The Multiplication of Innocence

January 4, 2013

“Why do we need a “negative” word to say what is primary? (Agent Swarm)

Hobbes, Turing and the Child

A certain humanistic fatigue has of late taken measure in a nonhuman perspectival turn; an indication of what philosophy is going through which the turn to a posthuman framework has been providing a rather disputable voice. It is simply a prolepsis, I should say, which only philosophy can feel about its own doing. Laruelle is therefore right when he castigates philosophy’s auto-performativity, “its deeply ingrained fetishism (Non-Philosophy Project, 88), among others.
Philosophy confronts a vacuum after saturating, let us borrow from the lessons of arithmetic, the function and computability of its truths, which rightly so has to entertain the unpredictable. Obviously this encounter does not strictly inform a purely philosophical search for a new voice; mathematics also has its history of looking for a new voice, a new function, etc. When a perfectly consistent system, one whose propositions are said to be true, is confronted with its own incapability to prove its negations, the challenge of Entscheidungsproblem, the decision problem, is set in motion.
Hilbert was among the first few to set this problem in motion by arguing in favor of the formalism of completeness, later challenged by Gödel. Gödel became the foster child not only of mathematicians but also philosophers who had much to benefit from his incompleteness theorem (we shall see why). Badiou is the most contemporary example of this philosophical embrace of incompleteness though he would radicalize the decision problem further into the Event.We all know that Badiou relies on set theory, the most fundamental system of mathematics. We also know that in light of Gödel’s incompleteness theorem mathematics met its serious challenge–there is the ‘unsolvable” contrary to Hilbert’s claim. The solution to the decision problem lies outside mathematics. But Gödel had no alternative in mind, that is, outside mathematics, except to embrace set theory’s infinity of infinities, and its many related axioms (of continuum, etc.), which extends the life of the Entscheidungsproblem to such an extent that the undecidable strictly becomes a mathematical business. In popular terms it only confirmed the perception that mathematics was not giving up its dream of mastery. It should not however cease to be mathematics. Doing mathematics is one thing; taking mathematics as something of an incorruptible property of existence is another. Overall, the controversy that Entscheidungsproblem sparked simply raised the curtain that mathematics is not an invincible discipline. This is rather an odd case of an extra-mathematical Event catching mathematics unawares.
Alan Turing was able to show that the problem of Entscheidungsproblem can be solved by extra-mathematical intervention but still using the very tools of mathematics, this time on a parallel relation (similar to the dualysis of nonphilosophy when it treats philosophy as an excess material or something to that effect).
After an attempt at mechanology (the famous experiment after his namesake), Turing wrote of the incompleteness theorem of Gödel: “The argument from Gödel’s and other theorems rests essentially on the condition that the machine must not make mistakes” (“Intelligent Machinery,” in Donald Michie, Machine Intelligence, vol 5 [1970], 3 ). He adds: “if a machine is expected to be infallible, it cannot also be intelligent” (Turing ACE Report). Hence, the incompleteness theorem and other theorems are psychologically at fault. They find their measure in a familiar humanistic orientation of thought that is premised on superiority, mastery and greatness.But mathematics is not the problem, rather its orientation, certainly the affective adult orientation of mathematicians with metaphysical and religious prejudices. The same problem in orientation applies to philosophy.
The above example of Turing may suggest that the extra-mathematical can provide philosophy the inspiration to get around its decisional problems (in Laruellean terms), already reeling from Wittgenstein’s scathing attack which is not without its merits. Philosophy was becoming increasingly metaphysical and humanistic, and stubbornly classical in the Greco-Judaic sense. The poststructuralist and postmodern turns which arrived later as critiques of metaphysics simply recast humanism in an operational play of difference that relies on identity, its concealed metaphysical substratum.
But let me digress for a while.
Hobbes and Leibniz were at odds with one another over many issues in philosophy, but the single most controversial issue that divided their positions is the question whether God is a substance or a mind. Hobbes took the question to be asking whether the universe was intelligently designed or simply a result of random organization of things which eventually produced the Leviathan (the Substance, the artificial soul). Leibniz, for his part, took the critique of design to be simply a question whether God (who has a mind, let us not forget, according to Leibniz) allows random organization in and through the things themselves. Now let us go back to Turing.
The mathematician seemed to have favored Hobbes not only for the mechanical bias of Turing’s mathematics but also for Hobbes’ insinuation that the universe was not formed by intelligence, that is, a computable One. Leibniz took a different direction. He says: “there must be in the simple substance a plurality of conditions and relations, even though it has no parts” (Monadology). What is Leibniz saying here? He is simply stating that the incompleteness of Hobbesian cosmological framework allows for the organization of the cosmos by an act of Supreme Mind, capable of making computable absent parts or functions ready for creation (computable: ready for the sufficiency of the entire cosmos). By the simple axiom of the plurality of conditions for creation parts are forced to emerge (which are already decided to be computable in the first place) that cannot stand as parts without their relation. Hence, they have nothing else to do than to become parts! Once again, the requirement is a certain idea of infallibility. But it is more than that.
Infallibility is the tip of the problem because it is premised on the assumption of incompleteness that itself is premised on the belief that no extra-mathematical intervention is possible to show mathematics how to prove its negations. The crux of Entscheidungsproblem is the celebration of the mathematical supremacy, the pure humanist ambition of Man. To digress further, it is in this sense that Da Vinci, with his mechanics that had no ‘ends’ , which did not demand negations, is anti-humanist at heart.
So Hobbes’ Leviathan is possible only if mathematical supremacy preconditions the artificial soul to manifest itself. It is a direct insult to Hobbes who was no mathematician. But Hobbes found an ally in Turing, the gnostic at heart, the heretic mathematician, who opposed the Leibnizian design and its modern incarnations. Defending a certain idea of quasi-emergence, he proposed the ‘unorganized machines’ (Da Vinci’s mechanics without ‘ends’) which, as Turing put it, are modeled “after the nervous system” (“Intelligent Machinery”). These machines, for their wider philosophical implications, allow us to look beyond ourselves as humans. I mean as humans with individual factory warranties. We are in good condition. The infallibility of our Maker is ours by extension. Yet, there is an idea of the human that resists this ‘goodness ‘. Neither evil, nor monster.

On hindsight  although Turing proved that replication is the logic of any machine the fact that it cannot prove its negation (can life trace its origin in replication or reproduction?) without outside orientation (genes need organisms to replicate) belies the naive belief that he is in favor of strong Artificial Intelligence (AI), or the consistency of self-replication within a system foreclosed to the outside. The machine must make mistakes or it is no machine, meaning, it needs fallible (reproducible) instructions just as genes need organisms which can reproduce in order to replicate themselves. But that is not exactly our point here, though we can relish our heretic achievement so far, which may be enough to belie the flat ontologist’s claim of flatness, so to speak.
Might not our point be, replication and reproduction have to be logically separable for life to persist? Such is the heretic claim of Freeman Dyson against the prevailing view that replication writes or encodes the origin of life. By his extra-mathematical intervention, such hereticism may also be ascribed to Turing.  The point is organisms, programs, and machines must exist all at once but differentially, yet no one instance is sufficient to overwhelm the other (Dyson uses the description ‘error-tolerance’) leading to homeostasis, for replication and reproduction to be possible, for life to continue. Reproduction (organisms) and replication (machines and programs as genes) are then free to communicate and exchange, even interbreed and cross-fertilize. But this gets trickier. Dyson writes in Origins of Life:
“Error tolerance is the hallmark of natural ecological communities, of free market economies, and of open societies. I believe it must have been the primary quality of life from the very beginning. But replication and error tolerance are naturally antagonistic principles” (87).
Hence, error-tolerance must be a recent phenomenon. The source of error is simplification, or extra-mathematically put, computable enough to desire a proof of its negation, its desire to become itself uncomputable. And it certainly carries a tyrannical agenda as the genes for 3 and more eons would dictate individual organisms. “Every species is a prisoner of its genes and is compelled to develop and to behave in such a way as to maximize their (organisms) chances for survival” (Ibid., 88).
Proximally, the ‘event’ that would prove the negation of mathematical truths lies outside mathematics. Evolutionarily speaking, it is something else. Towards the end of his book, Dyson observes:
“Life by its very nature is resistant to simplification, whether on the level of single cells or ecological systems or human societies. Life could tolerate a precisely self-replicating molecular apparatus only by incorporating it into a translation system that allowed the complexity of the molecular web to be expressed in the form of software. After the transfer of complication from hardware to software, life continued to be a complicated interlocking web in which the replicators were only one component…The tyranny of the replicators was always mitigated by the more ancient cooperative structure of homeostasis that was inherent in every organism. The rule of the genes was like the government of the old Hapsburg empire: Despotismus gemildert durch Schlamperei, or “despotism tempered by sloppiness” (Ibid., 89).
Without mincing words, this government might prove to be a fallible incarnation of Hobbes’ Leviathan, the artificial soul that is most tolerant of messiness but not of simplification.
Today, simplification has taken a new form in the guise of asserting that replication is All. There is a certain ingenuity to it, a provability, a computability. Replicators do replicate almost in a linear fashion as replication is about producing exact copies of a copy. If ever replication finds disturbance such as threatens its linearity it is almost certainly because  uncomputability overwhelms its simplification.  The only advantage of replication over the fallibility of organism is that the latter is almost certainly not going to outlast replication; as Freeman’s son George put it,  it is “not so much a consequence of the origins of life as a consequence of the origins of death” (Darwin Among the Machines, 31). Nick Land is powerful in this aspect: “Because we can die.”  Also almost certainly our power to die is our advantage over replication. Reality is never flat. There is always the uncomputable. Because we can die replication’s ambition of eternity is at risk. It needs to negotiate. We have the power to offer death if replication demands permanence. Its ambition is always threatening life to follow its agenda, especially in the modern technological age. (This is our minor case against Deleuze: What kind of life is he talking about when he talks of pure immanence?)  But we have a power that is more ancient than any ancient, the “deep formerity” Levinas would add (Otherwise Than Being, 19), as shown by our success so far over the tyranny of replication. Can we not describe this success as the hereticism of death? E. Cioran would have thrown at doubters of this power these terse lines: “I strive to conceive the cosmos…without myself. Fortunately, death is here to remedy my imagination’s inadequacy” (Anathemas and Admirations, 118).
Turing is so careful to preserve the uncomputable if only for mathematics, his discipline, to save its integrity. And the uncomputable is intuition which ingenuity must always prove as valid by concealing it under the blanket of formal rules. Turing notes: “The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings. It is intended that when these are really well arranged the validity of the intuitive steps which are required cannot be seriously doubted” (The Essential Turing, 135).
Intelligence is a product of developmental process and it is still evolving. It is not a product of a single infallible design but of randomness, modification, and collectivity (Simondon senses it with his ‘transindividuation’ but so does Bachelard with his idea of the poetic image as transubjective, which, as I put it elsewhere, has no obligation to stay in the self). Dyson summarizes Turing’s contribution in a rather journalistic way: “All intelligence is collective. The truth that escaped Leibniz, but captured Turing, is that this intelligence—whether that of a billion neurons, a billion microprocessors, or a billion molecules forming a single cell—arises not from the unfolding of a predetermined master plan, but by the accumulation of random bits of wisdom through the power of small mistakes” (Darwin Among the Machines,72 ).
Well said.
As with Nietzsche, we are one of those machines which can explode! (Selected Letters of Friedrich Nietzsche).
Turing’s extra-mathematical intimations are helpful for us here in our attempt to situate the posthuman turn. We would like to measure this turn against the gnostic precondition of refusal. We mean refusal as the non-precedence of the human (with ontological warranty) in favor of the human whose impossible attitude of tolerance (we will clarify this later) allows any ‘turn’ with respect to the idea of the human autonomy (the humanist mathematical ambition) to rather expose itself as a ‘refuse’. I am grateful to Terence’s notation: the noun conceals an act, a verb, refuse; the idea is captured in ‘refuse-All’, or simply refusal. Yet, refusal is either assumed by the subject or refused again. Leibniz is the epitome of the first; the heretic the second sense. The heretic rejects the refusal of the mathematician who refuses the gnosis of mechanics, of randomness and collectivity, so to speak. The heretic exposes the refuse of the humanist, ironically, by being tolerant of doctrinal illusions. To refuse is not to Negate. As with Laruelle, “The One is tolerant of doctrines.”
Rightly so, as a refuse the ‘turn’ of the human is by default of its cosmic origin in large combinatorial processes a needless repetition. Yet, the human turn in light of a certain disabused mind regarding, again, a certain notion of uncomputability takes a form of insistence. Insistence of autonomy, computability, in mathematical terms; evolutionary wise, coveting replication. The human autonomy: Always ‘of’ the humanist who is also in all likelihood a religious, metaphysical mathematician of incompleteness, a philosopher who is more of a poet than a child (we will see why). The humanist: Always ‘of’ his (the humanist) fetishised self-image.
Meanwhile, the precedence of large combinatorial processes, the self-creation of the cosmos, at first glance may seem to support the Leibnizian design. But the cosmos is; Leibniz is not.
The cosmos is un-Leibnizian. It is without design for a design anticipates appreciation, reflection, and calculation. Rightly so, it is appreciated and received by the humanist, like Leibniz. Not by a disbelieving mathematician like Turing, but only half-heretic. Not like the child who appreciates, reflects and calculates without ‘ends’. Only a child can shatter the sufficiency of the cosmos, the complete heretic!
Who needs a Meillasoux? We need more Da Vincis and Turings.
Yet the child also allows the cosmos to display its comedy, its magic to which s/he offers affection in return, an emotion, a smile, a curiosity, laughter, wink, a wow, even so, indifference, all on behalf of his/her innocence. (Michel Henry ‘affectivity’ is also an important turn for the heretic with the proviso that it is a child’s world that he had in mind).
Turing observes of the child, the unorganized machine:
“Instead of trying to produce a programme to simulate the adult mind, why not rather try to produce one which simulates the child’s? (“Computing Machinery and Intelligence,” Mind 59 [1940], 456)
He adds on another occasion: “Bit by bit one would be able to allow the machine to make more and more ‘choices’ or decisions. One would eventually find it possible to program it so as to make its behavior the result of a comparatively small number of general principles. When these became sufficiently general, interference would no longer be necessary, and the machine would have ‘grown up’” (“Intelligent Machinery,” 9)
Isn’t the world organized by grown-ups? Don’t we need innocence to shatter the sufficiency of this world?
Not by the multiplication of objects, the world’s refuse—the mathematician’s and the humanist’s refuse, his refuse-All of gnosis, the mechanical, the extra-mathematical, the uncomputable that awaits recognition, concealed under the blanket of knowledge, beneath which it is patiently waiting to be known but without the passion and interest a philosopher normally invests in fathoming nothing but an image of himself, which is also the humanistic way of testing his mastery by challenging the non-mathematical to prove its negations.
Or, if you may, the refuse is the very proliferation of the non-parts of Leibnizian universe which have needlessly preoccupied the most vocal critics of ontology today. Ah! the hypocritical refusal of the humanist that it his waste after all that sustains his refuse-All. This humanist has a pledge, the pledge of the humanistic anti-humanist—to rid the world of waste. But not of his right to the refuse. It can be salvaged. Bataille has always sensed the whiff of Konigsberg. This absurd creature is dear to Sisyphus, his model of taking all the pains of humanism—Come see how I suffer for your sins, but remember me, remember me! 
Cioran is bewildered: “‘The end of humanity will come when everyone is like me,’ I declared one day in a fit I have no right to identify” (Anathemas and Admirations, 20).
This humanist also happens to condemn hereticism, dismisses its polarizing figure—the figure of Heresy.
Might his goal not also be to rid the world of plurality of conditions and relations?
Oh, you Leibniz! Why did you return? To declare that there are parts after all, that the parts were there but you refused the Leviathan? How the after-life had changed you!
We all know the Inquisitor’s next step. The banishment of the born-again Heretic.
To shatter the sufficiency of the world, we do not need the multiplication of the humanist refuse, rather of children, these complete heretics, the multiplication of their innocence which we can only hope will pave the way for real intelligence, the Leviathan.
The Leviathan: it is indifferent. It can change at the behest of mistakes. The artificial soul. Real sovereignty.
The refusal of infallibility, one which relies only on non-sufficiency, of children at play.
{Excerpts from an unpublished essay of mine with the title Hobbes, Turing and the Child. The essay is still in its inchoate form by academic standards. I will be posting the full version of the essay here and in my academia account the sooner I can imagine I can have the right to it]
I’m grateful to Terence Blake ( and to Dave of for their previous comments on my post “Quiet Power of Actuality” of which this post is an elaboration, needless to say, an elaboration of my idea of gnosis that I still have no right, quoting Cioran, to identify as my knowledge or idea of gnosis. This reply is also inspired by Steven Hickman’s comments of on my previous posts on ‘gnosis’.


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5 Responses to “The Multiplication of Innocence”

  1. noir-realism Says:

    You made me go back to Heraclitus: Time is a child playing draughts; the kingship is the child’s. I also thought of refuse as it evolved into refuse = material waste … that which must be recycled out of other systems, the waste, and dregs of its detritus broken down and reincorporated. I was almost thinking of those powerful Oil Plants where I grew up on the South that break oil down into thousands of useful components through a myriad of pressure, heat, cold, etc. for use in plastics, pharmaceuticals, et. al.

    Maybe this is what we need is a combination and recombination of the dna/rna of philosophy: a new framework within which to reintegrate the refuse of the ancient systems. We’re in the midst of a great shift, a paradigm change, but no one has come up with the new framework that will recycle out of the old what is worth salvaging.

    I see this in Laruelle’s need to move toward neologistic terminology… what we need is a new language in which to describe these new thoughts. The old language as James Joyce said needs to be etymshmashed:

    Mr. Earwicker’s worldly misfortunes are climaxed by a lethal explosion: “the abnihilisation of the etym.”

    I like it you brought Turing and Cioran in…. Dyson as well! But where is Feyerabend? haha…

    Yes, I’d love to see the final essay… this one is assaying a little too broad! Yet, the drift is there… great post!

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