Moving down the same trajectory as in my previous post (see here), I’d like to once again articulate why our use of quantum set theory is important in conjunction with Laruelle, Deleuze, and Badiou.
Since at this plateau we are becoming-mathematicians, let us read a quick introductory summary of the practicality of set theory follows (see here):
The purpose of set theory is not practical application in the same way that, for example, Fourier analysis has practical applications. To most mathematicians (i.e. those who are not themselves set theorists), the value of set theory is not in any particular theorem but in the language it gives us. Nowadays even computer scientists describe their basic concept – Turing machines – in the language of set theory. This is useful because when you specify an object set-theoretically there is no question what you are talking about and you can unambiguously answer any questions you might have about it. Without precise definitions it is very difficult to do any serious mathematics.
Furthermore, to apply the “quantumness” aspect to what we have revealed, we find that Ernesto Rodriguez succinctly makes note of the practicality of quantum set theory in his 1984 dissertation abstract:
The work of von Neumann tells us that the logic of Quantum Mechanics is not Boolean. This suggests the formulation of a quantum theory of sets based on quantum logic much as modern set theory is based on Boolean logic. In the first part of this dissertation such a Quantum Set Theory is developed. In the second part, Quantum Set Theory is proposed as a universal language for physics. A Quantum Topology and the beginnings of a Quantum Geometry are developed in this language. Finally, a toy model is studied. It gives indications of possible lines for progress in this program. (see here)
With this understanding of quantum set theory, here we find the answer to what we can do with it:
Set theory provides foundations of mathematics in the sense that all the mathematical notions like numbers, functions, relations, structures are defined in the axiomatic set theory called ZFC. Quantum set theory naturally extends ZFC to quantum logic. Hence, we can expect that quantum set theory provides mathematics based on quantum logic. In this talk, I will show a useful application of quantum set theory to quantum mechanics based on the fact that the real numbers constructed in quantum set theory exactly corresponds to the quantum observables. [...] It is shown that all the observational propositions on a quantum system corresponds to some propositions in quantum set theory and the equality relation naturally provides the proposition that two observables have the same value. It has been broadly accepted that we cannot speak of the values of quantum observables without assuming a hidden variable theory. However, quantum set theory enables us to do so without assuming hidden variables but alternatively under the consist use of quantum logic, which is more or less considered as logic of the superposition principle. (see here)
That is, as Terence Blake rightly notes in his paper IS ONTOLOGY MAKING US STUPID?: Diachronic vs Synchronic Ontologies (see here), we have historically had both “diachronic” and “synchronic” approaches available to us. For all the talk of diagrammatic onto-cartographies, we must always bear in mind our lesson from the first day of philosophy class: that the map, the chart, the diagram, etc. is not the territory.
As such, by way of our sheaf logic and quantum set theory, it is not only that we only have these two approaches, but we have also an infinity of approaches that lie in-between these two ends. And, what’s more, each of these are to operate on the same even field of play due to the equality relation which constitutes them. Everything is on the table, many tables in fact, sometimes indeterminate and unobservable tables, and we are to orient ourselves appropriately given this radical plurality. Reminder: Any given ontology, or any given theology (including my Wilderness theology, as we have discovered here) is by definition a failure.
In our search for a transfer principle as full as possible, we have come to realize that such an attempt is by necessity incomplete, as Pavel Florensky rightly noted. In other words, Paradox is embedded not only into our observation of reality, but in the fabric of reality itself. This is the true radicality of how we are to interpret Heisenberg’s uncertainty principle (see here). Quantum set theorist Masahao Ozawa outlines it as follows ”…the uncertainty does not always come from the disturbing influence of the measurement, but from the quantum nature of the particle itself.”
Truth is in many ways like a Rorschach test. I think that it is clear enough that the Law of the Excluded Middle is simply not applicable here.
In retrospect, I can see that my initial attention to the double-style of Jacques Derrida, and then now to Francois Laruelle is precisely due to this logic of of the superposition principle. In Laruelle, there is not only a re-doubling of our interpretation of reality in the text as is the case in Derrida; rather, there is also a re-doubling of the Real itself. Moreover, even functioning within the diachronic/synchronic framework we will encounter others who are traumatized, who are dissociated, who are uncertain, who hold sympathies and reservations to both prevailing logics, who otherwise do not fit cozily in either end.
There is, as it were, not merely a relationality between objects, but a super-relationality which locates the absolute uniqueness (…and this is one key element that Badiou forgot in Logic of Worlds!) of each neighborhood, of each individual situation, of each locality, of each hospital room, of each trauma patient, of each rape victim, of each war veteran, of each handicapped, of each and every human being as a free absolute.
Indeed, these are the on-off/true-false Boolean ends at which we can understand each other clearly.
But it is important, too, that we attend to cases even where we cannot hear the speak. To avoid the conspiracy of silence, we must strive to listen even when the logics are neither explicitly diachronic nor synchronic, even when they are fuzzy. In fact, throughout most of our life we will remain somewhere in this intermittent and highly uncertain path, maybe towards one pole over another (I usually lean synchronic). Any articulation of a crystal clear diachronic or synchronic logic is only revealed to be momentary at best.
Ultimately, the “non-dissociative” demand for such rigorous clarity of thought, when all else remains unclear in those who are suffering, is absolutely inappropriate when approaching dissociation. The way in which we think about dissociation matters significantly in the way we are to approach the situation. This is well studied in medical papers such as Trauma-related dissociation: conceptual clarity lost and found (2004) by van der Hart O, Nijenhuis E, Steele K, and Brown D (see here), whose objective is to get across the notion that “Imprecise conceptualizations of dissociation hinder understanding of trauma-related dissociation.”
What we need, here, is a certain versatility which escapes rigorous notions of identification, abstraction, conceptualization, and categorization.
With this logic of superposition, we encounter states which are “in-between”, and therefore to some degree or another incomprehensible no matter our classification schema. This is a happening which brings us all the way back to the poesy of Novalis. With a non-Laruellean non-philosophy (see here), we achieve the possibility of a high degree of artistic, poetic, and otherwise creative expression and understanding in these moments of Crisis.
With this quantum set theory also comes not merely what Laruelle calls dualysis, but what I wish to brand as the hallmark of the non-Laruellean: radical paralysis. To those who see Laruelle as a “dead-end”, they are in one sense correct in doing so — yet to turn away because there’s no more theory beyond this point seems to me absurd. It is at this stage where I would probably scream at you and say: Don’t think, look! There are people suffering over there!
Just as there is revealed an identification with the “foreigner” as found in post-colonial discourses such as that which can be found in work of Homi Bhabha or R. Radhakrishnan, of the one cast outside of the boundaries, there is also in non-Laruellean non-philosophy an identification with the “crippled” who remain within the scene of the familiar, and who do so Nonetheless.
I borrow the provocative and problematic term “cripple” from Peter Sloterdjk’s new book You Must Change Your Life. From his chapter “Only Cripples Will Survive: Unthan’s Lesson”, pages 40-60, I’ve pulled some incredible quotes:
Living in the Nonetheless imposes an ostentatious zest for life on those who are determined to succeed. The fact that things may be different on the inside is no one’s business. The land of smiles is inhabited by cripple artistes. [...] The vaudeville people know more about ‘real life’ because they are those who have been thrown to the margins, the fallen and the battered. These ‘jostled humans’ are perhaps the only ones who still exist authentically. [...] Thanks to them, the circus becomes an invisible church. In a world of fellow travellers complicit in the collective self-deception, the circus performers are the only ones who are not swindlers – someone walking on a tightrope cannot pretend for a moment. [...] It is not walking upright that makes humans human; it is rather the incipient awareness of the inner gradient that causes humans to do so.
So to shift registers again, as Dr. Ozawa wrote in his 2007 paper (see here), quantum set theory builds upon the Many-valued Boolean logics of Takeuti, locating in through this transfer principle the realization that “[d]espite the difficulty pointed out by Takeuti that equality axioms do not generally hold in quantum set theory, it is shown that equality axioms hold for any real numbers in the model.” That is, we are to weave through our concern for liberty a thread of equivalence and equality.
In this way, it is not enough to be a Marxist, for one must also be a non-Marxist. It is also not enough to be a Christian, for one must also be a non-Christian. And so forth. One must have the dynamic ability to turn and re-turn to a state whereupon a fixed, non-dissociative identity is no longer an option: to become like a child upon their discovery of a life-threatening cancer, for example. In the last instance, we take up the identity of “the Victim” over that of the victor.
In this traumatic site, it may be said that everything is still on a table. It is mere a question of “At which table we will offer ourselves up to be eaten?” Revolutionary Maoist politics are still on a table, albeit it is on a table which is far, far away from the immediacy of the situation at-hand, so much to the extent that this table falls out of focus entirely. It is not that either Deleuze or Badiou or any of these thinkers are “wrong” per se; however, it is just that becoming the luxury meal of high-theory and politics is not even remotely available in many of the circumstances with which we face in our everyday immanence.
And so we must seek to stay in tune with the Spirit, oscillating between a concern for radical immanence and materialism as the Crisis commands of us. This is a ever-so-difficult position of tension to maintain, to keep the Vision-beyond-Vision of a skilled archer as I had suggested, or balance of an acrobat as Sloterdijk elegantly wrote. It is the position of being-in-tension whose name is STABILITY, and it is one whose pragmatics is modeled upon an sheaf logic of approximations.
Mutualization and Communization, therefore, are to be named the twin pillars which are to be set in place in order to keep the other from going too far astray in the wrong direction.
Sin – missing the mark?
To transfer, then, in between these two is to see as closely as possible to orient oneself properly with respect to the vision-in-One. When acting from the place of the One, to be inside this sphere in particular, there is a whole circumference of possible actions which can be made with our sheaf logic.
Can one inhabit, like the purple bacteria of Seth Lloyd’s Quantum Life at 34:00-37:00 or so, a “decoherence-free subspace” with others? I don’t see why not…
If I recall correctly, an archer would fire at a target from a distance, and another would shout Sin! in the event the bulls-eye was missed – or so I think it goes. Yet, this analogy doesn’t seem to capture the monstrosity of reductive logics. It is not simply an act of missing the mark which occurs when the Spirit ceases its movement, or a mere failing to hit it the target; rather, it is akin to turning around and firing your arrows at others in a random, decoherent manner, in an act of absolutely sublime or otherwise surrealist form of Violence, like the recent Newton elementary school and Aurora movie theater shootings.
There is Unitive strength found within a “concatenated quantum code” of collective solidarity, and this is the intended structure of our “church in the Wilderness”.
As the next step forward from our quantum set theory, we must arrive at a possible interpretation of physics itself, in what would be akin to an answer to the famous Leninist question, that spectral question that plagues “the radical Left”. The employment of set theory in particular is of great use to us because the understanding of infinite sets allows us to conceptualize elementary topology. That is, our aim is to think about otherwise neglected elements of spatiality and temporality in a way that best attends to the place of Crisis so as to transform the Wilderness.
If we change our understanding from What is To Be Done? to What is Becoming Done?, then I believe we have begun along the right path.