C. A. Hilgartner



I present not just a new 'idea', but rather, an actuality - a frame of reference new to the human race, and now ready for us humans to use.

I consider it a notational language - or at least, as including a notational language - of the "Let's Keep Track of What We Say" type. Please regard it not merely as different in detail from other notations, but as structured according to previously unheard-of principles.

To flesh out this frame of reference, I present some details concerning how it developed - how I happened to make some of the discriminations or distinctions (non-identities) on which its structure crucially depends. Then I present some of its implications, including that:



Today, I intend to tell a story about languaging, or "language", and about story-telling, and stories. In fact, I've already begun.

I divide my story into six "chapters" -- the first of which tells about story-telling.


Literary critics have a phrase which they use to point to a type of behavior which underlies any individual act of telling-and-listening-to stories, or writing-and-reading stories. It also underlies each and every cultural tradition or social institution of storytelling.

They call this behavior the willing suspension of disbelief.

Any storyteller must ask her/his audience to somehow suspend disbelief, and the audience MUST do it. Otherwise -- no go!

To expand the scope of these remarks a bit, the novelist Daniel Quinn defines a culture as "a group of people enacting a story." In other words, if we humans had no ability and skill in suspending disbelief - we would and could have no cultures.

These remarks apply also to scientists examining a scientific statement. We stiff-necked specialists have strict rules concerning just WHO we'll accept as "possibly a storyteller", and what KIND of stories we'll listen to, and under just what conditions we will and will not suspend disbelief, will or won't accept. In general outline, these remarks apply in particular to this gathering here-now.


My story centers about the construct of fundamental theoretical error.

In company with the Gestalt therapists Fritz Perls, Ralph Hefferline & Paul Goodman, I believe that any human who subscribes to what I would call a fundamental theoretical error has to work pretty hard to maintain her/his erroneous opinion. In opposition to such an error, the evidence appears "everywhere", so to speak, and will get noticed unless our mistake-maker will not or cannot notice it. Maintaining a mistaken view requires great skill and, above all else, tenacity. And it has to have a "payoff" -- as Perls, et. al., put it

In my story, the "payoff" of the fundamental theoretical error that most interests me consists of remaining "in synch" with the currently dominant world culture, subscribing to its fundamental theoretical errors.

My story accepts as a presupposition a story told by Alfred Korzybski (1879-1950), which tells about how he disclosed the great-grandmother of fundamental errors. I like to re-tell his story by saying that Korzybski generated a fundamental question, and found it necessary to take a quick tour of the universe to answer it. To paraphrase his question: "In a cosmos which has human observers in it, when and where may we legitimately use the logical construct of identity? Where and when does the notion of absolute sameness in all respects, or negation of difference prove valid? Under what circumstances does it apply?"

Korzybski returned from his quest with an answer to his question. His considered opinion: Never. Under no circumstances does identity survive scrutiny.

And then Korzybski makes an outrageous suggestion: Since identity never holds, he says, let's not rely on it.

Korzybski proposes that we reject identity -- disallow it as a valid "relation".

In fact, he claims that to subscribe to identity as a presupposition -- to rely on it in any way -- amounts to engaging in the archetypal example of "a human making a mistake."

I found a way to state this insight in more general terms, making use of the construct of term-pair -- in our narrative, exemplified by the pair identity/non-identity. I found that we have not one but at least two ways to handle the paired terms, identity and non-identity:

Having recognized this choice, any human who uses this term-pair, overtly or covertly, must choose which way to use it. Korzybski himself takes a stand, rejecting identity -- as do I.

Korzybski showed that the logical construct of identity embeds the ultimate error, and proposed that we refuse to rely on it - but he did not show us how to do that.


Here, I shall tell of a turning-point in my own research career, in which I confronted the unavoidable necessity to break with any and all traditions.

Let me begin with the anthropological linguist Benjamin Lee Whorf, who points out that

Among the "specializations" of the WIE type of language, I include the WIE logics, mathematics, sciences, philosophies, jurisprudences, religions, etc.

Let's "unpack" Whorf's aphorism. In another place, Whorf says,

To see what that means, consider first a discursive language of the western Indo-European (WIE) family, such as English. To generate a "complete sentence," a speaker or writer of such a language must place at least one "substantive" -- noun or noun-phrase -- next to at least one verb or verb-phrase: In a notational language, e.g., a logical or mathematical one, we use the construct of "well-formed formulation" (WFF) in place of the "complete sentence" of a discursive language.

In such notational languages, we usually do not use the terms noun (or substantive) and verb; rather, we use more restrictive terms such as things and relations between things, or objects and their attributes, or quantities and operations, etc. Then, in a symbolic logic or one of the mathematical theories of sets, for example, we generate a WFF by placing at least one "thing" next to at least one "relation", or a "quantity" next to an "operation", etc.:

These linguistic platitudes came sharply into focus for me after I found myself in an impasse. Almost a decade previously, I had started writing an original theory of human behavior, based on Korzybski's non-aristotelian premises. In striving to create a framework in which I could do my exploring with full mathematical rigor, I had found a friend. Collaborating with the late John F. Randolph, then Fayerweather Professor of Mathematics at the University of Rochester, I had found a way to state the non-aristotelian premises set forth by Korzybski in notation - in an algebraic dialect of the mathematical theory of sets. Thereafter, I treated that notational version of the non-aristotelian premises as my most fundamental presuppositions, and generated a set theory calculus of human behaving-and-experiencing. Thus I managed to write up my findings, the "content" of my theory, in a WIE mathematical language.

I became aware of having come to an impasse when I started looking at the foundations of my theoretical system. I faced the fact that I had used a WIE notation, which includes the modern Logical Axiom of Identity among its premises, to express the content of my theoretical system, which rejects identity. That sounded to me like a contradiction, of a kind not previously described -- one that arises between the presuppositions of the content of my theory and the presuppositions of the notational language I used to write up that content.

Having noticed that contradiction, I had spent several months trying to find some way around, under, over, beside, or through it -- without success. Eventually, I had recognized that I either had to solve a knotty problem, or quit: I had to find some way to abandon the mathematical theory of sets, and all other WIE languages -- and, from my chosen (non-aristotelian) premises, to generate a new notation and/or language framed so as to make it (them) strictly consistent with the "content" of my theory of human behaving-and-experiencing.

To get out of my impasse, I had to effect what Whorf calls "a complete severance from traditions." (Whorf, 1956, p. 247)

[Acknowledge Don Watson's comments on breaking with traditions.]

So I tried generating a non-WIE notational language. After some six months of failure and frustration, I had to face it -- I didn't know how!


Shortly after I had recognized that I didn't know how to write a non-WIE notational language, I received an invitation from a particular person, a physicist whom I shall call The Professor, and his eclectic research group. They asked me to give a 20 minute talk.

To begin my talk, I stated the fundamental question which my theoretical system asks and answers; and then I stated my most fundamental premise.

Fundamental question:

My audience seemed quite comfortable with this question. Then I emitted one more sentence, expressing my

Most central premise:

Suddenly, I found twenty-five people pounding on their desks and yelling at me.

They continued their pounding and yelling for over ten minutes.

Then The Professor stood up, and everyone else fell silent. He strode to the blackboard, drew several capital letters and drew squiggly lines from one to another, and embarked on a soliloquy on "States and Relations" in physics which lasted for another ten minutes.

Eventually, a graduate student raised her hand and, without waiting for anyone to recognize her, sang out, "If we keep arguing with his major premise, we'll never get to hear his results." At that, everyone fell silent, and The Professor sat down. I proceeded to give my talk. It seemed to me that no one heard a word I said. When I gave the non-verbal cues that I had finished talking, everyone got up and shambled out like zombies, without further acknowledging my presence.

Meanwhile, I had a new and astonishing observation to make sense of: I had spoken of "rejecting identity," and The Professor had responded with "states and relations." What connects these two constructs?

I remembered that Whorf's book contains a passage in which he brings together the construct of identity and various paired terms, including states and relations, in one place. The next morning, I found that passage (on p. 215), and spent all morning reading and re-reading that half-page. In the process, I called up the linguistic "facts of life" summarized in my preceding Chapter. Then I came to ask myself a new question:

I concluded that we do so by means of some 'rule' equivalent to Aristotle's "Law of Identity."

Stated in modern English, the Law of Identity says,

So we consider each 'noun' or 'noun-phrase' identical with itself, whereas we regard each 'verb' or 'verb-phrase' as not-identical with itself.

To test out this supposition, use the test-sentences or test-WFF's presented above. To begin, from our discursive example, take the noun-phrase the cat and substitute it for the C in both locations in the "Law of Identity":

Referring to "the cat who grinned," that seems acceptable enough.

Now take the verb-phrase grinned, and substitute that into both locations of the "Law of Identity":

That does NOT work.

You can process other discursive sentences similarly; and also, you can process notational "sentences" such as the ones given above. In each instance, substituting a "substantive" (noun or noun-substitute) into the "Law of Identity" works, and substituting a "verb" (or verb-substitute) does not.

So far so good -- tests of this sort cast no doubt upon my new generalization: Operationally speaking, we appear to distinguish between the nouns and the verbs by considering the nouns self-identical, and considering the verbs not-self-identical.

Neat enough, but -- so what?

I had committed myself to write a non-WIE notational language, but had found I did not know how. I had committed myself to do that, having already rejected the logical construct of identity.

Now that I knew HOW to tell the nouns from the verbs, I found that the distinction between them depends on a previously-hidden usage of the logical construct of identity, and so intrinsically violates my central premise.

What happened when I tried rejecting that usage of identity?

Which I then found myself able to do.

Since I figured out how to abandon WIE languages and started devising this non-standard notation, have the exponents of the alternative frame of reference done anything worth mentioning?

Yes, I and my collaborators have revised, or proposed revisions, to each of four major "fields of study":

These accomplishments mean we have laid the foundations for delivering on the promises Korzybski made, under the heading of "Works in Preparation," in the first edition of his Science and Sanity (1933). (In later editions, the editors found it more politic to remove that list than to fulfil these promises.)


1. This alternative frame of reference discloses a fundamental theoretical error encoded in the grammar common to WIE discursive and notational languages -- specifically, encoded in the way we distinguish between 'noun' and 'verb'. In my analysis, every 'noun' comes to look like a concealed 'is of identity' proposition, which violates the requirement that we distinguish between Name and Thing Named (Frege) or between Map and Territory (Korzybski). To express this violation in words, calling the be-whiskered, furry-faced organism by the noun "cat" amounts to asserting "cat(name) identical with cat(thing)".

(Remember: according to the tenets of Word-Magic, when you know the TRUE NAME of something, you have POWER over it.)

Further, at the level of sentences composed of noun-phrases (concealed 'is of identity' propositions) and verb-phrases, I find a more extensive violation. Using "bland" terms -- "pointers" -- so as to beg as few questions as I can, I say that I infer that "non-verbal" "doings" or "happenings" "occur", and that I can sort of describe these "doings" or "happenings" with phrases such as "dynamically-changing organisms transacting with their dynamically-changing environments," etc. However, we WIE provincials have accustomed ourselves to designating or describing such "doings" or "happenings" in ways not intended as "bland" nor as inferring that we have done any inferring: We use static-and-unchanging symbolic "things", which (according to our grammar) enter into more-or-less-transient "relations", to designate these "doings" or "happenings" which I regard as intrinsically dynamic. And - the most questionable point of all - we pretend that the arbitrary categories of our culturally- and linguistically-determined frame of reference make muster as COSMICALLY-VALID - "That's the way things REALLY ARE."

2. The act of unconcealing this hidden assumption, followed by the act of rejecting and replacing it with the Postulate of Non-identity, brings about the collapse of the WIE grammar, and with it, the collapse of the linguistic specializations based on it -- the WIE logics, mathematics, sciences, philosophies, jurisprudences, religions, etc.

3. Before I unconcealed this hidden assumption, I found that I could not write a non-WIE notation -- I didn't know HOW (mainly because I kept using two KINDS of terms, analogous to 'nouns' and 'verbs'). After I unconcealed this hidden assumption, I COULD AND DID write a non-WIE notational language, with no 'nouns' or 'verbs' (or any other WIE "parts of speech") in it. .

4. Earlier, I requested that each of you suspend disbelief while I told my story. I have now introduced the construct of a notational language built up on a derived grammar, and also, perhaps, ultimately a discursive language on a derived grammar -- neither of which rely on noun-verb distinctions. Before you resume the role of a disbeliever, consider that the next speaker, Dan Moonhawk Alford, can describe families and super-families of present-day living discursive languages which have no need of nouns.


Hilgartner & Randolph, "Psycho-Logics: An Axiomatic System Describing Human Behavior. A. A Logical Calculus of Behavior." Journal of Theoretical Biology 23:285-338 (1969a)

"B. The Structure of 'Unimpaired' Human Behavior." Journal of Theoretical Biology 23:347-374 (1969b)

"C. The Structure of Empathy." Journal of Theoretical Biology 24:1-29 (1969c)

"D. The Structure of 'Impaired' Human Behavior." (Hitherto unpublished; available from first author, at photocopying cost.)

Hilgartner, Harrington & Bartter, "Anomalies Generated by Contemporary Physics." Bulletin of Science, Technology & Society 9:129-43 (1989)

Hilgartner & DiRienzi, "A Non-aristotelian View of Quantum Theory." Physics Essays 8 (No. 4), 472-505 (December 1995))


Here I undertake to present just enough of the beginnings of my non-standard notation to allow you to get a taste of it. I deem that I will have done what I set out to do when each member of my audience, having succeeded in wetting the end of a big toe in this alien doctrine, shows a felt-reaction to it - which you might verbalize as "Hey! - Neat!" or "Ooh - Weird!", or whatever.

Remember: I knew I needed to abandon WIE languaging, of both the discursive and notational patterns. But I didn't know HOW.

I can use a quotation from Whorf to highlight the problem I faced:

SO: Whorf posits an "implicit and unstated [agreement]" --WHERE DO I FIND THE CONTRACT, so I can study its terms?

What I did with what I learned from The Professor and his group gives a clearer answer to this question than anything I've actually said. Since I wanted a rigorous language consistent with the "content" of my theory of human behaving-and-experiencing, I turned to Korzybski's premises.

Korzybski (1941) had set forth three undefined terms: structure, order and relations - and three postulates: Non-identity, Non-allness, and Self-reflexiveness.

I definitely won't get as far as the postulates today. But I will say a bit on the topic of undefined terms. After I came to understand what The Professor and his group had told me, I turned and focused on Korzybski's undefined terms.


I have lots to say on the general topic of undefined terms - none of which I'll have time for today.

But I must make three points:

a) In general, I maintain that, no matter what their "content," the undefined terms held by any human who languages (and the notion of languaging includes the extended processes by which a human generates a formalized axiomatic theory) bridge between those verbal constructs which s/he uses in her/his languaging and those non-verbal "doings" or "happenings" which s/he describes or models by means of her/his languaging.

b) But that "bridging between the non-verbal and the verbal" involves or consists of "slicing up the world". In other words, the "contract" I sought a few moments ago "resides" in the undefined terms held by the languaging human in question.

c). In principle, any human chooses her/his undefined terms - and in so doing, chooses to, and how to, "slice up the world."


0. Euclid and undefined terms.

1. End of 19th Century CE (e.g. David Hilbert (1862-1943): Premises of a formalized axiomatic system must include some terms for which we offer no verbal definitions.

a). To define means: To replace a more or less unfamiliar term with a somewhat more familiar one.

b) As we start framing a formalized axiomatic system, we HAVE no "already-familiar" terms.

c) Hence the process of providing rigorous definitions for our terms must embrace the process of explaining, or at least listing, what we have left undefined.

2. As Korzybski points out, undefined terms represent

a) I paraphrase that, holding an undefined term as "a special kind of postulate, the "content" of which the person who subscribes to it cannot state in words."

3. I maintain that the undefined terms of a formalized axiomatic system provide a bridge between those verbal constructs that make up the theory and those non-verbal "doings" or "happenings" which the theory purports to describe or model.]



1. To paraphrase Korzybski, I hold an undefined term as "a special kind of postulate, the "content" of which the person who subscribes to it cannot state in words."

In principle, we CHOOSE our undefined terms -- and when we do so, we choose just how we slice up the world.

Corollary: THE "CONTRACT" locates IN the undefined terms.

So if you don't know your own undefined terms, then you do not have the contract in view, and therefore cannot study its terms.

SO - What did I do that involved the undefined terms structure, order, and relations?

As noted, I decline to offer verbal definitions. But I do consider it legitimate to discuss how I use my undefined terms:

To remind people that I do not subscribe to the traditional presuppositions of WIE languages, when I deal with the undefined terms in a WIE language such as English, I treat them not as noun-forms but as verb-forms: (to) structure, (to) order, (to) relation. When I want to represent these in notation, I use single letters: S, O, and R - and I treat these terms as "not-noun, not-verb".

a) I use them to point to examples of those "doings" or "happenings" which interest me - specific examples of what I might call the dealings of one-particular-organism-as-a-whole-with-its-environment-at-a-date (as viewed by a specified observer). Succinctly, contacting or transacting or abstracting, etc.

b) On a higher "logical level", I hold that the undefined terms held by any particular human function only (or mainly) in her/his own behaving-and-experiencing, where they serve to bridge between i) her/his non-verbal observings of this-organism-transacting-with-its-environment, etc., and ii) her/his verbal-level representings of these observings.

c) In the most general sense, I hold that any undefined term I may subscribe to operates as a kind of postulate, a silent one, the tenets of which I cannot state in words at this date. (Korzybski, 1933, p.153)


1. The Summons

2. Recoiling from light touch

3. Fleeing

4. I interpret these observations


Korzybski suggested, in at least two places in Science and Sanity, that, given a specific usage of one of the undefined terms, you could perhaps say a bit more about it by COMBINING the other two terms - "structure" composed of "ordered relations" or of "related orders"; "order" composed of "structured relations" or "related structures"; and so on.

I can write that suggestion out in my growing notation as follows:




Take that as 'a first step' in actually deriving a grammar. Then how do we make sense of these strings of letters (strings of undefined terms)?

· Let the initial term (e.g. S): signify our organism's TOPIC (as viewed by our designated observer)

· Let the remainder "say something about this topic" (as viewed by our designated observer) - or in other words, take the remainder as signifying our organism's COMMENT on that topic.

Gestalt theorists infer that any sensing, any feeling, any moving (and I suggest, any languaging) done by an organism-in-its-environment-at-a-date looks (to a designated observer, a Gestalt-theorist) as if it takes on the configuration of a Gestalt (a "figure of focal interest [to the organism], against a (back)ground relatively empty of interest")

Then, given the organism's topic, let the remainder (his comment) specify a Gestalt on that topic.

Finally. use punctuation marks (or "instructions to readers") - e.g.: <...> (signifying "Read this as ground") and {...} (signifying "Read this as figure") - to set off the terms I designate as <ground> and {figure} .

Now bring together these conventions:

· Initial term: (e.g. S) -- signifies TOPIC

· Second term: (e.g. O) -- signifies the <(back)GROUND> of this Gestalt

· Third term: (e.g. O) -- signifies the {FIGURE} of this Gestalt

· Ultimate term: (e.g. R) -- signifies HOW FIGURE AND GROUND "HANG TOGETHER."

S <O> {O} R

CHECKUP: Do I have anyone in my audience who does NOT see this as the anlage (foundation) of an entire grammar?


To express in that notation: Yeats's

"How do we tell the dancer from the dance?"

(Someone suggested that I use the notation to re-interpret the Primer definition of "system". I would prefer to leave that as an exercise for general-systems-theorists to do.)

FIRST CUT: In undefined terms alone:

In general, I maintain that, no matter what their "content," the undefined terms of a formalized axiomatic bridge between those verbal constructs that make up the theory and those non-verbal "doings" or "happenings" which the theory purports to describe or model

S : the overall structure" -- the "doings" or the "topic" (in English, "TO DANCE")

First O: the JUST-PRECEDING movements of head, arms, hands, trunk, legs, feet, facial expression, etc.

Second O: THESE movements of the body-parts.

R: How first O and second O "hang together": "Figure and ground shift from "then-to-now" and from "there-to-here" (a general relationing I call _spatio-temporally ordered_), and logically, shift from 'lower'-to-'higher' "logical levels" (and perhaps, back again). (a general relationing I call _hierarchically ordered_)."

Please notice how much SPACE ON THE PAGE it takes to write out these representations of "doings" or "happenings" as undefined terms:

S <O> {O} R

SECOND CUT: In defined words:

Notice also what happens when we pretend we have defined some terms ("words"), and use those:

Motor abstracting <the previous movements of body parts> {these movements of body parts} hierarchically ordered and spatio-temporally ordered.


Now let me foreshadow-define some one- or two- or three-letter symbols.

(Time will not permit it here, but in later conversation I would gladly show some further steps involved in this process of defining.)

Abstracting: Abs

Moving: "motor-ing", indicated with on-the-line Mt or with subscript Mt

Dancing: a specific kind of "motor-ing", indicated with subscript D

"Intervals": indicated with right superscript then or right superscript now

Hierarchical ordering: indicated with Oh

Spatio-temporal ordering: indicated with Ot

Now put this together, using indexed undefined terms:

SMt <ODthen> {ODnow} Rh Rt

Using indexed defined terms:

AbsMt <MtDthen> {MtDnow} Oh Ot .