Multiple Form Logic and Lacan

A Lacanian view of Multiple Form Logic and Slavoj Žižek

Lacan's Real, imaginary and symbolic in Multiple Form Logic
A Lacan-Žižek interpretation of Logic implication in M.F. Logic
A Lacan-Žižek interpretation of Multiple Form Logic's Axiom 3

Jacques Lacan

Slavoj Žižek

1. Lacan's Real, imaginary and Symbolic in Multiple Form Logic

Distinction as Symbolic. Imaginary, Real

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 Žižek'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 Žižek, 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 Žižek locates the subject. The subject is, in other words, a void.

(Tony Myers, "Slavoj Žižek", 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.

2. A Lacan-Žižek interpretation of Logic implication in M.F. Logic

In Multiple Form Logic, logic implication is a configuration of Forms, where a (Symbolic) signifier is assigned (by the imagination) to a Real signified object. The Symbolic signifier is inside the boundary (of the Lacanian "imaginary") and the Real (signified) is "out there". The "implication operator" I, is the boundary of perception, i.e. the imagination itself:

Logic implication as an act of Perception

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!

In the simplification of a composite Form that contains a cluster of such implications, it is often possible to progressively reduce the complexity of the composite form, through the elimination of anything Symbolic which corresponds precisely to something Real. To see how this is done, using the "axiom of perception" (axiom 3), we need to interpret axiom 3 from a Lacan / Žižek point of view:

3. A Lacan-Žižek interpretation of Multiple Form Logic's Axiom 3

Seen in this light, the "Axiom of Perception" (axiom 3 of Multiple Form Logic) acquires an exact correspondence with Lacan's and Žižek'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 Žižek", page 28)

The "axiom of perception" (click on the image for more)

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 dissappear! It exists, because of the fact that 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".

The (Lacanian) "Symbolic" also consists of partial representations, or signifiers of "the Real" (=signified), selectively created within the space of "the Imaginary". If these partial representations ever became identical to (the Totality of) "the Real" and if the imaginary also became identical to "the Real", then everything (both imaginary and symbolic) would cancel out and dissappear!

Now, the fundamental distinction drawn by every (relative) being, is the Lacanian "imaginary". We could say that the very existence of the Lacanian imaginary, as a boundary around its own (symbolic) space is the "first distinction drawn by Mind" - a distinction which Žižek identifies with "madness", since it manifests initially as a void, or as a distinction with zero content:

It is this void that, for Žižek, 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 Žižek calls it, between the state of nature and the state of culture. Žižek'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, we have to 'get rid' of the Real before we can construct a substitute for it in the form of the Symbolic Order.
Žižek reads this vanishing mediator as a passage through madness and, by so doing, he conceives the subject (which is the vanishing mediator) as mad. Madness, therefore, is for Žižek a prerequisite for sanity, that is, for the 'normalcy' of a civilized subject.

-Tony Myers, "Slavoj Žižek", 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 "cancelled out", according to Axiom 3:

The Signifier X corresponding to the Real object X can be "cancelled-out"