

—W. V. Quine, 1986

[Quine cont’d:] Charles Morris, an admirer of Peirce [...] divided the domain of semiotic into syntax, semantics, and pragmatics. This trichotomy, taken up by Carnap, has been faithfully cited and adhered to for forty years, despite the fact, as I see it, that the separation between semantics and pragmatics is a pernicious error. I suspect that the durability of this trichotomy is due to its trinity.

And that is some serious Transatlantic ping-pong. But—a pernicious error? Well, that’s why Carnap is Carnap, Quine is Quine, and we are neither. Working backwards, compare (structurally—again, setting aside import,) Lacan’s triad of Imaginary, Real, Symbolic—to Peirce’s triad of Iconic, Indexical, Symbolic—to Bruno’s triad of Umbral, Vestigial, Ideal. Of course, just as in comparing the knot, the rings, and the sieve, these three nominally triadic schemas do not present exact one-to-one correspondence. Nevertheless, inasmuch as any triad betrays a remainder, you can retrofit any threefold you like to a fourfold in several ways, not all of which necessitate “the topology of a four-corners game” per se:

Žižek, for example, is fond of subjecting Lacan’s S,R,I to an anarchic, or ‘flat’ isomorphism, by which each Order contains within it the other two Orders as well as a partialized copy of itself—thence, the “Symbolic Real,” the “Imaginary Real,” and the “Real Real,” and so on (see Žižek’s For They Know not What They Do, 1992/2001, or Ben Wright’s lecture doc The Reality of the Virtual, 2004). We can apprehend at a glance how this operation yields NINE categories by arranging them as a two-stage Sieve (below at left).

Peirce, by contrast, gives us a unilateral hierarchy by monotonic inheritance, by which his overarching generic modalities of Firstness, Secondness, Thirdness are applied at three levels, of which his I,X,S sign types occupy the middle stratum. As he combinatorially configured them in a Pythagorean Tetractys (below at right), this operation yields TEN categories, as 1 + 2 + 3 + 4 = 10, with no need for magic beans, Jack.

A predilection for threes has invested song and story. We have the Three Fates, the Three Graces, the Three Magi, the Three Musketeers, the Three Bears, the Three Little Maids from School. [what of the Three Little Pigs? a telling oversight, given Quine’s brickwork fortifications, no? —ed.] Immanuel Kant’s metaphysical categories came in threes. Those of Quantity were Unity, Plurality, and Totality. Those of Quality were Reality, Negation, and Limitation. I could go on. He even boggled at a dichotomy of judgments into affirmative and negative, if only for want of its trinity, or threeness. He settled for affirmative, negative, and infinite. And where would Hegel have been without thesis, antithesis, and synthesis?

—W. V. Quine, 1986

How far must a Hegelian dialectician learn to count? Most of the interpreters of Hegel, not to mention his critics, try to convince us in unison that the right answer reads: to three [then] vie with each other in who will call our attention to the ‘fourth side’, the non-dialecticizable excess supposedly eluding the dialectical grasp, [yet] is the inherent condition of possibility of the dialectical movement.

—Slavoj Žižek, 1992

Once again, with Quine, you get the pithy reduction—with Žižek, you get the pathos of irreducibility. Meanwhile (as it were), Bruno unfolded his final semiotic-categorial schematization (On the Composition of Signs, Images, and Ideas, 1592) by the same logic as Peirce: namely, under his overarching ‘U,V,I’ triad, he enumerates and elucidates nine additional sign types in such a fashion that they can be configured and collected either to a flat isomorphism or, by way of one-to-one correspondence with Peirce’s subtypes, to a monotonic Tetractys (see The Model Mind §4; forthcoming).

At any rate, all the foregoing (including Kant and Hegel) authored schemas that can be geometrically figured by way of variations on the Sierpinski Sieve. For example—in the case of Lacan-according-to-Žižek, this Sieve schematization can be conceived and visualized either as subtractive—by which each ‘missing piece’ leaves three kinds of vestigial remainder, or as additive—by which (via strictly Hegelian negation-of-negation) each missing piece (or “non-dialecticizable excess”) is itself the composite (Symptom) of three kinds (Orders):

While the former (above, left) seems to hew closer to the strict Sierpinski subtraction, the latter (above, right) obeys the topological constraint of the rings—viz., that no two (Orders, etc.) constitute any capacity where in want of a third. We thus net a specific contrast: in the (Peircean) Tetractys, a segmented continuum grades to a central composite (the “1,2,3” node); in the (Žižekian) Sieve, a self-similar discontinuity at once self-composes and self-excises. Again, what may sound overcomplicated by way of text can be apprehended at a glance when accompanied by geometric visualizations. Ontography of this sort is, as we say, easier done than said.

Another durable trichotomy, somewhat outside of semiotics, was drawn in 1933 by Max Black in the philosophy of mathematics: there are logicism, formalism, and intuitionism. To this day any account of the philosophy of mathematics from south of our border, and most from north or northeast of it, can be counted on to begin with this trichotomy. I venture to say that, among other strengths, 3 is a prime factor.

—W. V. Quine, 1986

We venture to say that, should you forgive the nauseating color-code of our graphics, they should demonstrate how, despite appearing specifically incommensurable, the underlying structures share genetic continuity. For a final recapitulation: any of the foregoing can be topologically and topographically reconfigured—as was certainly the case with Bruno (and with Pico, and lest we play at historian, draw your own furthermores)—by way of the Circulus Universorum as Cusanus explicated it (below, left), as an addendum to his Figura Paridigmatica, by way of commentary on the Pythagorean Tetractys (the perennial paradigm for scaling one for two for three for fourfold schemas in general). In light of his singular diagram, we may fruitfully compare Cusanus 1440, Hegel 1807, and Bruno 1592:

But to the end that the quaternary distinction be perfected—the distinction which, alone, is the fulfillment of our inquiries—we are forced to surmise that the progressions [are] fourfold and disjunctive. In this way, then, we note, lastly, that in each world there are three trine distinctions; and so, in the universe we will arrive at the cube of three, as the diagram will show you. Every number is included in the number ten and every progression is completed in the number four.

—Nicolas Cusanus, 1440

In this turning point of the method, the course of cognition at the same time returns into itself. As self-sublating contradiction this negativity is the restoration of the first immediacy, of simple universality; for the other of the other, the negative of the negative, is immediately the positive, the identical, the universal. [...] now as the first negative is already the second term, the term reckoned as third can also be reckoned as fourth, and instead of a triplicity, the abstract form may be taken as a quadrupliticy; in this way, the negative or the difference is counted as a duality.

—G. F. W. Hegel, 1807

But by immortal God, what can be easier for people than counting? First, since there is one, there are two, three, four; second, because one is not two, two is not three, three is not four; third, because one and two are three, one and three are four. To do this is to do all; to say this is to say all; to imagine, signify and shape this makes all things objects to apprehend, to understand once apprehended, and to remember once understood.

—Giordano Bruno, 1592

It must be said, if Cusanus errs on the side of exaltation, Hegel makes the entire affair needlessly convoluted. By contrast, should you take the Bruno quote and simply exchange “immortal God” for “empty-set and power-set” you could found mathematics on axiomatic set theory (but for the “But by”). In short order, he enumerates (1) sequence, or repetition; (2) distinction, or difference; (3) series, or recursion; (4) action; (5) speech; (6) composition by (6a) imagination, (6b) signification, (6c) figuration, towards (7) objectivation, (8) apprehension, (9) understanding; thence to (10) reminiscence. Presto.

Last but scarcely least, we have the Holy Trinity. Father and Son make good substantive sense, at least by analogy (cf. Thomas Aquinas), but there is something tenuous about the Holy Ghost, suggestive again of trinity for trinity’s sake. [thus, unlike Žižek’s Wittgenstein, one cannot even imagine speaking of “Quine as a Hegelian” —ed.] [...] The stability of three comes down to brute and homely fact when we look upon the three-legged stool and contrast its firmness with the wobbly four legs or the toppling two. The underlying geometry is elementary. Three points always lie in a plane; four need not. Three points lie in only one plane; two lie in many. Again there is the rigidity of the triangle. The geometry of this is that two triangles with matching sides are bound to be congruent, while other polygons with matching sides are not.

—W. V. Quine, 1986

And what’s all that supposed to mean? What do you want it to mean? We offer this particular short-shrift short-cut as an indication of the degree (or depth) to which our cognitive (conceptual) categories will automate (or if you must, “self-organize”) their own schematization according to vestigial patterns. But “vestigial” of what? Take your pick (or “posit your presupposition”). Does the Sierpinski Sieve ‘plot itself’—and if not, who or what plots it? Well, there’s three non-questions; so at least we’ve satisfied one rule—if only Via Negativa—but if your own Comedic trilogy must wax Divine, you can always take it up with Dante.

“What does the Joker want?”

Nick Cave:   We’ve actually done a version of ‘Heathen Child’ with a four-minute guitar solo [...] I've always been a big Robert Fripp fan, but I didn't know him at all. He’s a really weird dude. I mean really weird.

Pitchfork:   How so?

Nick Cave:   He speaks about himself in the third person, like: “The guitarist feels that his performance on this take was the preferred one.” He’s like the Buddha via 10 Wellington Place.

pitchfork.com, 2010

What, then, does the Joker, who wants to disclose the truth beneath the Mask, convinced that this disclosure will destroy the social order, represent? He is not a man without a mask, but, on the contrary, a man who is his mask—there is nothing, no ‘ordinary guy,’ beneath it.* [fn*] Let us recall a similar story about Lacan: those who got to know him personally, to observe how he behaved in private, when he was not maintaining his public image, were surprised to learn that he conducted himself in exactly the same way as in public, with all his ridiculously affected mannerisms.

—Slavoj Žižek, 2010

Of which neither should surprise us one bit. However, should we wish to wolf down a table-scrap, we do find it odd that Žižek missed the mark in (Heath Ledger’s iteration of) the Joker’s redoubled faux-confession, viz., his duplex wound being $elf-inflicted / by his Father. That is to say, in contrast to Žižek’s surmise (“he tells different people different stories about his scars, mocking the idea that some deep-rooted trauma drives him”), yet still within the mode of Žižek’s pop-cultural cannabalism (Verso blurbo: “the Elvis of cultural theory”? or recto, false choice: “fat El-Žek” or “skinny El-Žek”? etc.), the late Ledger’s later Joker supplies the more Christological supplication than oft alleged of one Neo; wan Eno’s oblique strategy reversed, taking “life imitates art / art imitates life” as an allegory for itself, we have little difficulty imagining Žižek (presup)positing that (“of course”) Heath Ledger himself had to die to retroactively seal his Methodically Messianic mutatis mutandis self-allegorization—for otherwise, his Jolly Roger would have heralded mere theatre, and not the evident memetic (and/or mimetic) fallout from his traumatic suspension (in person and persona).

next: 3.2 “The spirit is a bone.” »

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