by OMADEON ©2010
1. Lacan’s Real, imaginary and Symbolic in Multiple Form Logic
Multiple Form Logic can be interpreted in terms of Jacques Lacan’s three realms of the “Real“, the “Imaginary” and the “Symbolic“. I.e. Reality is an External Space, located outside the Imaginary, as well as outside the Symbolic. The imaginary contains the symbolic, endlessly (re-)creating (inside its own space) Symbolic representations of the Real.
Slavoj Zizek‘s Lacanian philosophy is even closer to Laws of Form and Multiple Form Logic than Lacan’s. E.g. his view of “the subject”, or “Cartesian Cogito”, is a Distinction with Void content. Tony Myers describes it as follows:
For Zizek, Descartes‘s cogito is not the substantial ‘I’ of the individual, but an empty point of negativity. This empty point of negativity is not ‘nothing’ but the opposite of everything, or the negation of all determinacy. And it is exactly here, in this empty space devoid of all content, that Zizek locates the subject. The subject is, in other words, a void.(Tony Myers, “Slavoj Zizek”, page 37)
I.e. the Cogito is an “empty point of negativity“, which is also “the opposite of everything”. This is consistent with the nature of brownian Distinctions or Multiple Forms, as negations. As an aside, since the nature of the imaginary is “the opposite of everything“, it follows that the opposite of the opposite of everything is everything. I.e.
The Second Axiom of Multiple Form Logic is consistent with these considerations.
The boundary of perception (or the Lacanian “imaginary”) I, contains the “premiss” P, as a Symbolic signifier of the Real “conclusion” R (object signified), which is “out there”.
- So, Logic implication is (nothing but) the Act of perception, itself!
Seen in this light, the “Axiom of Perception” (axiom 3 of Multiple Form Logic) acquires an exact correspondence with Lacan’s and Zizek’s account of the Imaginary, the Real and the Symbolic:
“…if the Symbolic was not an incomplete or insufficient account of the Real, if, that is, we could apprehend the Real directly, then we, as subjects, would disappear. The reason for this is that if everything was exactly as it was meant to be, if everything could be grasped in its fullness, if there was no discrepancy between the way you saw the world and the way I saw it, if -in other words- every signifier perfectly matched every signified, and every sign matched every referent, there would be no signifying chain. All there would be is the Symbolic Order in perfect correspondence with the Real.”(Tony Myers, “Slavoj Zizek”, page 28)
Algebraically, all this is (verifiably) very true in Multiple Form Logic, too. In Multiple Form Logic, the imaginary is just a relative distinction, which is floating inside the Real. If this was ever to became identical with the (entirety of the) Real, then it would disappear! It exists, because it is relative; not absolute.
NOTE (for readers familiar with “Laws of Form“): This inherent relativity of Multiple Forms makes some of their algebraic properties very different from those of (absolute) Forms in “Laws of Form”.
It is this void that, for Zizek, enables the transition from a state of nature to a state of culture. This is because if there was no gap between a thing (or an object) and the representation of that thing (or word), then they would be identical and there would be no room for subjectivity. Words can only exist if we first ‘murder’ the thing, if we create a gap between them and the things they represent. This gap, the gap between nature and the beings immersed in it, is the subject. The subject, in other words, is the missing link, or ‘vanishing mediator’ as Zizek calls it, between the state of nature and the state of culture. Zizek’s point here is that the transition from nature to culture is not a story that can be told in terms of an evolutionary narrative, such as that offered by Hegel. Rather, the withdrawal-into-self which culminates in the cogito has to be presupposed as the vanishing mediator between the two, the missing link around which the transition is organized. In other words, Zizek reads this vanishing mediator as a passage through madness and, by so doing, he conceives the subject (which is the vanishing mediator) as mad. we have to ‘get rid’ of the Real before we can construct a substitute for it in the form of the Symbolic Order. Madness, therefore, is for Zizek a prerequisite for sanity, that is, for the ‘normalcy’ of a civilized subject.
(Tony Myers, “Slavoj Zizek”, page 37)
To ‘get rid of the Real’, in Multiple Form Logic, from an algebratic point of view, all we need to do is apply Axiom 3 in reverse: -Anything “Symbolic” (X) which corresponds precisely to something “Real” (X) out there, can indeed be “canceled out”, according to Axiom 3.
In the following image, the Signifier X corresponding to the Real object X can be “cancelled-out”:
4. The Divine Madness of the First Distinction and Slavoj Zizek
In a previous quote, Zizek’s view of the Imaginary as a “madness” which is also “the prerequisite of sanity” was mentioned. In reality, this is not so much an issue of “madness”, as much as an issue of a pre-logical cleavage of Being: A boundary that generates all the Laws of Logic, but pre-exists any Logic (as well as anything Symbolic). Nevertheless, perhaps the best possible account of such a (divine) madness is by Elytis, described in “the Consistency of Odysseus Elytis ‘Genesis’ with George Spencer Brown’s Laws of Form”.
5. The Lacanian “Real” is Multiple Form Logic’s “One”
Axiom 1 of Multiple Form Logic is in reality a construction; it defines Logical One as the Union (or the Totality) of all possible forms, so that:
1 + X = 1
Evidently, the Lacanian Real has a similar property, since the union of any object with the Real, is the Real itself:
Real + X = Real
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