The efforts that go into solving complex mathematical problems, the failures as well as solutions, must be deriving from that set of solution for which such endeavor strives, which then shows that all such work, indeed all work, is determined in nature. We should note what this means. Math appears to human beings as a phenomenon of the universe that has only one solution; that is, the formula of mathematics not only implies a single solution, but further that the separate instances of solution imply a single application under which they derive their individual solutions, and, that this consistency that we call mathematics thereby brings into relief the situation that finds false or temporary solutions. This situation thus can only implicate that the ‘processor’ is at issue, but that this processor then being subject to math, in that it notices math as such, thus also is part and moving towards the single solution.
This explication thus derives the maxim that thought itself, the course that thinking of thoughts take, is necessary, which is to say rather poignantly, not based in any essential choice or free will — and this next calls forth the issue of the significant event — except in as much as free will does indeed operate as free agency in reality. We cannot then but ask; if math is presenting itself toward necessary solution, why is it that we are capable of finding solutions that do not or only temporarily complete the function? How is it possible to be incorrect in a solution in a mathematically determined function ? Why or how are some solutions that work now or for a while, later found out to be incorrect?
This introduction here will be taken up more thoroughly in a subsequent essay, but for now suffices to show how the problem is set initially.
The answer sought by such questions may indeed involve transcendental thinking as a particular kind of thinking, but we must not forget that it is just this feature or type of thinking that has gotten to this place that is reasoning that transcendental thinking is the problem. It is not enough to remove defined categories of transcendence, it is not enough — indeed, it is redundant — to posit a segregation of types of thinking, as if there has been a line of ‘false thinking’ that was occurring while another line of ‘correct thinking’ was taking its place, because, as we have argued, such categories that supposedly derive from ‘transcendent free’ definitions themselves rely upon transcendent and immanent operations. The difference occurs (see my essay “The Impossible, part 4”, and others) only in the patterned discursive schemes of transcendent and immanent elements, how the base is situated to allow for such meanings of terms to convey the truth of objects. Besides; what is ‘transcendental thinking’ anyways? How can we begin to formulate how this manifests? In ‘necessetarian (sp?) probabilistic reasoning’? How does one transpose one’s own thoughts to account for another human being’s thoughts without necessarily inferring that it is probable that the other person’s thinking is the same as or similar to the first person’s? Perhaps I am misconstruing Miellassoux’s idea but the ridiculousness of the formulation is almost too ridiculous to even spend the time and space to describe how ridiculous it is; it sounds like he is proposing to bring in the thought police. It is no wonder that early essays of Direct Tangents brought up the obvious analogy involved with the apprehension of institutional philosophy as a sort of religious hierarchy in the addressing of Laruelle (but keep in mind, my confrontation of Nonphilosophy was toward its proposal of method and not so much its meaning).
Here we are faced with the problem of removing that which is responsible for bringing us to the place where we have to remove that which is responsible; if the teacher has served her purpose, so that we must find a new teacher, what then is this situation is the teacher?
We now come to the inevitable place of elucidating the problem involved with finding the truth through the resolving of contradiction. Such a real method operates through the setting aside of such reasoning that would prove its fallacy. This, as I have said, is the effect of conventional faith in reality; the method re-solves contradiction, reasoning that the reason that would reason that its method is faulty, is itself faulty, so the elemental or categorical fault argued is merely displaced into different terms — of conventional method that finds the truth of the human being through its objective terms, terms that are seen to arrive from objects in themselves, through (Kantian) intuition. Hence I say that conventional reality usurps all meaning unto itself, and the main operation of consciousness is to distance itself from its determination, to thereby grant reality.
Hence we inevitably find now two situations for the human being in the world. One that is real, that sees itself as it proclaims its absolution over all the universal history as unassailable, and another which by default against what is real is thus not real, that sees such a proclamation as merely one such proclamation in a series of unknowable proclamations of true-real universes. The former always sees its capacity for True Objects transcendentally imbued into the terms that have been laid through time in symbolic immanent certitude, that it and only it has the ability to decipher for, is absolute Truth. This real method usurping all symbolic transmission into itself for its universal and eternal proclamation of truth, past civilizations and events being ‘ignorant’ or ‘misunderstanding’ or ‘superstitious’ in their absolute primitive nature relative to our current absolutely more progressed nature, is always functioning in its denial of contradiction inherent in the mode of consciousness for bringing, allowing and granting objects their absolute substantiality in reality. The latter view sees that due to the inherent contradiction involved with real discourse, such a real-true description of cosmological and historical truth must find its veracity through an intrinsic mythology that operates viably through faith.
I am no mathematician. Nevertheless I shall endeavor a (very) brief synopsis of Alain Badiou’s ideas set forth in his book ” Being and Event” and now his thesis may be applied directly to the issue at hand.
His book centers around one problem; the void, how can we determine the void as void? The problem’s solution has been conceptualized in discourse (in many ways, but philosophically by all the ‘turns’), but the correlationalist presentation always routes the void as void back into a contradiction of the concept, which is to say, void as not void due to the act of the concept. The void as void should be beyond conception, yet even as we may understand what the potential of the meaning of void is, we have conceived it, which is to say, brought it out of the void into reality as essentially not void; the meaning of void contradicts itself. So I venture a tentative proposal: It is thus the meaning of void as void as contradiction, ‘settled’ in the concept as not-concept, relinquished as its framing, that amounts to the significant event, which is to say, that which ‘begins the count’. Further, because we (the instrumentality of reality) are human, this accounting here indicates the best we can say, or the least we can conceive, of the situation.
It is by this formulation that we have a justification of Aquinas speculative and practical arenas of discourse, but also the mark that is the motivation for what distinguishes reality as a unitary maxim. Contradiction is primarily understood as the criterion for what is true; i.e. the moment of contradiction shows where truth is not found, or more properly, it is a void against which truth is distinguished: contradiction shows what what is ‘false for what is true’ of a proposition, and the proposition is seen as an indicator of absolute reality as potential. It is this ‘mistake’ in meaningful formulation that thereby gains the stature of discourse and begins the real hegemonic ideological count of history. But this situation is less a mistake than it is a marker of what is true. For the mistake is found when all reality, all that can be, that which is allowed to be counted as true, is accounted for by such discourse. The distinction of Aquinas already does not have a distinction between the human being and its discourse, a hard correlationalism, both aspects are understood apriori as involved in the same unitary motion; which is to say, the human being and discourse arrive in a necessary probability, a potential to gain the truth of reality, the world, the universe, and this potential, as QM argues (but his presentation is a little off) is reason, a potential of the human being as a member of the unity of the universe to access the truth of the universe. By this universal and apparent mandate, the discrepancy is of the unity and so the activity of humanity, as distinct from the ‘lower creatures’ that apparently do not have such cognition, is the involvement towards understanding the unity, the universe. The void as such in this human involvement is entirely mythological since the human impetus that is apparently instilled a priori gains for itself a ‘prime mover’, so to speak, an agent or agency as a fundamental, albeit anthropomorphic, force that is the cause of all causes, or for another term, God. Yet, even if this prime mover is discounted as false or otherwise not verifiable, the argument that may arrive at such conclusion is likewise relying on the very (causal, singular, agency) impetus it supposedly seeks to disrupt through identifying terms, such identification likewise relying upon an assumption that terms are identifying actual True Objects, or at least real to those who use(d) them. Hence in the progress of conventional history we begin with what we disclaim, or, we succeed in bringing the void into the concept as if the concept is reflecting the potential involved in the meaning of the void, yet accessing this situation as if the concept itself, the meaning of the void, is itself essential, that is, prior to the the void itself. The notion of ‘The Name’ resonates this situation.
Hence we have irony. The problem of the void as void against the human conception of void as void, the instigation of the experience of the void asmultiple, and the experience that is its multiple, or that which posits experience of the void as that which accounts for the multiple — this statement arises in the midst of irony, the contradiction that evidences a discrepancy of which is solved through faith. Faith as a distinguishing feature of identity, is that which is the suture of the void to experience and marks duality; fidelity to the Event is thus to the void as contradiction, what can be called the ‘Significant Event’; or, fidelity to the concept by which an event arises, as a retrograde positioning for meaning, can be called ‘conventional reality’. Where the void is contained in the concept, prone to the question of either/or, thereby we can argue the veracity of transcendent items, thereby does the event begin the count of the multiple as any event may begin the count in fidelity, which is the problem inherent of sets of sets,that any event is multiple, and hence what is of the multiple grants a necessary transcendent that is not contained in the infinite sets. Thus the issue here is not in the determination of sets; the determination of sets occurs through the Name and its definition. Rather, the issue has to do with bringing the void as void into the formulation of sets without such bringing being likewise a set. The issue, as Badiou I believe has put it, concerns the Naming of the Void.
This is thus the problem of reality itself, for such a conception of void as void is relying upon a transcendent by which to support its claim. Transcendence is the extrapolation of meaning to the object in itself; in other words, meaning ‘reaches out’ to grasp what is beyond meaning and thereby establishes the True Object. This is the same to say that we know of an object by intuition of its truth; whether or not it is true in an absolute sense is of no consequence because the meaning of the object operates for consciousness as its truth. Bare sensory impressions have no baring upon what is true in the same way as explained in the earlier segment concerning Otto, that such sensory experience is excluded in the ‘frankness’ that is the (conventional, meaning of) telling of the experience. For as one might have understood, it is not that certain spiritual-type experiences are left excluded in the telling of them and ‘regular’ experiences are actually told or avoid this exclusion, but rather indeed all experience is frankly excluded.
To reiterate; it is the issue at hand that would have us describe this situation of division, the point of contention. If I have not been clear, it is due to the side of knowledge that would have discourse be able to convey the actual truth of the experience, but not only this, more so that an individual sees the consistency in the correlation of experience of thought to discourse, and its various arrangements that decide upon various other truths that contribute to the gaining of Big Truth, e.g. discourse is an experience that influences or concerns thought; thought is an experience that can concern discourse; discourse is an expression of thought and this is an experience; etcetera. Reality is gained through the potential that links the term to object in a necessary manner such that the individual is especially privy to having the ability to come upon true objects. I have called this situation, where a human being is oriented upon objects in this way, conventional faith, for it is faith that sutures the transcendent idea to the meaning of the object truthfully. It is this situation of reality, where the terms manifest through their potential to identify true objects, that is called the situation of the pure multiple. This is the issue that Miellasoux avoids through proposing that math may be a new or proper basis for truth, and because his view appears correct as it sees a need for an adjustment, but maybe a break, and yet because he is stuck in a proposal for a reiteration of reality, the pocket veto as I am developing the idea is an attempt to explain and account for his situation as an occasion of one who appears to address the point of contention but who nevertheless merely uses the issue as a means to establish real identity.
This is the problem of duality. The pure multiple accounts for the void as a set. Without going into the precise wording and formulations that Badiou and mathematicians use, a group of elements is a set. The real issue of this situation is exactly the defining of the meaning of void; this is located as the meaning of the pure multiple that all sets can likewise be elements of other sets. The real transcription of this is the definition of terms. A term is definition; hence we have identified at least one pure multiple set: the set ‘definition’ is the ‘term’. In this way the cardinal ‘term’ is established by ordinals that are the ‘definition’. It is a pure multiple because each cardinal can be identified as an ordinal of another cardinal set; this is to say, each term that has definition can be used as a part of the definition of another term, for example, ‘definition’ consists of definers that function to establish what the term is, but also terms are used to establish what the definitions may be. Each term as set establishes what definition may be used as well as what order may be used to establish the definition that establishes the term. Hence we can have a first real set of infinity, and its inherent problem.
Again, the issue concerns thus how such pure multiple may arise; this is the issue of the void. Conventional reality may posit a void against which such multiples exist, but such a position thereby likewise exists as a set of multiples and defies that it was ever the void; infinity itself is highly conventional in this way. Hence, the only way to escape this situation of the pure multiple in reality is to posit that the meaning of the void remains inviolate as a (not-) thing unto itself, and this is exactly the position of the transcendent, which is not void except as the term itself is sutured to the True Object by faith in its meaning. More precisely the problem has been phrased as the problem of a set that is not included in another set, or, the set that includes all sets, but is in itself not another set, the ‘non-set’ to which belongs all sets. The problem has been historically formulated as impossible; all sets can be included by yet other sets. That is, according to Badiou, until Georg Cantor found that there is a set that cannot be said to belong to any other set, and therefore does not belong even to itself: the void.
The solution to this problem, as it is a human problem, must then be organized by addressing how one appropriates the Object, what I have called one’s orientation upon the Object. The situation that is capable of appropriating this solution must be that which does not fall into the recouping of sets in another set. This can only be accomplished through a divergence from the situation founded in the pure multiple; to wit, real conventional discourse does not exhibit or hold in the potential of itself in itself an ability to come upon the solution, for it only deals in pure multiples. Therefore, in the attempt to find relief from the effervescent conventional imposition of multiples, (recall Laruelle’s concern of nonphilosophy being made into another philosophical object?) I go straight to what might be seen as a ‘source’ from where all meaning gains its stature for truth: significance, and in so much as such significance has to do more with effect rather than definition, to delineate such necessary divergence, in line with Badiou’s exegesis, I propose the ‘significant event’. Accordingly, this solution thus must be said to be not real, that is, for human meaning, ironic.
End part 6