C. A. Hilgartner
I feel grateful to Ralph E. Kenyon, Jr. for providing this opportunity to engage in public debate on my contributions to theoretical general-semantics. Kenyon has paid sustained attention to my work from August 1978 to the present, focusing in particular on the non-standard notation devised by my research group. Since the fall of 1988, he has offered a number of suggestions as to how we might re-write our presentation of this notation so as to make it more accessible to those outside the immediate group which created it.
Between 1973 and 1978 I and my associates wrote some six papers in which we developed our formalized system of representation . Since then, we have USED our non-standard notation in various applications, extending our experience with its peculiarities and our understanding of its implications; but had not returned to the task of revising the notation so as to incorporate and make public these findings. At this point, spurred by Kenyon's difficulties with and persistent misunderstanding of our notation, we have come to recognize some of the problems of presentation that have given persons outside our research group trouble with the published version of the notation, and some ways we might minimize these problems.
The dispute which elicits this Reply centers about two apparently conflicting claims:
a) Hilgartner & Associates claims to have found it possible and feasible to build up an alternative formalized notation based on the premises proposed by Alfred Korzybski: namely, on the undefined terms structure, order and relation and on the postulates of Non-identity, Non-allness and Self-reflexiveness . We claim to have done this, and to have found the resulting formalism useful. In particular, we assert that it confers predictability in the study of living systems.
b) In his paper entitled "The Impossibility of Non-Identity Languages," which appears in this issue of the General Semantics Bulletin, Kenyon makes remarks critical of my frame of reference, and presents arguments attempting to prove the impossibility of creating what he calls "a non-identity language."
Here, I shall examine the apparent opposition between Kenyon's claim and our own, and shall attempt to reconcile them. I must first call attention to several problems: First, Kenyon offers no explicit definitions -- of terms, topic, or the context within which he writes. For example, he extensively discusses three sub-usages of the logical construct of identity -- but does not explicitly define his primary term identity. He mentions but does not define, and does not use, the term non-identity -- a central term in the topic of non-identity languages, which he claims to address. In general, Kenyon makes it difficult to figure out what he means by what he says. Second, what Kenyon calls a non-identity language, and attributes to me, seems to differ so drastically from what (I believe) I have actually done using the Postulate of Non-identity that -- especially in view of the ambiguity of his text-- it will take extreme care to spell out any connection at all between the two.
In order to document this alleged lack of connection, I shall present some of the presuppositions and premises of my frame of reference and of my alternative notation -- enough to make it apparent to readers that my collaborators and I have indeed developed a non-standard frame of reference (and, possibly, a notation) fundamentally different from the familiar Western Indo-European (WIE) frames of reference and notations. I expect that, when considered even in brief detail, both the antecedents and the consequences of our alternative frame of reference and notation will seem surprising, even to exponents of general-semantics. Then I discuss some of the implications of what Kenyon describes as "a non-identity language." Thereafter, I examine some of Kenyon's comments to refute them one by one.
At the heart of his contribution to theory, Korzybski advocates "the complete elimination of identification."  He writes,
Identification, or the confusion of orders of abstractions, in an aristotelian or infantile system, plays a much more pernicious role than the present official psychiatry recognizes. Any identification, at any level, or of any orders, represents a non-survival [semantic reaction] which leads invariably to the reversal of the natural survival order, and becomes the foundation for general improper evaluation, and, therefore, general lack of adjustment, no matter whether the maladjustment is subtle as in daily life, or whether it is aggravated as in cases of schizophrenia. A non-aristotelian system, by a complete elimination of 'identity' and identification, supplies simple yet effective means for the elimination by preventive education of this general source of maladjustment. 
Furthermore, Korzybski clearly indicates how far he intends us to take this recommendation. He specifically includes self-identity among the usages of the logical construct of identity which he would eliminate:
... it must be stated that ‘identity’, defined as ‘absolute sameness’, necessitates ‘absolute sameness’ in ‘all’ aspects, never to be found in this world, nor in our heads. Anything with which we deal on the objective levels represents a process, different all the ‘time’, no matter how slow or fast the process might be; therefore, a principle or premise that ‘everything is identical with itself’ is invariably false to facts. From a structural point of view, it represents a foundation for a linguistic system non-similar in structure to the world or ourselves. All world pictures, speculations and [semantic reactions] based on such premises must build for us delusional worlds, and an optimal adjustment to an actual world, so fundamentally different from our fancies, must, in principle, be impossible.
If we take even a symbolic expression 1 = 1 , ‘absolute sameness’ in ‘all’ aspects is equally impossible, although we may use in this connection terms such as ‘equal’, ‘equivalent’, [etc.]. ‘Absolute sameness in all aspects’ would necessitate an identity of different nervous systems which produce and use these symbols, an identity of the different states of the nervous system of the person who wrote the above two symbols, an identity of the surfaces, [etc.], of different parts of the paper, in the distribution of ink, and what not. To demand such impossible conditions is, of course, absurd, but it is equally absurd and very harmful for sanity and civilization to preserve until this day such delusional formulations as standards of evaluation, and then spend a lifetime of suffering and toil to evade the consequences. 
B. HUMANS ASSUME; WHAT WE DO FOLLOWS FROM WHAT WE ASSUME
Implicit in his approach, Korzybski assumes that humans assume, that we cannot NOT-assume. We can assume this, or that, or SOMETHING ELSE, but we cannot assume nothing at all. In other words, he assumes that what we DO follows from what we ASSUME, in a manner analogous to the way a theorem follows from the premises of the system. "Assumptions lead where they lead, and nowhere else," as Korzybski used to put it. In this sense, then, the constructs of (to) assume and assumption serve as explanatory principles, which allow us to account in strict logical terms for the subtleties of human behaving-and-experiencing.
In my own writings, I distinguish between an explicit and a tacit sense of the logical construct of identity. a) In its explicit sense, I define the term identity as "absolute agreement in all respects, or negation of difference."  When logicians, mathematicians, and other workers utilize the construct of identity in their formalized systems, for the most part they utilize it in this sense. b) In its tacit sense, I define this term as referring to situations in which a human non-verbally TAKES some B as if it ‘WERE’ some A -- e.g., TREATS ‘map’ and ‘territory’ as freely interchangeable, identical. By the dictionary definition of the term mistake, to do that constitutes a mistake. I often refer to identity in its tacit sense as map-territory identity.
As an assumption, I regard tacit identity as restricted and restrictive. In fact, this assumption appears so restrictive, so indiscriminate, that I hold that its presence among the premises of a system disqualifies or invalidates that system. NO ONE, I maintain, could knowingly subscribe to tacit identity. Stated in words, the assumption of tacit identity holds (erroneously) that "One need not distinguish between A and B ."
I find that the grammar common to the Western Indo-European languages, discursive (e.g. Dutch, English, French, German, Greek, Latin, etc.) and also formalized (symbolic logic, set theory, analysis, topology, etc.), encodes a previously unnoticed usage of the disqualifying assumption of tacit identity. We WIE provincials tacitly hold that our language has a cosmic validity: The world, we assume, REALLY DOES consist of static-and-unchanging "things," exactly suitable to designate by self-identical nouns, which enter into transient "relations", exactly suitable to represent by not-self-identical verbs.  But that would mean that the structure of the world and the structure of our language matched "perfectly". As a corollary, then, the disqualifying assumption of tacit identity underlies the explicit sense of the term identity.
C. DEFINING GENERAL-SEMANTICS: NON-IDENTITY 'REASONING'
In keeping with Korzybski's recommendations, I define the term general-semantics in terms of what I might call non-identity 'reasoning'. When expressed in English, such 'reasoning' hinges on disallowing the construct of 'identity' in any guise or form, explicit or tacit. For example, it uses vocabulary items such as (to) make a distinction or (to) distinguish or differentiate or discriminate (between), or (to) eliminate a usage of tacit identity from the premises of the system, or the binary relation of IS NOT, as in assertions that A IS NOT B or A ¹ B , etc.
For a worked example, see Note , in which I show how Newton's great advances depend in principle on non-identity reasoning: For example, in proposing the Law of Universal Gravitation, Newton eliminates at least one usage of the Postulate of Tacit Identity from the premises of the theories of mechanics of his day (e.g. the theory which Newton himself previously held).
Rigor in general-semantics, then, consists in establishing, as unmistakably as possible, that the construct or passage in question presupposes-and-follows-from the Postulate of Non-identity (and/or the other non-aristotelian postulates). If someone's argument or chain of inferences demonstrably ends up depending on non-identity 'reasoning', I include it among the body of constructs which makes up general-semantics. However, if this person's argument or chain of inferences demonstrably STOPS with identity-based 'reasoning', I exclude it from the body of general-semantics constructs.
D. A CHOICE OF TWO WAYS OF HOLDING IDENTITY vs. NON-IDENTITY
In rejecting identity, including self-identity, Korzybski posits that identity and non-identity function as parts in (antecedents of) the behavior of some particular human organism, as s/he deals with her/his environment at a particular moment in her/his life. In effect, Korzybski discloses a previously unnoticed choice which that person faces: S/He can hold the term-pair identity/non-identity in two different ways. S/He can (a) "like" or "prefer" identity and "dislike" non-identity; or s/he can (b) "like" or "prefer" non-identity and "dislike" identity.
The modern WIE logicians, mathematicians, etc., clearly belong to group (a), the "prefers identity" group. Korzybski defines himself as the first member of group (b), the "prefers non-identity" group.
I too define and declare myself a member of the "prefers non-identity" group. Moreover, in my frame of reference, I can show that non-identity 'reasoning' satisfies the criteria for classification as more general than identity-based 'reasoning' -- or, identity-based 'reasoning' qualifies as a special case of non-identity-based 'reasoning'. 
Kenyon, although he calls himself an exponent of general-semantics, appears to me to belong to the "prefers identity" group.
DETAILS OF KENYON'S COMMENTARY
At this point, I turn and examine some of the details of Kenyon's commentary. I start with Kenyon's picture of "a non-identity language"; and then examine some of the comments he addresses to me, my frame of reference and the alternative notation I have generated.
A. Kenyon on "non-identity languages"
Kenyon, P. 43:
We often hear the cry, from us general semanticists, that the structure of our language is not i) similar to the structure of events. We use the extensional devices to remind us of this fact and bemoan the lack of a language with a structure similar to the non-verbal "reality". Let us examine what would happen if we try to devise a language with a structure which does ii) mirror the structure, as we understand it, of non-verbal iii) "reality", the event level. I shall show that such a language is impossible. ...
(i) Kenyon appears to use the term similar to the structure of in a non-standard fashion. As I have shown elsewhere, this term makes sense only with reference to a particular, specified or specifiable purpose.  For example, consider a given 'map' -- a hand-drawn line-map of an urban neighborhood, which you received along with an invitation to come to Marion, Ohio, and have dinner with me at my home. This map qualifies as similar to the structure of its 'territory' if and only if, by "following" the map, you find my home. If you "follow" the map and do NOT arrive at my home (or have to make a phone call for corrected directions), then for the purpose of guiding you to my home, the map does not qualify as similar to the structure of the territory. If you get mixed up and fail to "follow" the map, then the question of similar to the structure of receives no test.
Since Kenyon does not mention a specific purpose, he makes HIS term similar to the structure of sound like an "absolute". But that allows the possibility of using that term to imply that his "non-identity language" stands in an entirely accurate, exhaustively complete one-to-one relation to a unique, fixed "reality", such that every point of the 'reality' gets represented by one and only one point of the map, and no point of the 'reality' gets left out of the map. This locution spells out "an exhaustively complete, entirely accurate one-to-one relation," which here, in the context of the map-territory analogy , amounts to a relation of map-territory identity. At the very least, Kenyon does not rule this possibility out.
In my opinion, rigor in general-semantics consists in establishing, as unmistakably as possible, that the construct or text in question presupposes-and-follows-from non-identity -- ruling out map-territory identity. By my standards, in this passage Kenyon fails to show rigor.
(ii) Kenyon appears to use the term mirror the structure ... of as a rough synonym for similar to the structure of. Again, the way he uses it suggests map-territory identity (or at least, does not rule that possibility out).
(iii) In keeping with the way he uses similar to the structure of and mirror the structure of, Kenyon uses the term reality ("as we understand it") and events or event level in ways which suggest that he assumes the existence of some separate, fixed "really-real", an outside world which 'exists' prior to and independent of any observer.
My frame of reference does not posit any independent "outside world". Instead, it posits an underlying specific delimited setting. I can express this specific delimited setting in English by means of a run-on phrase such as ONE PARTICULAR organism-as-a-whole-dealing-with-its-environment-at-a-date; or by a single word such as transacting , or contacting . I and my associates posit "a world inhabited by organisms transacting with -- in contact with -- their environments." But instead of regarding "the organism" and "the environment" as separate THINGS, which occasionally collide with one another, we regard my environment as "the other side of my skin," and me as "the other side of the environment's skin."  With the Gestalt therapists Perls, Hefferline & Goodman, we say,
We speak of the organism contacting the environment, but it is the contact which is the simplest and first reality. 
And from this "simplest and first reality," this setting, we INFER organism and environment, or I and it, or I and thou, etc. These constructs, then, do not represent "independent reality," but rather, designate THE INFERRED.
Furthermore, the (inferred) organism guides her/his "doings" or "choosings" by sensory-derived and therefore intrinsically inaccurate, incomplete and self-referential 'maps' of the (inferred) 'territory' in question. Hence our 'organism' remains in principle inaccurately-informed, incompletely-informed, and self-referentially-informed about said 'territory'.
Kenyon, P. 43:
To strive for precision about what 'impossible' means in this context, we need to consider what we normally mean by 'language'. If by 'language' we mean a symbol system used for communicating, then a non-identity "language" is truly impossible. If, on the other hand, by 'language' we mean i) a token system satisfying certain structural rules, but having nothing to do with communication, then this kind of (un-interesting and useless) "language" may be possible to construct, but cannot be used for communication.
(i) Kenyon contrasts "a symbol system used for communicating" with "a token system satisfying certain structural rules." I hold the opinion that the construct of satisfying certain structural rules applies to any language whatsoever. Does Kenyon mean to imply that "a symbol system used for communicating" (whatever he means by the term communicating) does NOT "[satisfy] certain structural rules"?
When examined, Kenyon's example of contrasting types of "symbol systems" fails to support his point. If a symbol system follows "certain structural rules," then it encodes non-identity 'reasoning' -- it excludes some symbolic possibilities while including others -- and may prove useful to someone as a way of representing something. In fact, the history of mathematics contains numerous examples of abstract languages arbitrarily built up to satisfy certain arbitrary rules, which someone later found suitable as a way of representing some 'territory' which s/he needed to represent. I particularly remember the examples of the general theory of relativity and the calculus of tensors, and of quantum theory and matrix algebra.
Kenyon, P. 50:
(Remember, the language does not embody identity in any of its forms, and its structure mirrors physical "reality".)
If, indeed, the structure of the 'language' DID "mirror" physical 'reality', then it would probably drive its users to distraction. For example, it would not provide for editing the stream of speech, e.g. to remove pause vocalizations, false starts, etc., or for summarizing, digesting, distorting, or even commenting on what happens. In using the 'map', one would have to re-experience -- mirror -- THE WHOLE 'TERRITORY'.
Furthermore, before one can deliberately seek "to devise a language with a structure which does mirror the structure ... of non-verbal "reality"," one has to KNOW the structure of the "reality" in question. And that raises the interesting question of HOW one "knows" the structure of non-verbal "reality". Not to address the question amounts to taking the position that "I JUST KNOW how things REALLY ARE" -- a position familiar within the WIE tradition up until the revolutionary developments of the last century or so in geometry, mathematics, physics, etc. The revolutionary disciplines revolted against precisely that position.
In his hedging phrase concerning 'reality' "as we understand it," Kenyon neglects to say which "WE" he refers to. That suggests that he posits more unanimity among humans concerning how humans picture the worlds "we" live in than I can credit. For example, does Kenyon mean to include, within his "we," such non-WIE viewpoints as that of the African philosopher Kwasi Wiredu? While writing in English and publishing in refereed WIE philosophy/logic journals such as the Notre Dame Journal of Formal Logic, etc., Wiredu maintains his membership in the Akan speech community. The bi-lingual philosophy which he writes contrasts Akan and WIE constructs, and the markedly different World-Views pertinent to each. Where traditional WIE philosophers act as if they had attained "universality" in their search for "truth," Wiredu shows again and again that, from an Akan point of view, they develop instead a "parochialistic universalism" and arrive at "tongue-dependent truths". 
I suggest that Kenyon uses his hedging phrase to conceal (from himself, among others) the fact that he does not distinguish between WIE viewpoints and the larger construct ("domain") of human cultural viewpoints. Using the terminology of the blank delimited domain vs. the undelimited domain: within the setting of "human cultural viewpoints," Kenyon appears to blot out any awareness of the full scope of "human cultural viewpoints" by failing to distinguish between term-complement ("non-WIE views") and setting ("human cultural viewpoints"). And that in turn means that he relies on at least one usage of the disqualifying assumption of tacit identity, and so posits an undelimited setting in which the construct of WIE viewpoints stands opposed to everything else.
Meanwhile -- assuming that I have sufficiently understood what Kenyon says about "non-identity languages"), and have not COMPLETELY misunderstood and mis-stated the implications -- I find that I must (as I have just explained) nominally agree with Kenyon when he asserts that "... such a language is impossible." However, I do NOT agree that Kenyon's picture of a "non-identity language" accurately models the frame of reference or the notation which I have developed.
B. Kenyon's critical comments
Kenyon addresses my work, and mentions me by name, in at least 6 paragraphs. Each contains significant mis-attributions.
Kenyon, P. 48:
i) As part of the belief that lower levels of abstraction are "closer" to "reality", some general semanticists seek to devise languages with structures more similar to the structure of non-verbal "reality" (as we believe it to be) than is the structure of the language we currently use. When Korzybski indicated the extensional devices for use in pointing toward the region where non-verbal "reality" differs from our language structure, he started the trend among general semanticists.
ii) It would seem only natural that one of his followers continue the "implied" direction and attempt to design or engineer a language with a structure similar to non-verbal "reality" with the purpose of achieving the "ideal" Korzybski seemed to be pointing toward.
iii) Dr. C. A. Hilgartner (Andy) has spent 25 years of his life working toward exactly that goal.
iv) According to Andy, he has "built up [his] language theory three times and shot it down twice". Unfortunately, it's time for a third shooting.
(i) As I mention above (point (iii) made in replying to P. 43), my frame of reference does not -- I repeat, NOT -- posit any "external reality" at all.
(ii) NOT MY INTENTION. Originally, in 1963, when I first started writing in theoretical general-semantics, I set out to develop a theory of human behavior based on the non-aristotelian premises of Korzybski, to see what happens when someone takes non-identity seriously. Later (December 1971), I took on the task of elaborating a formalized notation based "from the very beginning" on the non-aristotelian premises. I regarded establishing what such a language might prove "good for" as a later task, possible only after first DEVISING such a language.
iii) NOT ACCURATE concerning my "goal." MY AVOWED INTENTION: to generate a theoretical system and notation based "from the very beginning" on the non-aristotelian postulates of Korzybski.
(iv) Kenyon misquotes me slightly. I have, indeed, publicly stated that I have shot down my theoretical system (theory of human behavior) twice and built it up three times. I don't know what Kenyon means by the term "language theory"; but, appropriating the term to mean what I might mean by it -- e.g. a theory which accounts in a comprehensive manner for the observable details of one or more of the natural or discursive language(s) -- I never claimed to have a "language theory," and don't claim that now.
By the way, I consider the distinction between a traditional "natural" language and a formal, self-conscious notation important. Speakers of a natural language must find themselves able to speak about "everything" -- at least, "everything" that bears on their individual and social survival -- whereas the speakers/writers of a formal system find themselves able to discuss NOT MUCH, while discussing that little RIGOROUSLY. Although he ostensibly criticizes my NOTATION (no one has yet invented/created a DISCURSIVE non-aristotelian language), Kenyon scarcely mentions this distinction.
Kenyon, P. 48:
i) I regret to report that a careful analysis of the problem shows that the difficulty with creating such a language is more than just a technical matter. It is, in principle, flawed by a misconception regarding what language does for us; in short, the task is not possible.
ii) Andy keyed on certain of Korzybski's insights and attempted to design a language which satisfies several general-semantics notions and principles. To take the observer into account was a goal that seems to be achieved. iii) Moreover, to embody the notion of abstracting so that that which is selected is indicated (easy) and that which is not selected is also indicated (not so easy) seems to have been incorporated.
iv) However, when Andy claimed to have built non-identity into the language he went too far. According to Andy, his new formal language "disallows" identity in all three forms. Even if such a goal were desirable, and there is significant question regarding whether it is, Andy has not achieved it.
(i) Kenyon does not PRESENT his "careful analysis" in his paper, not here and not elsewhere. That makes these two sentences into an unsupported assertion -- one of many contained in his paper. Furthermore, by "nesting" the phrase what language does for us within a dependent clause, Kenyon conceals a claim which I believe he cannot back up -- namely, that HE has NO misconceptions concerning "... what language does for us ...." To have NO misconceptions on a particular topic, in my opinion, remains possible if and only if one's views on that topic -- one's 'maps' -- show map-territory identity with whatever "happenings" make up that topic (the relevant 'territory'). In accordance with my chosen premises, I deny that possibility.
(ii) NOT MY INITIAL GOAL -- later, we noticed that what we had written accomplishes that.
(iii) Kenyon misunderstands the constructs of Gestalt and polar. What he says here implies that the figure and background of a Gestalt "exist" as independent "things", which occasionally bump into one another -- in other words, as noun-forms or noun-phrases governed by Aristotle's Law of Identity. Thus he regards it as "easy" to indicate "that which is selected," but "hard" to indicate "that which is not selected." But when someone uses the Gestalt terminology correctly, the constructs of figure and background function in a polar fashion: one of them cannot "exist" or "occur" without the actual or implied "existence" or "occurrence" of the other. Thus "background" BOUNDS "figure," and "figure" bounds "background" -- they mutually determine each other. I can express what we humans DO in terms of sensing, feeling, moving; and whether you notice or not, I assert, every moment of your own sensing, feeling, moving has the structure of a Gestalt: a figure of focal interest to the organism (you), against a background relatively empty of interest. "Easy" and "hard" have no relevant meaning in this context.
(iv) The notation I have developed precludes "confusion of orders of abstractions", recognizes the impossibility of the static-and-unchanging, and systematically includes the observer -- in other words, it disallows Identity in any guise or form, explicit or tacit. Kenyon may disagree with me concerning the value of this achievement, but the fact that he limits his discussion to explicit identity does not grant him grounds to deny that I have made progress in this area. Indeed, if I have made no progress here, what has him so upset?
The insights Andy used to provide direction for his effort seem to be good ones, and may be used in enhancing our consciousness of abstraction;
i) they can even be used to develop a formal language which does allow identity1 and identity2.
ii) No language, however, can be engineered in such a way as to completely eliminate identity3 because that form of identity is not always a function of the structure of the language. It takes place in the nervous system at lower levels of abstracting than verbal. Even flat-worms do it.
iii) The structure of our language can not change the fact that we see the trapezoidal window as oscillating when it feels to be rotating. My earlier discussion has shown that identity3 is a general activity of nervous systems and not a property of language structure alone.
iv) One cannot engineer a language with a structure that always prevents what happens at neurological levels.
(i) NOT THE GAME I PLAY -- as I said above. If you start by disallowing/disesteeming Identity, and end up allowing identity1 and identity2, that means you have made a MISTAKE.
(ii) "Even flatworms do it." -- Do WHAT?
If Kenyon means "recognize food, etc., and ingest it so as to stay alive," of course flatworms do such things. But those activities represent something entirely different from the two kinds of identity -- explicit and tacit -- which I discuss in my writings.
Perhaps Kenyon means that we can "train" flatworms to behave in certain ways unusual for flatworms (something I have some familiarity with -- back in 1962-64, while collaborating with E. Roy John at the Center for Brain Research of the University of Rochester, I supervised some of the 'conditioning' research on flatworms). However, I maintain that no flatworm of my acquaintance ever attained much by way of linguistic skills. I don't recall seeing even one of them striving to develop and use a formal language, much less making, or not making, fundamental errors in the course of using one.
Maybe Kenyon means something else entirely. But since he doesn't say what he does mean, his triumphant short sentence sounds less like a carefully thought out statement and more like a battle-cry:
Humans must identify!
(in whatever sense of the term identify Kenyon intends here).
Korzybski introduced the construct of "copying animals in our nervous reactions". Humans can act more or less like animals, but animals can't copy humans in their nervous reactions. Kenyon seems not to have taken that insight into account here.
(iii) Kenyon's comments about the trapezoidal window, if I have successfully untangled them, attribute to me the opinion that a properly-constructed, "identity-free" language would allow its users to avoid getting "fooled" by the trapezoidal window -- it would enable them to see "what really happens." In fact, I have dealt with the trapezoidal window in great detail -- in notation.  Not only have I made no such claim, I have gone to the other extreme, and shown what a human can learn by accepting and reconciling the contradictory sensory messages given by visual and tactile modalities concerning the trapezoidal window.
Kenyon appears not to recognize that the construct of "what really happens" posits tacit identity (in the guise of a total isomorphism between "what ACTUALLY happens" and "what we SAY happens").
I hold that any human CAN and sometimes DOES manage (in Kenyon's words) to avoid "react[ing] to one level of abstracting as if it were another level of abstracting" -- and that where s/he does not so manage, the consequences may turn out life-threatening. Furthermore, I published a paper containing a worked example taken from my own behaving-and-experiencing in which I demonstrably started out making a fundamental error of this type, and ended up revising my own assumptions so that I ceased making that error (and found other things to do instead).  By disclosing and testing the assumptions underlying my own non-survival-oriented behavior, and replacing them, I practiced what I regard as non-identity 'reasoning'. For me, the assertion that "identity3 is a general activity of nervous systems" appears already disconfirmed.
(iv) I should say not! WHO asked "Language" to do THAT?
Kenyon, P. 49:
i) It is only through our use of language to build a complex model of the abstraction process that we can point to where in the model of that process identification3 takes place. The language in which we build this structure has terms which are self-identical (identity1), and it includes various verbs which allow identifying2 and identifying3.
(ii) 'To be' is popular because it does both jobs, verbally representing the processes that we undergo predominantly at non-verbal levels. The very model itself is a complex organization of many distinct instances of the process into a relatively invariant structure.
(i) Once more, Kenyon asserts -- rather than demonstrates -- that "language" requires that its users "prefer" identity (and never mind about non-identity) -- that IS the way 'things' REALLY ARE.
(ii) This example seems particularly funny, in light of the fact that, for more than 20 years, I have made it my practice to write in (my variant of) Bourland's 'E-prime' -- "The English language minus all forms of 'to be' (e.g., am, are, be, been, being, is, was, were, ain't, I'm, aren't, isn't, wasn't, weren't, etc.)."  What, then, do Kenyon's comments in this passage have to do with my discursive-language writings -- much less, with my notation?
I know that Kenyon once knew that I write in E-Prime, because in the past he has chidden me about doing so, and generously advised me to return to using 'to be'.
Apparently he forgot something here.
i) Andy says we should build a language whose structure neither embodies nor allows any of the three forms of identity.
ii) Well, any term or symbol must embody identity1, (if it is to be written more than once).
(i) As far as I can remember, I have never written about "the three forms of identity." That terminology came through to me as new in Kenyon's paper. I have used phraseology of more general scope than that, rejecting identity more comprehensively than Kenyon appears to regard as possible, e.g.
"As my most fundamental premise, I reject identity in any guise or form, explicit or tacit." 
Kenyon discusses only EXPLICIT 'identity', sub-dividing it (as he says) into three variants.
(ii) As for "writing "the same" term more than once", Kenyon appears to confuse continuity with identity.
Korzybski makes it lambently clear how we can manage to generate "similarities" without relying on the construct of 'identity'. He writes,
In simple words, we obtain similarities by disregarding differences, by a process of abstracting. 
Not only do we choose to ignore differences, we also choose which differences to ignore.
Consider a particular example of a written stream of speech, and a particular person reading this stream of speech at a particular moment of her/his lifetime. Take the present paragraph, from the initial word "Consider ..." to the period at the end of the present sentence; and take a particular "word," e.g. speech, as our focus -- our term1. How can someone read it more than once without 'identifying' it as "THE SAME term"?
By the trick of first designating my term1 toward the end of sentence two of the three-sentence paragraph, I have insured, as best I knew how, that you will re-read the passage in question; and will do so with a discernably different purpose the second time than you had the first time you read that passage. For you, to re-read the word speech, as you try to find every usage of it in the designated passage, might "feel different" than it did to read it for the first (and second) time in the course of reading my text initially. Thus usage3 of term1 (say, when I designate it) discernably differs from usage1, IS NOT usage1 (or usage2), of term1 -- nor, when I index them, do I give them "the 'same' name." To "identify1 them as "the same term"" focuses on SIMILARITIES ONLY, and asserts that these 'similarities' REALLY EXIST, "OUT THERE." When I send my eyeballs skipping down the lines of print, I can USE usage1 at its proper place in the "chain of argument," and can also USE usage2 at ITS proper place in the argument, etc., acknowledging both the absolute uniqueness of each and the similarities between them. However, as a "good" exponent of general-semantics, I insist on relying on non-identity reasoning -- I insist that the 'similarities' don't "exist OUT THERE." Rather, I create those 'similarities', for my own purposes, in the process of reading the "chain of argument."
Andy Hilgartner characterized words as being self-identical, and therefore not having a structure similar to "reality" (which we characterize as continually changing).
Funny -- I thought that usually, I assert not that "words" ARE self-identical, but rather that native speakers of Western Indo-European languages such as English TREAT their "words" (especially, their noun-forms or noun-phrases) as self-identical, and PRETEND, or ASSUME, that there exists an external "reality" for their "words" to correspond perfectly to.
Kenyon, P. 50:
The business of life consists in organizing our life experiences into a categorization scheme so that that scheme may be used to effectively respond to future life situations. In this scheme, experiences in one category are identified2 as being "the same".
While they are not the same, the degree to which they differ does not make a noticeable difference in terms of our responding behavior.
Also, our individual responding behaviors will differ from time to time, but often not to the degree that our classification scheme need be changed.
Here Kenyon completely undercuts what he appears to say in the rest of his paper. He admits in so many words that his categorization scheme rests on already-discovered error, of which he remains aware. He asserts that, "In this scheme, experiences in one category are identified2 as being "the same"." Then he admits that this identifying encodes a mistake: "WHILE THEY ARE NOT THE SAME, ..." Then he proceeds to "explain away" his acceptance of this already-discovered mistake, on the grounds of the indiscriminateness of the behavior of those who use this traditional framework: "... THE DEGREE TO WHICH THEY DIFFER DOES NOT MAKE A NOTICEABLE DIFFERENCE in terms of our responding behavior." (emphasis mine)
Finally, with his phrase to the effect that, "... our individual responding behaviors will differ from time to time, but often not to the degree that our classification scheme need be changed," Kenyon appears to call for a kind of rigidity, "hardening of the categories." This phrase does not suggest to me that Kenyon holds himself in readiness to take a single disconfirmation as conclusive, requiring the rejection of the hypothesis ("classification scheme") in question. Instead, he implies that he expects to decide which hypothesis to regard as disconfirmed by some kind of majority vote, or by dismissing views which deviate from the bias of some preferred traditional viewpoint, etc. Experimenting with a more flexible system might provide advantages.
Kenyon, P 50:
In practice we will periodically revise both the classification scheme for organizing our experiences as well as that which organizes our behavioral options, but for some periods of time the categories will be unchanging. During such periods each category will be self-identical (identical1 to itself)."
In contrast, I say: we DISREGARD CERTAIN OF THE DIFFERENCES, and so create 'similarities'. THE 'SIMILARITIES' DON'T EXIST 'OUT THERE'.
Kenyon, P. 50:
When we communicate with others, what is of interest as time-binders is sharing with them information about our individual categorization schemes themselves.
We will cite examples in the process, but that which constitutes time-binding is the passing on of the information we have learned about organizing our life's experiences. We talk about the self-identical categories themselves."
I find it impossible to define time-binding without the construct of self-correcting -- "generating, testing and judging hypotheses or guesses", etc. And self-correcting requires the assuming of map-territory non-identity. (I deny that we can -- or should -- hold categories as self-identical.)
Kenyon, P. 50:
"Now, a language which has self-identical terms is ideally suited for communicating about such a category scheme, in which the categories are self-identical. However, a language in which there are no self-identical structures cannot communicate about anything that is self-identical. Every "correct" expression in the (non-identity) language would have to be unique. (Remember, the language does not embody identity in any of its forms, and the structure mirrors physical "reality".) Since there are no self-identical structures in such a language, there is no way to refer to self-identical categories. Therefore, the language cannot be used to talk about the very things which are of the most interest in time-binding. Since no two expressions are the same, nothing can be expressed twice. And, since we cannot express anything more than once, it can never be talked about again. In a nutshell, a language without "identity" cannot be used for communication. Bob Pula has been expressing a concern over the past several years as to what totally non-identifying persons would be like. Well, totally non-identifying language users cannot be time-binders, because they cannot communicate."
Two of my closest collaborators teach linguistics (Ron Harrington, and Martha Bartter). They tell me that they, in common with most linguists, agree as to how to delimit what the term language designates: People DO language. People do it so as to "communicate" (an explicitly purposive term), by socio-cultural (time-binding) AGREEMENT. And they can and do change this agreement: Every time humans speak and listen, or write and read, they alter the agreements of language to some degree. However, most linguists agree that they don't know what language IS, or even what language has to "have" in order to "communicate." They do agree that all languages so far examined work by context and a series of perceivable differences. When a speaker speaks, her/his "words" NEVER come out the same way twice, even to a casual observer. A hearer can understand what a speaker says because the hearer HEARS differences (e.g. the differences between 'pat' and 'pad', including the phonemes /t/ vs. /d/ -- as shown by minimal pair analysis), and "language" uses highly redundant spoken forms to repeat "information" that might otherwise get lost (hearers "rectify the signal-to-noise ratio" by a kind of self-correcting experimental logic).
In other words, EVERY INSTANCE of a given "word" qualifies as UNIQUE -- differs discernably from other instances. Human speaking and hearing, writing and reading appears to operate by precisely those non-identity strictures which Kenyon asserts would "make communication impossible."
Kenyon, P. 50:
"On the other hand, suppose the language was modified so that one expression could be "correctly" written more than once. Since the second writing is the same expression as the first writing, the language is embodying the very identity it is supposed to prevent."
See Korzybski's argument on 1 = 1 . Furthermore, here Kenyon offers us a model of "rigorous reasoning", which goes like this:
a. Set up the rules you intend to follow, and build up your system.
b. Arrange to break your stated rules.
c. Conclude: "Look! The system breaks its own rules!"
Kenyon ends his discussion by saying that "This paper has shown several results:" He then presents as conclusions three sentences which look remarkably similar to various assertions he makes in his paper and fails to support.
In summary, I say:
When Kenyon speaks of "Hilgartner's work," I haven't ANY idea of what he sees, or what he means.
I reconcile the conflicting claims concerning what (I believe) I've done and what Kenyon SAYS I've done by documenting what looks to me like the lack of a connection between the two -- no connection, period.
For over ten years, I have repeatedly told Kenyon, "You appear fundamentally to misunderstand what I intend, what I have done, where it heads," and so on. Kenyon's comments on my writings, often detailed and technical, still continue to come through to me as having a tone of, "Oh, no, I understand perfectly -- and you're doing it wrong."
I don't intend to take on the job of telling Kenyon what to believe, or assume. (To me it does seem that he "likes" identity rather than non-identity.)
But I prefer that he not ascribe his views to me.
Meanwhile, I hold that where Korzybski advocated "the complete elimination of 'identity' and identification," he meant it. Not merely where convenient, and not solely within some restricted domain, and not just as a caution, in order, in Kenyon's words, to "help us remember that we can identify" -- but rather, as the most basic foundation for our living.
Korzybski's analyses deal mainly with examples from daily life and from ordinary discursive language. As a contrast to the patterns he finds there, he holds up the geometry, mathematics, physics, etc., of his day. In my analysis, the revisionist science of the first half of the twentieth century demonstrably encodes one less usage of tacit identity than does classical science, for its advocates discriminate between term complement and setting, and so posit a blank delimited domain instead of an undelimited domain as the setting for their proposals.  Hence Korzybski's esteem for these disciplines seems warranted. But Korzybski also foresees the possibility of a non-aristotelian revision of our science in particular, and of human knowledge in general. 
Now my own work (building on Korzybski's summary and extension of the advances embodied in those revisionist sciences) offers further development in the direction of non-aristotelian systems and non-identity 'reasoning'. I claim to have disclosed a previously unnoticed usage of tacit identity encoded in the grammar common to both the WIE discursive languages and the WIE logical, mathematical, scientific, etc., languages.  Less politely stated, that means that the WIE logics, sciences, etc., include among their premises a hidden untenable assumption, a reliance on the disqualifying assumption of tacit identity. And as Korzybski points out, any reliance on identity, at any level, tends to direct us away from our own survival. Clearly, under the guidance of the currently available, identity-based science, we have thus far continued moving toward species suicide and annihilation of the biosphere, instead of toward mutual fostering of our health as a species and the health of the biosphere -- toward the enhancement of the realm of the living.
The discovery of that hidden usage of tacit identity opens the way toward eliminating that untenable assumption -- toward developing an alternative formalized notation, consistently based "from the very beginning" on the non-aristotelian premises of Korzybski. Such a notation has to start from considerations more fundamental than, and logically prior to, the presuppositions which traditional WIE logicians, mathematicians, etc. regard as the most basic of beginnings. I claim to have developed such a notation.
This discussion highlights a clear choice in general-semantics. So far, the general-semantics community represents the only portion of the human race which has even toyed with the possibility of consciously practicing non-identity 'reasoning'. But up until now, the efforts to explore non-aristotelian systems and non-identity 'reasoning' have taken place within a setting based on unrecognized usages of the disqualifying assumption of tacit identity. These have rendered the best efforts of the general-semantics community to practice rigorous non-identity 'reasoning' self-contradictory and ineffective.
Now, assuming that my analysis of the structure of the WIE grammar turns out not entirely mistaken, we exponents of general-semantics do have a choice: We can continue clinging to the unexamined identity-based doctrines of the past, and continue moving in counter-survival directions -- or we can seek to implement "the complete elimination of 'identity' and identification." As a way-station, we can accept and espouse the developing doctrine of non-identity, and risk trying to turn the species in pro-survival directions. The task before the human race, if we want to survive as a species well into the next century, includes criticizing and re-working the current versions of the identity-based WIE logic, mathematics, physical science, life science, philosophy, jurisprudence, religion, etc. As Korzybski foresaw so clearly, we humans have come to a point in our development where we need to re-work and re-formulate the entire body of human knowledge, the time-binding heritage -- and have also come to a point where it seems possible to do so.
REFERENCES AND NOTES
 In the order of their composition, these include: a) Hilgartner, C. A.(1977/78). "Some Traditional Assumings Underlying Indo-European Languages: Unstated, Unexamined, and Untenable." General Semantics Bulletin Nos. 44/45, pp. 132-154. b) -----, (1978a). "The Method in the Madness of Western Man." Communication 3:143-242. c) -----, (1975). "A New Formalized Language Based on Entirely Non-Traditional Premises." (Unpublished.) d) Hilgartner, C. A. & Ronald V. Harrington (1977). "Non-aristotelian Numbering." (Unpublished.) e) Hilgartner, C. A. (1978b). Appendix V to ""International" or 'One-World' Languages: "You Can't Get There from Here"." ECO-LOGOS: A Magazine of ONE-WORLD Environment Concepts, Vol. 24, No 90. f) -----, (1980). "A Complete Severance from Traditions." Presented at the Centennial Conference on General Semantics, New York City, 27 October 1979. Printed in General Semantics Bulletin No. 47, pp. 112-9.
 The non-aristotelian postulates of Korzybski include, as undefined terms, structure, order, and relations, and as postulates, Non-identity, Non-allness, and Self-reflexiveness. Instead of using the undefined terms to state the postulates, here, for the sake of intelligibility, I'll state them in terms of the map-territory analogy, as presented in footnote 11.
Non-identity: Presume that the map IS NOT the territory for which it stands.
("The word is not the thing it stands for.")
Non-allness: Presume that no map includes representations of ALL the characteristics of the territory.
Self-reflexiveness: Presume that no map exists free of some kind of representation of the map-maker.
The cautionary principles expressed by postulating map-territory non-identity, non-allness and self-reflexiveness underlie the scientific method and make it the most devastating form of criticism yet devised. Remember, the scientific method can accomplish one and only one thing: To provide a basis for selecting between guesses. In a fully specific setting (e.g., with reference to such and such kind of happenings, as tested by these specific methods, as judged by this criterion), it can either show one's hypotheses, assumptions or other guesses as in error; or else, THIS TIME, can find nothing wrong with them. It cannot prove them true for now or forever. Whenever one violates the tenets of non-identity, non-allness, and self-reflexiveness, one thereby allows the possibility of starting from already-discovered error, and thereby predictably reduces the predictability of one's guesses (maps).
The expression inaccurately-informed, incompletely-informed and self-referentially-informed stands as shorthand for "relies on the non-aristotelian premises of Korzybski."
 Korzybski, Alfred (1933). Science and Sanity: An Introduction to Non-aristotelian Systems and General Semantics. Non-Aristotelian Library Publishing Co., Chicago, p. 194.
 Korzybski, 1933, p. 187.
 Korzybski, 1933, p. 194-5.
 Webster's (Second) New International Dictionary of the English Language Unabridged, second edition, p. 1236. Springfield, MA: G. & C. Merriam, 1961.
 Hilgartner, 1977/78.
 Newton, universal gravitation, and non-identity: Exponents of general-semantics sometimes criticize Newton for his identity-based reasoning, as manifested in his constructs of absolute 'space' and 'time' and the hidden assumption that light propagates at an 'infinite' velocity. I maintain that in generating his contributions, e.g. his system of mechanics, Newton utilizes non-identity 'reasoning'.
Prior to 1665, the commonly held, unquestioned view or map maintained that "Things like balls or apples just naturally fall, while the Moon naturally stays up there -- that's the way things are."
Unquestioned here means that those who held the view did not treat it as a provisional construct, but rather, tacitly treated this map as somehow identical with the territory. Galileo and others had done earlier work dealing with topics in mechanics, including problems involving falling objects. But in 1665-6, we know of no one besides Newton who had considered that the moon could fall, much less asked how come it didn't.
Exponents of our alternative frame of reference describe human "doings" or "happenings" in the Gestalt terminology of a figure of focal interest to the human in question, against a background relatively empty of interest. In sequential "doings", an earlier Gestalt becomes the background against which a new figure develops, to produce the next succeeding Gestalt.
In effect, in developing the construct of universal gravitation, Newton changes what he assumes. His first Gestalt in the relevant sequence has as its background the traditional view, which tacitly assumes map/territory identity; and has as its figure, a questioning of the traditional view, which in effect distinguishes between map and territory: What if the commonly held view amounts to only a surmise, instead of expressing 'the way things really are'? This Gestalt then becomes the background of the next Gestalt encoded in Newton's insight. In expressing its figure, Newton devises an alternative map: What if the ball (or apple) and the Moon BOTH fall -- and the apple reaches the surface of the earth whereas the Moon doesn't. How would I account for that?
Newton immediately sought some test which would give him convincing grounds for selecting between the two views -- he resorted to astronomical facts and to computations, using his brand-new theory of fluxions (or as we now call it, the calculus), to choose between the traditional view and his alternative. From data he had on hand, he computed the centripetal force on the moon (the force drawing it toward the center of its orbit) produced as a function of the gravitational attraction to the earth, and the centrifugal force (the force on the moon drawing it to fly off away from the center of its orbit) produced as a function of the moon's mass, the distance between the centers of earth and moon, and the moon's period of orbit.
Newton solved for that value for the period of the moon which would make the centrifugal force equal to the centripetal force. His first rough calculation gave the period of the moon close to its true value, about 27.25 days. (Bronowski, Jacob (1973). The Ascent of Man. Boston: Little, Brown & Co., 1973. Paperback edition, London: Futura, 1981, p. 142)
Thus, to use the language of assumptions, Newton made his advance by replacing (at that point of his theory, at least) one usage of the tacit assumption of map-territory identity with a usage of the assumption of map-territory non-identity.
 We can express the criterion of logical generality as follows:
Given: A concerted body of observations, and at least two theories, C and D , which purport to account for (at least some of) these observations. Then we can show D as more general that C if the following conditions hold:
a) That we display a restricted and restrictive assumption Z ;
b) That we show that Z forms an intrinsic part of the premises of C and no part of the premises of D ;
c) That by introducing or eliminating Z , we can inter-convert between C and D . Specifically,
i) By systematically introducing Z into the premises of D , we can collapse it into a structure logically equivalent to C ;
ii) By systematically eliminating Z from the premises of C , we can expand it into a structure logically equivalent to D .
 Hilgartner, C. A & John F. Randolph (1969a). "Psycho-Logics: An Axiomatic System Describing Human Behavior. 1. A Logical Calculus of Behavior." Journal of Theoretical Biology 23:285-338, p. 302.
 The Map-Territory Analogy: Seeking to make his non-standard system accessible to his readers, Korzybski puts forth an image which focuses on the relations between a map and the territory which it (allegedly) represents. I interpret his image as an analogy which compares the construct of living to the process of map-making: To say that an organism lives means that it generates 'maps' of that 'territory' composed of what goes on in and around the organism, and then it guides its doings and choosings by its maps. Further, I hold that this analogy implicitly puts forth the setting which underlies my korzybskian theoretical system. Here let me develop the map-territory analogy into a way of connecting between a) the term-pair identity/non-identity and b) the behaving-and-experiencing of humans.
When one uses a map to guide one's behavior, one can in principle distinguish, or neglect to distinguish, between map and what the map refers to. Where one neglects to distinguish between them, I regard this as undiscriminating and refer to this kind of undiscriminating as postulating map-territory identity. This neglect manifests itself in a) treating the territory as a "closed" and, to a first approximation, completely-known system, and b) treating the map as if it yielded some kind of "absolute certainty"; and in c) holding oneself unwilling even to consider questioning, testing or revising the map. At the other extreme, one can consciously distinguish between map and what the map refers to. I regard this as discriminating and refer to this kind of discriminating as postulating map-territory non-identity. This discriminating manifests itself in a) remembering to treat the territory as "open" and in principle unknown, and in b) treating the map as more or less tentative and approximate, as incomplete, and as created from one's own point of view for one's own purposes; in c) remaining willing to test the map for accuracy; and in d) holding oneself in readiness to revise it at need.
 Modified after Dewey & Bentley, who distinguish between
i) the mechanical, one-way interacting characteristic of the non-living. Since non-living systems engage in no "doings" or "happenings" more elaborate than having a shape, a physical state, etc., mechanical interacting can produce no alteration more profound than changes of shape, of physical state, etc.; and
ii) the organic, two-way transacting of characteristic of living systems. Such transacting leaves both participants fundamentally and profoundly altered, in some sense that affects the further living of the living system(s) involved.
(Dewey, John & Arthur F. Bentley (1949). Knowing and the Known. Beacon Press, Boston. Paperback edition, 1960.)
 Perls, Frederick M., Ralph Hefferline & Paul Goodman (1951). Gestalt Therapy: Excitement and Growth in the Human Personality. Julian Press, New York, pp. viii-ix, 227-8.
 Hilgartner, C. A., M. A. Bartter & R. V. Harrington (1988). "To Improve Predicting in the Study of Living Systems." Presented at the Annual Meeting of the Ohio Academy of Science, 30 April 1988.
 Perls, Hefferline & Goodman, 1951, p. 227-8.
 Wiredu, Kwasi (1980). Philosophy and an African Culture. Cambridge: Cambridge University Press.
 Hilgartner, C. A. & John F. Randolph (1969b). "2. The Structure of 'Unimpaired' Human Behavior." Journal of Theoretical Biology 23:347-374, pp. 348-356.
 Hilgartner, C. A. (1963). "General Semantics, Psychotherapy, and he Logic of Science." Unpublished ms; revised 1967. Truncated version, ETC.: A Review of General Semantics 25:315-324 (1968).
 Bourland, D. David, Jr. (1965/66). "A Linguistic Note: Writing in E-Prime." General Semantics Bulletin Nos. 32 & 33. Also, E. W. Kellogg, III. (1987). "Speaking in E-Prime: An Experimental Method for Integrating General Semantics into Daily Life." ETC: A Review of General Semantics 44(2):118-28.
 Hilgartner, 1977/78, p. 132.
 Korzybski, 1933, p. 165.
 Hilgartner, C. A. 1978a, pp. 217-221.
 Korzybski, 1933, pp. 7-18, especially 17-18.
 Hilgartner, 1977/78.