by OMADEON ©2010

Jacques Lacan

Slavoj Zizek

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.

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

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!

3. A Lacan-Zizek 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 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)

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 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”:

See also:

• The “Axiom of Perception” in Multiple Form Logic (brand new animated GIF slide-show presentation)

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

See also:

• The constructivist definition of “1″ in Multiple Form Logic also exists in Odysseus Elytis’ poetry

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This post contains some cool philosophical and scientific ( Logic) material, EXCLUSIVELY posted here in public, after its recent first appearance in the “Laws of Form Forum” Yahoo group (where I am a member since 2003).

Dr. William Bricken has also given me his permission to re-post what follows.

-Who is Dr. Bricken?

Dr. William Bricken is currently a Research Professor of Education at the University of Washington and a Consultant for Interval Research Corporation, where he is working on unifying hardware and software approaches to computation. Dr. Bricken’s prior positions include Principal Scientist of UW’s Human Interface Technology Laboratory, where he designed and implemented the Virtual Environment Operating System and interactive tools of the VR environment; Director of Autodesk Research Lab, which developed the Cyberspace CAD prototype of virtual reality; and Principal Research Scientist at Advanced Decision Systems, where he pioneered high-performance inference engines, visual programming systems, and instructable interfaces. Dr. Bricken holds a multidisciplinary Ph.D. in Research Methodology, Educational Psychology and Computer Science from Stanford, and degrees in Statistics (MS Stanford), Education (DipEd, Monash University, Australia), and Social Psychology (BA, UCLA). Before entering industry, Dr. Bricken was a Assistant Professor of Education at University of Hawaii and at Monash University, specializing in General Methods of Teaching…

______________________

On Jul 25, 2009, at 2:18 AM, omadeon2 wrote:

Mr. Bricken,
Congrats for your eloquent and detailed response to Mr. Harvey,  explaining the relationship between LoF and Boolean algebra.

Now, since this is a closed group (visible only to members) I must ask for your permission, to copy this comment of yours in my  public blog
http://lawsofform.wordpress.com …as an answer to similar objections, raised there.  (I believe by a person who has also asked similar questions here).
Thanks in advance (if permission is granted)

[......]

William Bricken:

Sure, any postings I personally submit to this list can be taken as being in the public domain.

Um, so in response to requests to “show me the difference” between LoF and Boolean algebra, here’s a demonstration of difference by counting  to two:

• Basis objects: Laws of Form – { () }

• Boolean Algebra – { 0,1 }

Spatial notations address different representational concepts than do string notations, just as a picture of a house conveys different experiential concepts than the word “house”. Spatial notation is  iconic, to some extent it represents what it means, whereas string notation strictly separates syntax and semantics.

The “isomorphic with Boolean algebra” interpretation of LoF imposes a particular set of representational concepts on LoF that are foreign to LoF, concepts such as “commutative”, “dual”, “arity”, and “object”.  LoF illustrates a single concept, “containment”, with a single token  (the same concept takes two tokens in string notation). LoF has a  singular basis, the minimal basis for Boolean algebra is two.

Since iconic languages are based on different concepts, they suggest a different way of seeing. Since they incorporate meaning, a great way to understand how they work is to spend time using these languages to  solve difficult problems. (see footnote)

And since both LoF and Boolean algebra can be interpreted as “logic“, there’s a (somewhat conventional) dilemma. LoF shows that there are different *formal* ways to organize our thoughts (and perceptions, emotions, etc) to achieve the same objectives. Although the output of a silicon circuit and a “LoF machine” would be identical, the internal architecture of each is substantively different. Output equivalence is not isomorphism, for that you need also to show some sort of process equivalence.

Nonetheless, LoF shows that we can achieve rational thought by visualizing bounded spaces and by deleting irrelevancies, as well as by the traditional means of rearranging textual symbols and “reading” strings to bring them back to life.

-William Bricken

Footnote: my CS professor told us that to begin to understand Boolean computation, we should prove (ie algebraically, not by exhaustive search) the distributivity of if-then-else (a three-valued Boolean  function commonly used as a branching structure in software languages): Show

(IF (IF a THEN b ELSE c) THEN d ELSE e) =
(IF a THEN (IF b THEN d ELSE e) ELSE (IF c THEN d ELSE e)

This can be done by hand, but it gets messy…

For folks with access to languages and implementations, it would be  quite possible, should there be an interest, to build a benchmark list of twenty or so logic problems that are good for comparing algorithms (um, not to “race” algorithms by comparing speed of computation, cause  that is very hardware dependent). When theorem provers were just  getting refined, in the early 80s, researchers found that their  implementations worked great for some problems, and poorly if at all  for others. Turns out that implementations exhibit a feature that  mathematical theories do not, they are sensitive to internal process and representation.

Morphism arguments give no consideration to the efficiency of  achieving proof of an arbitrary assertion. Algorithm complexity  theory works toward putting bounds on the computational cost of worst  case and average case theorems. And benchmark comparison is intended  to assess the utility of an implementation.

___________________

NOTE (by Omadeon): The original text by Dr. Bricken that inspired my request to re-post, is this:

On Aug 6, 2008, at 3:05 PM, Alex Harvey wrote:

Does anyone has access to Flaws of form, or can anyone provide a  summary (and rebuttal?) of their criticisms?

Hi Alex,

Ahh, one of my favorite subjects. It is from Cull&Frank that we get

(1) “At best, Brown has produced a new axiomatization for Boolean algebra.”

In their article, Cull&Frank demonstrate that they have almost no understanding of LoF.

If I had to identify the crux of their misunderstanding, it would be

(2) “By allowing “1″ to replace “mark” [they write SB's form of the mark here], “0″ to replace the blank, “V” for concatenation, and “XOR“ [they write the circled-plus token here], the axioms appear as 1 V 1 = 1 [and] 1 XOR 1 = 0″

This is analogous to saying “let’s replace plus by minus, and then addition will be subtraction”.

A couple more quotes that indicate their, um, arrogance:

(3) “Brown violates the most basic truth of information theory: at least two symbols are required to convey any information.”

(4) “Brown merely replaces the ordinary ideographic notation of mathematics with a positional or analytic notation.”

(5) “… the shape, nature, etc. of the signs one chooses to convey information with are irrelevant to the mathematical content of what is conveyed.”

• Cull&Frank are basically advocating a very common attitude: if it is different that what I know, then it is wrong.

An alternative perspective is that Brown (well, actually C.S. Peirce did this at the turn of the 20th century) provides an example of a system that falsifies assertions (1),(3),(4), and (5) above.

LoF *is* ideographic and conventional mathematical notation is not.  Conventional notation *is* positional and LoF is not, so statement  (2) is at best, confused.

Consider the various logical interpretations of the mark, i.e:

True, not False, False implies False, True or False

This is sufficient to demonstrate that LoF is not Boolean Algebra (although it can be interpreted as Boolean Algebra). There is a many- to-one map from Boolean Algebra to LoF, so LoF is not isomorphic to Boolean Algebra. By replacing “blank” by “0″, the many-to-one map is degraded into an isomorphism, permitting these blind men to claim that because they are holding onto the elephant’s leg, all elephants are trees.

Since the deeper meaning of the absence of a mark is that emptiness permeates the representational substrate (a rather obvious observation), to replace emptiness by “0″ would require arbitrarily many “0″s. That is, C&F are viewing the representational space as positional and structured, permitting, for instance, only one correct place to put the “0″. This is also apparent in the idea of writing “V” for concatenation.

Since LoF is a *spatial* notation, concatenation is not well defined. It is better called “sharing a space”, invoking none of burdensome structure of a linear, typographical notation. And with sharing space (think of a bunch of people in a room), there is no “V” that connects objects within the space into pairings.

Yes, SB violates C&F’s understanding of “information theory”, cause C&F forget that the Shannon/Weaver brand of information theory (that I presume they had in mind) addresses sequential streams of binary variations, not spatial arrays. I’m sorry, but since LoF is prima facia evidence of a system that uses only one token (in space) to communicate information, it seems rather bizarre that C&F would imply that they are not even able to look at LoF forms.

Aside: here’s another grand example of this type of blindness:

Additive systems for whole numbers have been in use for several thousands of years. You “add” by shoving piles of objects together; it is a visceral and visual spatial experience. In symbolic arithmetic, you add by memorizing token combination rules (the addition table). The common rules of algebra deny that additive systems exist.

Let’s see, for completion: interpreting “spatial containment” as XOR is deeply wrong. In particular, the essential property of LoF forms that permits their interpretation as Boolean Algebra is *pervasion*, that any form on the outside has complete access to the inside, at any depth (SB is not very clear about this, but Peirce is). The mark does  not exclude crossing from the outside inwards, this asymmetry frees  LoF of the dualism that permeates Boolean structures. So freed, it is  then simple to build “logic” without any concept of False. Or, to be a bit more accurate, Truth is confounded with Existence.

There are many other aspects of self-contradiction in C&F’s article,  indicting that the abusive tone is just that, not based on study or reflection, but a tirade against the unknown.

-William Bricken

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“Multiple Form Logic“ is my own extension of George Spencer-Brown‘s Laws of Form. Wikipedia’s recent references to it have been good news. They include two links to my older site http://multiforms.netfirms.com, which is still valid, although there is now a preferred mirror-site, hosted  in my personal domain:  (http://omadeon.com/logic).

These Wikipedia references were apparently written fairly recently, by some (unknown) people (probably researchers from the official Laws of Form Forum). Here they are:

1) http://en.wikipedia.org/wiki/Laws_of_form#Related_work

The Multiple Form Logic, by G.A. Stathis, “generalises [the primary algebra] into Multiple Truth Values” so as to be “more consistent with Experience.” Multiple Form Logic, which is not a boundary formalism, employs two primitive binary operations: concatenation, read as Boolean OR, and infix “#”, read as XOR. The primitive values are 0 and 1, and the corresponding arithmetic is 11=1 and 1#1=0. The axioms are 1A=1, A#X#X = A, and A(X#(AB)) = A(X#B).

2) http://en.wikipedia.org/wiki/Laws_of_form#External_links

Τhe Multiple Form Logic, by G.A. Stathis, owes much to the primary algebra.

BTW, in case you got the… wrong idea(!) I did not write these references! Oh no! Besides, although I  feel greatful towards these… nice people, I do not agree with… everything they wrote! E.g. as regards their reference to “Multiple Form Logic, which is not a boundary formalism”… I believe that -on the contrary- Multiple Form Logic IS a “boundary formalism”; a very fundamental and radical one, in fact! My view is also that Multiple Form Logic changes  the way we think of boundaries, as such; enhancing the ontological nature or (if you prefer) the existential fabric of  (our Reality consisting of -) boundaries, in (at least) two ways:

• 1) To start with, boundaries are multiple (rather than the Unique, one-and-only Form in “Laws of Form”). Other multi-valued extensions to “Laws of Form” have been proposed by others, e.g. Ben Goertzel’s “Ons Algebra”.

• 2) Secondly, to our amazement -perhaps- boundaries are also (or can also be) mathematical “first class citizens”; i.e. boundaries are entire expressions (inside their own  system) themselves! (This entails  a conceptual difficulty of a need for a paradigm shift, as well as a practical difficulty of  visual representation; a challenge for Visualisation software; e.g. “DreamProver“  -my own visual theorem prover, totally un-funded, delayed, long overdue; more about it… soon! – hehe)

Dream-Prover Snap-shots (click to see a short article about it)

Furthermore, leaving aside my Theorem Proofs in Multiple Form Logic and More Theorem Proofs (about William Bricken’s system, etc)…

• Mr. Ralf Barkow (a Computer Scientist) showed some interesting possibilites for unifying Multiple Form Logic with the Pile System (invented by Erez Elul).

• Some cool alternative proofs of Multiple Form Logic theorems have been produced by Mr. Art Collings, a professional mathematician.

Now, although Mr. Art Collings is  an uncompromising critic of my work (!) I think that his criticisms have been of immense benefit! His professional mathematical expertise has helped me clarify some very important issues, while his objections to some of my (occasionally… wild) philosophical claims (hehe) have been extremely valuable and thought-provoking, despite the fact we (usually) don’t agree. E.g. Some time ago he had expressed strong doubts (HERE) about the “completeness of Multiple Form Logic, saying  that it would be (probably) impossible to prove. However, soon afterwards, I produced a verifiable formal proof  of  the contrary, which he then verified (which… was nice of him). He  subsequently produced his  own (different) proofs, after doing  some research. Interestingly, these communications took place (more-or-less) in public: -In the (semi-)public “Laws of Form Forum“, a Yahoo Group where William Bricken also participates. Some interesting logical problems have been solved (with mathematically sound answers) in those public communications. However, there is still, a… tiny open problem:

• My proof of Theorem T12 (here), stating that William Bricken’s “Boundary Algebra” is “a special instance of Multiple Form Logic” is still not accepted by William Bricken himself, on (more-or-less) philosophical grounds!Nevertheless, this proof has been accepted by other researchers, e.g. Ralf Barkow. Also, Mr. Tasos Patronis (Ph.D),  a Greek mathematician who -I must admit- is also a good friend of mine (OK, so maybe he is a bit biased -hehe)

• The real problem however, in this case, is not the proof itself (which is undoubtedly consistent) but whether or not certain philosophical and mathematical (meta-)criteria are also satisfied, validating my… wild claim that Multiple Form Logic is more generalised and more fundamental (as a “theory of boundaries”) than Bricken’s  “Boundary Logic”.

William Bricken’s main objection is that Multiple Form Logic is a “higher abstraction” than his “boundary logic”. So, philosophically (he argues) it would be wrong to regard it as “more fundamental” than his system. However, my contentions are:

• 1) that this is not a drawback, but a formal advantage (since Bricken’s logic follows, as a “special instance” -provably-only one type of Form in precisely by assuming M.F. Logic) and

  2) that all Forms are multiple - from the very beginning – i.e. that Multiplicity is fundamental, in this Universe!…( Go(d) figure… )
  

Ah well – all this is a loooong  story, beginning here:

• http://www.omadeon.com/logic/proofs_2007.html

(and the rest is in the “Laws of Form Forum“archives).

P.S. Art Collings (much to the delight of William Bricken) made use of the (well-known) fact that the “XOR” relation can be re-expressed as a composite expression containing only ORs and NOTs, to prove that one can -indeed- construct (without adding any new axioms or unproved assumptions) a Multiple Form Logic system by using the XOR relation as a new abstraction,  inside Bricken‘s system. However, it appears that Bricken’s system itself follows (provably) as a special instance of Multiple Form Logic, if (and only if) all different forms are fused into one .

-So… which is the “chicken” and which is the “egg”?

• Well, devotees of the “Simplest Egg” in the Universe (that can probably make the smallest… omelet) say “boundary logic” is “more fundamental”.
• Proponents of Simplicity… NOT necessarily being associated with “the One” but probably (a) being of a strange new Fundamental Quality (that can be) called “A Priori Multiplicity”… can say that (omelets being in need of many eggs, anyway) …Multiple Form Logic is “more fundamental”.

Still others, may blatantly theologize:  -Is there one God, or many Gods?

• Hm… does it… matter, how many Gods you imagine?

- Ah Well, …It may turn out, actually… . . .  . that it doesn’t matter!!!

• What does appear (to matter) however, is not “the number of Gods” but the number of… sacrifices(!):
  
• Worshipping the Logic of Only One God (=Truth Value) …it turns out that you need an exponentially larger amount of Deductions (Proof steps, i.e. logic computation) than for the Logic of Multiple Gods ….er… Forms. More about this astonishing fact will be explained further, during the course of events to come. (Appetizers are here).
  

I rest my case… 

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Eddie Oshins (1945-2003):

Eddie Oshins ’66 died late last year (2003), after a forty-year struggle with mental illness so severe that it would have justified a life of treatment, hospitalization, and withdrawal in anyone less brilliant and less courageous. In fact, Eddie is one of Reed’s greatest scientific achievers. In the late seventies, Eddie cracked the mathematical/ physics formulae smuggled out of a Soviet Gulag. Writtenon toilet paper in a virtually unreadable hand and notation, these were Yuri Orlov’s breakthrough insights on “grey logic”: of what happens between the “0” and the “1” in computer language: neither is not or is, but maybe. At the time of his death, Eddie was working on the “quantum physics” of  schizophrenia: something that fits in well with his own, brilliant popularization of Orlov’s math as adding the Yin/Yang to cybernetics. Before Orlov, Eddie was one of the few to “stand up” to the “current wisdom” that computers could “think.” Eddie, I think now you can fly free from the fear that never paralyzed you for long and just laugh, as you almost always could.

- Thomas Forstenzer, “goodbye, Eddie Oshins” (2004)

• The Quantum Psychology Project®: Oshins Biography

• Oshins’ Resume

FILE: Rooted in Genuine Stupidity.A1.5.15.99

DRAFT OF A FULLER PAPER TO BE ELABORATED IN THE NEAR FUTURE. “What is Quantum Psychology?“ Note I: “Rooted in Genuine Stupidity” by Eddie Oshins Copyright -(c) 1997, 2001 Eddie Oshins. All rights reserved to the author.

I thank Sky Chaney for inviting me to write three short essays introducing my Quantum Psychology Project at the Mental Research Institute for the new MRI electronic journal. Note 1 overviews how I created my “Genuine Stupidity Logic” model as a new scientific model for psychology in the mid-1970s. Note 2 will discuss (1) how I was subsequently called upon to serve as scientific representative and editor for imprisoned Soviet scientist Yuri Orlov’s similar “wave logic” model, and (2) how I was lead to coin the term “quantum psychology” in 1982 to describe this class of science in order to distinguish my own quantum effort from Orlov’s nonquantum approach. Note 3 will elaborate upon what I mean by quantum psychology being a “scientific model.” I will explain how quantum psychology is science but not quantum physics.

CAVEAT: In 1994 David Finkelstein mentioned that, unbeknown to me, both he and Elihu Lubkin had previously used the expression “quantum psychology” in physics during the 1970s in a somewhat more casual manner. My more specific usage has been to identify and distinguish the formal, interpretive, critical, and empirical aspects of my psychological model, and appears to be in harmony with their usage in physics.

In contrast, my scientific approach is at fundamental odds with Stephen Wolinsky’s more recent, metaphoric adaptation of “quantum psychology” for his own therapeutic enterprise. For instance, Wolinksy associates his work with Pribram’s “holographic” understanding of quantum physics which Oshins has shown to be irrelevant to quantum physics or quantum psychology (Oshins, 1991). In subsequent notes, I hope to explore further some of these aspects of my Quantum Psychology Project(R).

BACKGROUND: In the mid-1970s, I began to examine a controversy in the psychological literature concerning the nature of schizophrenia as a logical phenomenon (Oshins and McGoveran, 1980). Initially, I was interested in the formal arguments between (1a) the intrapsychic approach of E. von Domarus, Silvano Arieti, and others, and (1b) the interactional/communications approach of Bateson, Jackson, Haley and Weakland concerning, respectively, (2a) von Domarus’ principle of “identification by predicates” and (2b) “double-bind theory.”

The intrapsychic perspective viewed schizophrenia as a logical deficit in which, instead of reasoning, e.g.:

“Socrates is a man.

All men are mortal.

Thus, Socrates is mortal.”,

a schizophrenic supposedly reasons, e.g.:

“I am a virgin.

The Virgin Mary was a virgin.

Thus, I am the Virgin Mary.”.

The double-bind point of view saw schizophrenia as a consequence of the individual trying to accommodate an inviable communications context in which he: (1) believes it is necessary to discriminate and “chose” between alternatives on more than one logical level, each of which disconfirms the other; (2) is not able to step out of the “choice” context which would enable him to comment on the inviability of these “options;” and (3) comes to expect such infeasible experience as ordinary.

I did not see these models as being in contradiction but as addressing opposite sides of the boundary between the intrapsychic and the interpersonal/systemic systems. I thought that much of the disagreement was due to an inadequate appreciation of the alternative theories and to an insufficient symbolic representation for defining and comparing the differing points of view. As I understood that these issues were considered important in psychiatry, I began to try to construct an intellectual tool to clarify the matter, as I understood it.

At that time, I was also looking at “fuzzy logic” and “the laws of form,” which are two variant logics developed by computer scientists attempting to model thought by generalized classical logics. I saw that there was a way to combine, with minor modifications, certain concepts from these artificial intelligence approaches to psychology and language into a “nondistributive” logic (technically, a “lattice”) as is found in quantum theory. The “laws of form” approach likened Epimenedes’ paradox (“This statement is false.”), and self-referential paradox in general, to the arithmetic equation ( x = -1/x ). I took this arithmetic equation and converted it into a MATRIX eigenvalue equation [Xf = ?I(X?1)f], where X is a 2×2 matrix, f is a two spinor, -I is the additive inverse of the multiplicative identity, and X?1 represents the multiplicative matrix inverse to X.

Matrices have the property that their multiplication is order-dependent. Indeed, in describing Heisenberg’s creation of quantum mechanics, Max Born stated: “ … And one morning … I suddenly saw light: Heisenberg’s symbolic multiplication was nothing but the matrix calculus, well known to me since my student days.

…I recognized at once its formal significance. It meant that the two matrix products pq and qp are not identical … that matrix multiplication is not commutative …” (Oshins and McGoveran, op.cit., ft.nt. 6). In quantum physics, there is a measure of the difference in such ordering, called the COMMUTATOR, which is precisely a measure of the INTERACTION between the measuring and the measured system … the knower and the known. Since I was proposing a competing model to the “artificial intelligence” efforts, I decided, tongue-in-cheek, to call my approach “genuine stupidity logic.” (The change to “quantum psychology” will be elaborated upon in Note 2.)

Within the logic framework, this order dependent interaction provides the logical equivalent of a type of REPRESENTATIONAL AMBIGUITY between constructs viewed as reference frames. Such an interpretation provides an operational approach to complementarity, whereby one construct restricts the simultaneous availability of another construct while being necessary for unambiguous specification in a different context. A type of metalogic results involving the metalinguistic choices between competing, contrary points of view or frameworks.

The pertinent issue, here, is not whether [‘A’ is ‘true’] or whether [‘A’ is ‘false’/‘not-A’ is ‘true’], but whether the (A, not-A)-system is the appropriate context. For a complementary metalogic to apply to a description, there would exists an equally good (B, not-B)-system that could adequately describe the same phenomena so that ‘B or not-B’ is also ‘true.’ In the book Change (Watzlawick, Weakland and Fisch, 1974), the authors correctly express the failure of the distributive law for a complementary metalogic in their own language when describing reframing and second order change: [‘A or not-A’ is ‘true’] but this does not mean that [‘A’ is ‘true’] nor that [‘not-A’ is ‘true’] since the (A, not-A) system, itself, might be an inappropriate context for the particular, influencing situation . The therapist has the ability then to reframe the constructs used to characterize the phenomena in a manner that subverts the problem.

In still other language, to assert ‘Statement-A’ — a proposition about a property of a “physical observable” — and to assert“ ‘Statement-A’ is ‘true’ ” are different. [“ ‘Statement-A’ is ‘true’ ” is “false”] is NOT the same as [“ ‘Statement-A’ is ‘false’ ”], i.e.,[“ ‘Statement-not-A’ is ‘true’ ”]. Both ‘Statement-A’ and ‘Statement-not-A’ might be inadequate to the context. Within such a metacontext, neither statement would be ‘true’ nor would be ‘false’ if there existed a competing, complementary ‘Statement-B’ which were the appropriate choice. In other words, the (A, not-A)-constructs compete with the (B, not-B)-constructs for simultaneous availability as contexts although the (A, not-A)-constructs might be appropriate given an (A,not-A)-context.(Examples can be found in Oshins (1995), and will be discussed further in future notes.)

When such “experimental contexts” are not decidable, physicists speak of this metalogical ambiguity as “nonselecting measurement.” It occurs through a highly nonclassical type of “superposition” of states of information. This type of “quantum parallel processing,” which I have called “synaptic spanning,” results in complementarity for the competing, metalogical contexts. I saw this framework of complementarity and metalogical ambiguity as an intellectual tool to envision both the intrapsychic equivocation process discussed by von Domarus and the metalogical communications of “double-binds” and “second order change.” Furthermore, I replaced the distributive law of classical logic, ie. [A and (B or C) = (A and B) or (A and C)], by my PRINCIPLE OF METALOGICAL AMBIGUITY for competing/complementary contexts:

“If one does not distinguish between two unit predicates A & B, there will always exist a third possible unit predicate C such that (A or B) = (B or C) = (C or A),” A, B, & C are equivalent “perspectives.” There is no operational way to distinguish between A, B, & C. (This is discussed further, for example, in my chapter in Propagations (Oshins, 1995).)

In the beginning of Change (Op. Cit.), the authors had stated that the order of two operations did NOT matter for the mathematics of “group theory,” which they were recommending. From my perspective, it was this very property that allowed for the kind of interactions which I had proposed. I saw that the logical structure used by physicists in talking about physical propositions could be adapted to the logical structure used by psychologists to talk about psychology and linguistic propositions. Since much of this psychological work had originated at the Mental Research Institute, in 1976, I took a trip from New York to California to discuss my ideas there. I never moved back, thus, beginning what became my Quantum Psychology Project.

REFERENCES:

* Substantial errata to Oshins (1995) is at http://quantumpsychology.com/MRI-errata.html.

• Oshins, E. (1991). About models and muddles, part I: Why Brown’s Laws of form and Pribram’s “hologram hypothesis” are NOT relevant to quantum physics and quantum psychology. In Manthey, M. (Ed.), Alternatives in physics and biology. Cambridge, England: Alternative Natural Philosophy Association, c/o Dr. F. Abdullah, City University, Northampton Square, London ECIV 0HB, UK.
• Oshins, E. (1995)*. “Quantum psychology & the metalogic of second order change”. In J.H. Weakland & W.A. Ray (Eds.), Propagations: Samples of MRI influence over thirty years.
• Oshins, E. and McGoveran, D. (1980)*. … thoughts about logic about thoughts …: the question ‘schizophrenia?’ In Banathy, B.H. (Ed.), Systems science and science, Proceedings of the 24th annual North American meeting of the Society for General Systems Research, pp. 505-514.
• Watzlawick, P., J. Weakland, and R. Fisch. (1974). Change: principles of problem formation and problem resolution, New York: W.W. Norton.

(end of article)

Related links:

• Stanford University Wing Chun – In Memory of Eddie Oshins

• Evolutionary Quantum Computation: Its Role in the Brain, Its Realization in Electronic Hardware, and Its Implications for the Panpsychic Theory of Consciousness

• Quantum Consciousness . Stuart Hameroff

• Sets to Quarks, Reflections, Subsets, and XOR – HyperDiamond Feynman Checkerboard (Tony Smith)

• Ons — a theory of truly elementary particles, explaining the emergence of structure from void in physics and psychology (Ben Goertzel)

• The CONSISTENCY of ODYSSEUS ELYTIS-”Genesis” with George SPENCER-BROWN’s “LAWS of FORM” « OMADEON

• How Equality is embedded in Multiple Form Logic (Animated GIF Presentation of a Theorem Proof) – Omadeon

• GetWiki | Laws of Form

• Laws of Form – Wikipedia, the free encyclopedia

• SOME-THING FROM NO-THING (G. SPENCER-BROWN’S LAWS OF FORM)

• “Equality Logic” is EMBEDDED in Multiple Form Logic « OMADEON

• THE ADVANTAGES OF MULTIPLE FORM (BOUNDARY) LOGIC — A COMMON SENSE APPROACH

• Axioms from Interactions of Actors – Interactions of Actors Theory (doc)

• The Self And The Other: The Purpose Of Distinction (ResearchIndex/pdf)

• Polyphony and embodiment: a critical approach to the theory of autopoiesis

• G. Spencer-Brown – Wikipedia, the free encyclopedia

• Omadeon’s postings in the “Laws of Forms” forum

• G. Spencer Brown’s Laws of Form & John Lilly’s Take on It

• Η Λογική των Πολλαπλών Μορφών (The Logic of Multiple Forms -in Greek) (Introduction for Greek readers / Εισαγωγή για τους Έλληνες αναγνώστες)

• Multiple Form Logic: An extension of George Spencer-Brown’s LAWS of FORM

• Multiple Form Logic, by G.A. Stathis, “generalises [the primary algebra] into Multiple Truth Values” (Laws of Form – Wikipedia)

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This blog’s header depicts the two fundamental axioms or “initials” of George Spencer-Brown‘s “Primary Arithmetic“: The image on the left is the “Law of Calling” and the one on the right is the “Law of Crossing“, i.e.

Law of Calling

Law of Crossing

There is a certain revival of George Spencer-Brown’s ideas, taking place nowadays, and this blog will -hopefully- contribute to creative public discussions about GSB’s ideas.

George Spencer Brown

There is already a Yahoo group dedicated to “Laws of Form” (started many years ago by Mr. Richard Shoup) called the “Laws of Form forum”. However, all discussions in that Yahoo group are private, i.e. not visible to non-members (and to Search Engines).