C. A. Hilgartner




Count Alfred Korzybski,on the page facing the title page of the first edition of Science and Sanity, lists some "Volumes in Preparation," and also some other titles for which, he promises, "The Names of the Authors … To Be Announced Later." In that page alone, Korzybski outlines an ambitious program for his new discipline of general semantics.


I and several associates have, over the past thirty-plus years, generated an alternative frame of reference which synthesizes Korzybski’s non-aristotelian premises, other aspects of general semantics, and contributions from a number of other workers, including the anatomist and cyberneticist Gerd Sommerhoff. In a number of domains, including that of biology, we have considerably advanced Korzybski’s program.


Meanwhile, contemporary biologists have inherited a vast legacy of experimental findings. But at the level of theory, today’s biologists, in my considered opinion, have committed themselves to fundamental error. In this presentation, I shall


(i) disclose at least one aspect of this error;


(ii) show its roots in the assumptions encoded in the grammar of western Indo-European (WIE) languages such as English or the mathematical theory of sets; and


(iii) argue that those who subscribe to this error, as they transact with and within the net of living organisms known as the ecosphere, render themselves less and less fit to transact with an ecosphere, and render the ecosphere, the planet, less and less hospitable to living, transacting organisms. Hence, under today’s conditions, the holding of this error poses a threat to the continuance of life on earth, or at the very least, to the continuance of HUMAN life on earth. Finally,


(iv) I shall propose a theory of biology demonstrably free of this fundamental error.


I hold that exponents of general semantics may well have special insight into many of the precepts which underlie this alternative frame of reference, and into the non-aristotelian biology which it supports. If so, my presentation can open up extraordinary opportunities (and perhaps, responsibilities) to such workers. By using the additional insights presented insights, they – we – can begin the process of working out more sustainable, viable patterns of living and of using these to replace the error-based, non-viable patterns of living now in place.


A. To begin, I shall briefly detail the condition of today’s biological theory.

B. Then I shall summarize the standards, logical and empirical, to which I hold myself as a theorist.

C. After that, I shall summarize the assumptions encoded in the WIE grammar , and

D. Show how these assumptions have structured the study of living organisms throughout the roughly 2500-year history of biology, and

E. Show how the developments in biology of the last 165 years have led to the current condition of fundamental error, and

F. Present my proposals for an alternative frame of reference, and for a theory of biology which Korzybski might have consented to call "a non-aristotelian biology."


Since I choose to rely on the non-aristotelian premises as my most fundamental assumptions, I must, on that account, acknowledge that no matter how much care I may take in preparing it, my presentation will end up to some degree inaccurate, incomplete, and self-referential.



Figure 4



Let me start by characterizing the current condition of biological theory, as I see it.


My desk dictionary defines the term biology as follows:


biology n. 1. The science of life and life processes, including the study of structure, functioning, growth, origin, evolution and distribution of living organisms.


However, today’s biologists assert that terms such as life or living lack rigor, so that no one can offer satisfactory definitions for them. Historically speaking, their predecessors some four to five decades ago explicitly denied meaning to such terms, on the grounds that "… there is no definite boundary between the living and the non-living …." (Stanley, 1948)


What difference in "the study of … living organisms" do you suppose it might make, when the practitioners abandon the key terms used to define – set the boundaries of – their discipline?



Figure 4 (lower half)



My approach to biological theory, which I frame in mathematical languages of known structure (such as the mathematical theory of sets), can and does define these terms, in a manner that makes them consistent with my chosen premises. Furthermore, the theory-based line which it draws between the constructs of living and non-living runs about where most people (including biologists) would want it to run.




Figure 5

1. The Construct of Theory


I regard the construct of theory as somewhat complex. Any theory has, at the least, a logical, an empirical, and a predictive structure.






Figure 6

On logical levels:


a. Premises: Of any theory that I’ll put my name to, I require that it stem from the non-aristotelian premises of Korzybski.


Not only must the theory stem from those premises, but also, I require that I HOLD the theory as inaccurate, incomplete and self-referential.


b. Self-referential: I require of myself that I frame the theory so that it takes into account the biologist (observer)(me).


c. Rigor: I require of myself that I frame the theory in some notation of known logical structure.



Figure 7

On empirical levels:


The theory must account for widespread "OBSERVABLES"


a. It must draw a theory-based line between the constructs of living and non-living.


b. It must show the constructs of organism and environment as INTRINSICALLY INSEPARABLE. Two aphorisms appear pertinent:


The Gestalt therapists Perls, Hefferline & Goodman (1951) write,


We speak of the organism contacting the environment, but it is the contact[ing] that is the first and simplest reality. (Perls, Hefferline & Goodman, 1951, p. 227)


Hilgartner & Miller (1992) assert,


The environment forms the other side of my skin; I form the other side of the environment’s skin. (Hilgartner & Miller, 1992)


Figure 8

On predictive levels, the theory must both define and follow the pattern which I call self-correcting:


a. The theory must lead to consequences (expectations) which we humans can ACT ON (by way of experiencing or experimenting).

b. These actions must lead to an outcome.


c. We must then judge the expectations in terms of the outcome, and


d. Reject the expectations (and eventually, the theory) if the outcome disconfirms (contradicts) them.



Figure 9 (& 10)




In this heavily epistemological frame of reference, we deal at every moment with questions like, "What do I mean?" and "How do I know?"


Any listing of the tools I have used in this inquiry should start with my presuppositions. As the most fundamental premise which I can state in words, I reject the logical construct of identity in any guise, explicit or tacit – one version of Korzybski’s Postulate of Non-identity.


(I define identity as "total and absolute agreement or negation of difference".)


Please notice that I cannot even mention this postulate without invoking the logical construct of identity. Otherwise stated, the constructs of identity and non-identity form an opposing or polar term-pair: They function as mutually-defining or inter-defined constructs, where neither one "makes sense" without the other.


The notion of polar term-pair gives us one way to understand Korzybski’s great contribution: He points out that there exist (at least) TWO ways to hold this term-pair. In effect, those who use the term pair at all cannot help but "like" one member and "dislike" or "ignore" the other. One can "like" identity and "dislike" or "ignore" non-identity (as our linguistic forbears did). Alternatively, one can "like" non-identity and "dislike" identity. Once a choice becomes possible, any human who uses this term-pair at all must choose which way to use it. Korzybski himself takes a stand, declaring himself one of the company – the first of the company – of those who explicitly prefer non-identity.


Almost everyone who studies general semantics at all encounters the notion of non-identity, e.g. in the guise of the Postulate of Non-identity. But let’s assume for the moment that you may have little familiarity with the notion of polar term-pair. Please allow me to offer you a way to handle this (more or less) unfamiliar construct, with respect to the specific term-pair of identity vs. non-identity. I shall suggest you use observations of overt behavior, along with a couple of phrases from ordinary vocabulary, as rough substitutes for these more abstruse constructs.


(a) In place of the construct of to hold as not-identical, I suggest you use "To distinguish (between … and …)" Likewise,


(b) In place of the construct of to hold as identical (or to identify), I suggest you use "Not to distinguish between … and … ".


This pair of locutions will help make plain what I regard as one of the most important assumptions encoded in the grammar of WIE languages (and some other tongues too). We also need the construct of languaging as something humans DO, where I define languaging as "the collected processes of speaking-and-listening, writing-and-reading, signing-and-"reading" signing, etc."


Figure 11

In order to language in English or set theory, EVERY speaker, listener, etc., MUST make a large number of distinctions: S/he must distinguish between



In contrast, NO speaker (etc.) HAS TO distinguish between


or, in general, between


In other words, the grammar of the WIE languages presupposes or encodes map-territory identity.


Figure 12

"Well, "I can imagine someone asking, "what ‘is’ wrong with a little map-territory identity?"


In answer, I suggest we look more closely at just what the term means. In order to satisfy this condition, every point of my map must represent one and only one point of the territory, and no point or aspect of the territory goes un-represented. But if that condition holds, then the observer doesn’t matter: This condition eliminates the observer from consideration.


Furthermore, if this condition holds, then I have "PERFECT KNOWLEDGE" of the territory. Now, as one who subscribes to the Postulate of Non-identity as my most fundamental presupposition, I deny the possibility of "perfect knowledge." Instead, if someone claims such knowledge, I regard it as a delusion (a belief held regardless of the evidence) or a pretense.



Figure 13



As another tool, I have adopted and re-worked the construct of transacting. (Dewey & Bentley, 1949). I use this term to point to the ongoing interchanges which take place between an organism and its environment, which leaves both altered.


For an example, I request that you take a deep breath. Inhale deeply, and then exhale. By doing that, you took in something on the order of 40 mg of oxygen, and excreted about 52 mg of carbon dioxide. In other words, you altered the chemical composition of the air in this room by a measurable amount, and you altered your own chemical composition by a comparable amount.


If you should wish to minimize the significance of the changes you bring about by breathing, allow me to remind you that during mosquito season, female mosquitoes find their prey – you – by "smelling" the carbon dioxide you excrete. They detect the local increase in carbon dioxide you produce, and follow this gradient "upstream" toward areas of higher concentration of carbon dioxide, in order to find you and suck your blood, and thereby get the high-protein meal they need so their eggs can mature.



Figure 14

LIVED THEORY (transactional)

As Korzybski points out, we humans ASSUME (indeed, we cannot NOT-ASSUME). Furthermore, I hold that we guide what we DO by what we assume, in the process putting our assumings to test. When the smoke clears, so to speak, and the situation reaches an outcome, we can judge what we assumed at the outset in terms of how things turned out, and reject and discard the assumings which appear disconfirmed by the outcome.


In other words, we humans operate by a pattern analogous to the logic of Western science.


Different kinds of situations require different kinds of assumings – and we will maintain relations between our various assumings. But a structure composed of interconnected assumings and presuppositions makes muster as a theory – which I designate as a lived theory (in contrast to the abstract theory generated, and written down, by logicians, mathematicians, scientists, etc.).


Figure 15


Above, I pointed out that the grammar of the WIE languages (set theory as well as English, etc.) encodes map-territory identity. When we let the presuppositions encoded in our grammar



Figure 16

A human who LIVES a dualistic theory



Figure 17

A human who LIVES a transactional theory



Figure 18

LOGICO-LINGUISTICS: What we can and can’t say in a WIE language



Figure 19

Lexical items



Figure 20

Grammatical pattern



Figure 21

Referential or empirical pattern



Figure 22

REPRISE (part 1): WHAT (in a primary sense) WE DO and do not EXPRESS



Figure 23

REPRISE (part 2): Some things we DO NOT EXPRESS



Figure 24




Figure 25



From the earliest recorded observations concerning biology, biologists have sought to DESCRIBE and to UNDERSTAND the "purposive" – we now say "apparently-purposive" – activities of living organisms. For example, consider a honeybee harvesting pollen and nectar from more or less trumpet-shaped flowers. As she enters one of the flowers, the bee brushes against the pistil, shedding grains of pollen caught in her bristles onto its sticky surface (and so pollinates the flower, a crucial step in its reproduction). A little further into the flower, she brushes against the stamens, which thoroughly dust her with their pollen-grains. Once far enough into the flower, the honeybee uncurls her long tube-shaped proboscis, inserts it into the puddle of nectar at the base of the flower, and ingests it into her crop. Once outside the flower again, she combs her bristles and packs the pollen between the "pollen-basket" bristles on one pair of legs. (Pollen and nectar form the staples of the diet of honeybees.) Then she flies to another flower, and repeats the process. Eventually, she returns to the hive, where she increases the hive’s stores of food by disgorging the nectar and unloading the pollen.


From a traditional-biological point of view, every detail of the "doings" or "happenings" I describe, e.g. each aspect of the anatomy and behavior of bee and flower, appears "purposive"– an example of an adaptation of organism to its environment. Bee and flower appear adapted to one another, for the ‘purpose’ of their mutual survival..


For over 2,000 years, biologists EXPLAINED these observed "doings" or "happenings" in terms of the doctrine and vocabulary of teleology. This vocabulary includes constructs such as








Final causation



When someone uses this doctrine and vocabulary, in effect s/he TREATS the "doings" or "happenings" referred to as manifestations of some "ultimate purpose" (Greek, teleos, teleos). The earliest biologists regarded the teleos as a daimon, a lesser deity, a "genius" – which makes teleology frankly and explicitly an animistic view. Let me make my point painfully explicit. Consider some details of the anatomy, physiology, behavior, etc., of a particular species: – e.g. the modern horse (Equus caballus), living on the plains, for example, size ("stands 14 hands high at the shoulder"), mammalian quadrupedal gait, ("can run about 30 mph"), hoof structure ("runs across the turf on one toenail"), dentition ("has teeth that can chew GRASS!"), etc.

Where a biologist uses a teleological term – asserts that organisms of this species show particular ‘adaptations’ (without going into mathematical detail concerning what s/he means by the teleological term) – then this biologist in effect asserts that the teleos does the organism’s adapting for it.


Someone who takes a teleological/vitalist stance, then, holds that "The whole (of an organism) amounts to more than the sum of its parts." S/He holds that in a living organism, an immaterial "something", let us call it soul or mind, ANIMATES the non-living matter of the organism’s body. Where the organism shows adaptation or coordination, the teleos DOES the adapting, etc., for the organism.


In contrast, someone who takes a mechanist/reductionist stance holds that "The whole (of an organism) equals the sum of its parts." S/He discredits or ignores the notion of teleos – and with it, the whole topic of the "(apparently-)purposive" activities of living organisms.


By twentieth-century standards, neither approach appears adequate or acceptable.



Figure 26

A perennial dispute within biology



Figure 27

Dualism in biological theory



Figure 28

Mechanist/Reductionist Biology

Consider in particular the school of mechanist/reductionist biology which originated in Germany in about 1830, with Johannes Müller (1801-1858) and his students. As a deliberate research strategy, these workers (especially the students) set out to replace the teleological vocabulary of biology with the philosophy of mechanism and the methods, vocabulary and linguistic habits of physical scientists. In keeping with the boundaries of the physical sciences, these methods entail the practice of studying "isolated systems". Where these altered methods lead to altered views, these workers subjected these views to experimental test. This entailed a willingness to take living organisms apart, and to study the PIECES, looking for "mechanisms" that would "explain" how the organism "works."



Figure 29

From about 1830 onwards, the confrontation between advocates of mechanist/reductionist views and advocates of teleological/vitalist views grew increasingly sharp. Over and over again, the mechanists showed themselves as brilliant in designing and performing experiments; and over and over again, their views survived testing. The vitalists, in contrast, showed no particular skill in experimentation; and virtually none of their views survived scrutiny. Today, we remember Müller and his students (who included most of the creative scientists of Europe in the latter half of the nineteenth century, in the physical sciences as well as the biological sciences); but we have forgotten even the names of their vitalist opponents.





Figure 30

Figure 1 lists a few topics from the litany of research results resulting from 165 years of mechanist/reductionist research in biology.


Figure 1 about here. (Research results...)


As the successes of the mechanists (which include such empirical discoveries as genetic inheritance and its cytological and stereochemical basis, intermediary metabolism, endocrine systems of mammals, insects, plants, etc., the workings of vertebrate immune systems, vertebrate blood clotting, neurophysiology, etc., etc.), became more and more evident, increasing numbers of biologists came to adopt these approaches, and to extend them. The scope and magnitude of the resulting body of research findings beggars the telling. Today most biologists don’t know of alternatives to their current theoretical framework, and cannot imagine even needing any.



Figure 31

But these successes have come at a hitherto unreckoned price. When they use these borrowed languages, biologists have had to handle those discoveries after the fashion of "isolated systems".


Figure 32

Any language encodes constraints: No matter what we may use it to represent, any language abstracts out and describes only those aspects which fit within its own pre-existing boundaries. The language(s) of chemistry and physics have boundaries carefully designed and maintained to exclude apparently-purposive "doings" from consideration. Thus when biologists use these languages, they inadvertently blot out a core topic, and so blur the boundaries of biology.


Figure 32 (lower half)

Also, in the beginning decades of the twentieth century, biologists encountered some puzzling "borderline cases":



Using the old characterization for the term "life" in terms of the "attributes" of irritability, locomotion, reproduction, respiration, etc., they found no way to classify such "borderline cases" as either living or non-living. That further blurs the boundaries of biology.





Figure 33

The glitter of those "isolated" discoveries, then, has served to obscure the central failure of contemporary biology: the fact that nowadays, biologists have no shared, agreed-upon and tested model for apparently-purposive "doings" nor generally-accepted definitions for terms such as life or living which meet modern logical standards of rigor.



Figure 34

By the 1940’s, biologists had concluded that the definitions for terms such as life or living had collapsed. One statement of this conclusion, (from Wendell Stanley, the first person to crystallize a virus), goes as follows:


With the realization that there is no definite boundary between the living and the non-living, it becomes possible to blend the atomic theory, the germ theory, and the cell theory into a unified philosophy, the essence of which is structure or architecture. The chemical, biological and physical properties of matter, whether atoms, molecules, germs or cells directly dependent upon the chemical structure of matter, and the results of the work with viruses have permitted the conclusion that this structure is fundamentally the same regardless of its occurrence. (Stanley, 1948; emphasis mine)


In so many words, Stanley proclaims the ultimate success of the mechanist/reductionist program.



Figure 35

We humans have had half a century to get used to that conclusion, which has become widely accepted.


But please look again at what (as I see it) Stanley asserts:


"With the realization that there is [within the non-verbal territory] no definite [verbal-level construct of a] boundary between [the verbal-level constructs of] the living and the non-living,…


I regard the CONSTRUCTS of the living, the non-living, and the boundary between them as TERMS, belonging to the domain of map – and further, constructs central to how we define the term biology.


Stanley, however, expresses himself as if he expects to find these verbal-level TERMS within the non-verbal TERRITORY that biological science purports to describe. He declares the territory DEFICIENT because he can’t find the map already pre-formed within it.



Figure 36

This stands as a fundamental error – a logical-and-empirical error, which contaminates (poisons) many of the broad conclusions drawn from otherwise useful findings.


Logically speaking, mathematicians (e.g. Frege) criticize this kind of logical maneuver as confusing name with thing named. Logicians (e.g. Turbayne) call this a sort-crossing error.

General semanticists (e.g. Korzybski) call this confusing levels of abstraction. I call it map-territory identity. We concur in calling it A MISTAKE.


Scientifically speaking, Stanley holds his own map (mechanist/reductionist view of biology) as "True", and declares the territory DEFICIENT because it "fails" to match his map.


Stanley’s dictum offers an excuse: His conclusion PARDONS himself and his colleagues for failing to provide theory which accounts for what biologists set out to account for.


Further, it contains an implied dogma: Since (in his view) the territory ‘IS’ deficient, he implies that ‘Nobody else will EVER manage to offer logically and empirically satisfactory definitions for terms such as life or living.’



Figure 37

In a physiology teaching laboratory, I saw a sign, informing those studying physiology that:





Figure 38

I regard Stanley’s quoted conclusion as INCOMPETENT – logically and scientifically – and I REJECT IT.


I also regard it as HAZARDOUS TO LIFE ON EARTH.


\ In my opinion, a scientist may NOT allow her/himself to explain any mismatch between theory (map) and observations (territory, or evidence for a territory) by declaring the TERRITORY deficient.


Nevertheless, the conclusion which Stanley expresses got widely accepted. After about ten years, it passed out of the realm of discussion and into that of dogma, becoming part of the non-verbal practice of what now passes for "biology".


Most of today’s biologists unquestioningly, even unawarely, regard the topic of definitions for terms like life or living as a dead issue.


Today’s biologists cannot draw a theory-based line between the living and the non-living. Hence their "science" has nothing to say about living organisms, about biology.






Figure 39




Figure 40

Figure II gives an abbreviated listing of the premises of my Non-identity-based theoretical system and notation.


Figure II about here. (Premises)


Obviously, this listing represents more material that we could cover, even if we devoted a whole day to it. To allow me to summarize my main proposals for biology, let’s discuss a selected few of these topics, mainly those displayed in square boxes in Figure II. In particular, I’ll say something about

(a) setting (and the related constructs of transacting or contacting);

(b) multiordinal;

(c) the derived grammar which underlies this theoretical system;

(d) polar term-pairs and also larger groupings of mutually-defining terms, such as the five-term grouping made up of organism, environment, abstracting, abstraction, and an ordering on abstracting (or to express this ordering colloquially, the notion of logical "levels"); and

(e) the construct of directively correlated.



Figure 41



Logic of opposites. In this discussion, I display the structure of three different versions of the logic of opposites – the relations between a term and its opposite or negation or contradictory or complement. In particular, I discuss the Laws of Thought of Aristotle, the modern logical axiom of identity, and, within my Non-identity-based theoretical system, the logic of opposites as rules for negating a Gestalt. Finally, I spell out the relations between the presuppositions of these constructs.


When he proposed the Laws of Thought (Figure III), Aristotle paid little or no attention to the implied context or setting for those rules.


Figure III about here (Laws of Thought)


Now, millennia later, we can summarize those rules by specifying that version of the Logic of Opposites which he presupposes. I designate this version as undelimited; and since we know nothing about the "things" designated other than that they satisfy the Law of Identity (they "ARE" identical with themselves), I designate this version also as blank (as contrasted with a specific domain, in which we know at least something else about its "contents"). To display this construct, let me draw a Venn diagram consisting of a single circle inscribed on an undelimited plane. I label the inside of the circle with a C and the outside with a Not-C .


Figure IV about here. (Single circle)


Then everything within the circle "IS" C (Law of Identity); every point on the plane, then, must either "BE" C or Not-C (Law of Excluded Middle); and none can "BE" both C and also Not-C (Law of Contradiction). For over two millennia, WIE mathematicians and logicians treated the Laws of Thought as the foundations for syllogistic reasoning, and thus the basis for their ability to generate "secure" inferences.


In 1902, Bertrand Russell proposed a paradox concerning "Sets which do not belong to themselves," which in effect pulls the rug out from under the then-current version of the mathematical theory of sets in particular and any scheme of inference based on the Laws of Thought in general. Russell does not frame it in these terms, but his paradox prompts people to recognize that the Not-C specified in the undelimited version of the logic of opposites embraces "Everything Else." For example, if C signifies night, Not-C includes not only day, but also tomatoes, and male sexual functioning, and Cantor’s transfinite cardinal numerals, and foreign policy, etc. Somehow that does not seem like a stable basis for secure inferencing.


Perhaps you can imagine how unhappy that development made the WIE logicians, mathematicians, and so on. A great deal of reflection and effort, including the Theory of Types proposed by Russell himself, went into the attempts to find a way around the issues raised by the paradox. Eventually, in 1908, Ernst Zermelo published a new set of axioms for set theory , which succeeded in setting the paradox aside (for a while) and restoring a situation ALMOST equivalent to the status quo ante bellum ("the existing condition before the war").


Zermelo did not frame his proposals in exactly these terms, but in effect he handled the difficulties which arise from the commingling of Not-C with "everything else" by the logical trick of making a distinction (or eliminating a usage of tacit identity). To display this distinction,

let me draw a second circle around the first, thereby partitioning the original Not-C of the blank undelimited version of the Logic of Opposites into an "‘inner’ Not-C" and an "‘outer’ Not-C". Let us then call the ‘outer’ circle D and everything within it the blank delimited domain D .


Figure V about here. (Two concentric circles)


Then we can designate the whole configuration, including the "‘outer’ not-C", as the blank delimited version of the Logic of Opposites. Further, instead of the term "‘outer’ not-C", we might designate this ‘outer’ portion (which DOES embrace "everything else") by the term "Not-C-and-Not-Not-C" .


This proposal keeps "everything else" at bay, and restores – more or less – the applicability of the Laws of Thought: Within the circle D , every point "IS" itself; every point either belongs to C or to Not-C ; and no point belongs to both C and Not-C . Furthermore, we can now do what Aristotle had no means to do: express this version of the logic of opposites in notation, as the modern logical axiom of identity:


" x Î D: x º x .


For an advocate of the blank delimited version (such as Zermelo), Circle C (the figure that separates C from Not-C ) demonstrably differs from Circle D. Or in other words, for such a person there exists a collection of points x which belong to the area located between the two circles.


$ x : x Î {The ‘inner’-not-C }.


For exponents of the blank undelimited version (such as Aristotle), however, no such points exist. Otherwise stated,


Circle C º Circle D .


Since they do not distinguish between Circle C and Circle D , such exponents need only one name for the circle(s) – for them only one circle "exists." I call this previously unacknowledged usage of º an example of tacit identity.


Then the difference between the presuppositions of these two versions of the Logic of Opposites hinges on the presence or absence of this usage of tacit identity.



Figure 42

A large part of my proposals for biology amount to setting up an alternative frame of reference, and showing that it offers advantages for the study of living organisms. My proposals for biology include, and depend upon, yet another version of the Logic of Opposites – one which stems from Korzybski’s premises, especially the Postulate of Non-identity. In order to present these proposals, I will have to make this version of the Logic of Opposites intelligible. That means


(a) specifying the relevant sense of the construct of setting,


(b)showing setting as a multiordinal term,


(c) mastering the relevant vocabulary – not just a polar (or mutually-defining or inter- defined) term-pair, but a polar n-tuple or term-cluster – here, a ring of five polar constructs – and


(d) specifying a version of the logic of opposites as the context for the rules for negating a Gestalt.


A non-identity-based setting. Here, I use the construct of setting to designate a (symbolic) "domain of discourse" which serves as the locale of certain ‘kinds’ of (symbolic) "doings" or "happenings" - in particular, "doings" or "happenings"


a) which, by presupposition, do not satisfy the Law of Identity ("happenings" not- identical with themselves), and

b) which (to use a run-on phrase) appear to involve "one particular organism-as-a-whole- dealing-with-its-environment-at-a-date, as viewed by a specified observer".


I invite you to regard this domain of discourse as "existing" or "occurring" on various "logical levels." Thus, when you regard it "in the abstract", I invite you to visualize it as some sort of "undifferentiated ground" where such "happenings" might occur. On another, subsidiary "logical level", e.g. when/where you imagine, or see, actual "doings" or "happenings" to which you might apply my run-on phrase, I invite you to regard these as a "differentiation" of, or on, that "undifferentiated ground". Then the "doings" or "happenings" will appear to you highly specific, involving definite characters such as "I" and "it", or "I" and "thou", or "organism" and "environment", etc.


Multiordinal. Someone who takes the rejecting of the logical construct of identity as her/his most central premise must allow for a new kind of ambiguity: Say that we use a given term several times, each time on a different "logical level". Say also that we take due care to avoid unintentional punning – we see to it that each time we use the term, we utilize it yet again in a single specified one of its defined senses. A person who relies on the Postulate of Non-identity cannot depend on having this term always have "the same" meaning – s/he must face the possibility that, as we switch from one "logical level" to another, the meaning of the term may shift in unpredictable ways. Korzybski refers to this special kind of ambiguity as the multiordinality of terms. In particular, I take the construct of setting as multiordinal, and by way of example will specify two main "logical levels" and at least one subsidiary "logical level" for each, on which to use it.


Consider Main Logical Level1 , the (symbolic) domain of a-human-generating-and-using-formalized-notation – of particular interest to someone attempting to generate a notational language of known structure, suitable for framing a general theory of biology, or a non-aristotelian revision of quantum theory, or whatever. I regard the setting on this "logical level" as the "domain of discourse" within which a (symbolic) human might build up and/or use some such notation. Given a particular human in a time-and-place, transacting with her/his immediate environment – and here, that means, intent on building up a notation – whom I observe: I regard the setting "in the abstract" as the "undifferentiated ground" on which such "building up" can, and does, take place. If and when this human actually comes to grips with the task of notation-building, that means that s/he "particularizes" "her/himself-and-this-formerly-undifferentiated ground" – s/he engages her/himself in elaborating and transcribing undefined terms, postulates, etc., within and upon the chosen medium in this environment, in the process engaging in the kind of two-way, mutually-altering interchange which I call transacting.


Taken in this sense, the topic of setting lies outside the scope of today’s presentation.


Consider Main Logical Level2 , a (symbolic) domain of more ordinary-seeming human assuming-and-experiencing, by which the human seeks to maintain her/himself more or less intact-and-growing for at least a few moments more. I regard the setting on this "logical level" as the domain of discourse within which such (symbolic) human experiencing can take place. Given a particular human in a time-and-place, transacting with her/his immediate environment, whom I observe: I regard the setting "in the abstract" as the "undifferentiated ground" on which such experiencing can, and does, take place. If and when this human actually engages with her/his here-now environment, that means that I regard her/him as having "particularized" "the generality of this-formerly-undifferentiated ground, including her/himself" – s/he engages her/himself in dealing with her/his environment. I observe a particular "I"-and-"it", or "I"-and "thou", or "organism-and-environment", etc., engaging in the, mutually-altering interchange of transacting.


This sense of the topic of setting I will now take up.



Figure 43

Since I take biology as the main focus of this paper, let us consider an example – some biological experiencing. As vocabulary items with which to describe the fully-differentiated situation, I offer a grouping of five mutually-defining (or inter-dependent) terms: the polar "term-n-tuple" or term-cluster of





Abstraction and

An ordering on abstracting (or the notion of "logical levels").


(Elsewhere, I have used the construct of polar term-pair. In this context, it becomes especially apparent that I need to generalize that construct.)


Against this setting, I observe a particular situation, which includes a North American lawn by daylight, with air containing about 20% oxygen at roughly one atmosphere of pressure, moist soil, grass, a population of earthworms (Lumbricus terrestris), and a male robin (Turdus migratorius). Here I regard the robin as the organism which I observe, and the other aspects of this situation as making up the robin’s environment. That uses two members of my ring of five terms.


Robins belong to the order of passerine birds, whose primary gait for non-airborne locomotion consists of hopping. However, a hunting robin moves by placing one foot before the other – he strides or stalks, without much head-bobbing. Here-now, our robin stalks about through the grass; he freezes, turns his head this way and that, and then very suddenly thrusts his beak into the ground. After a vigorous display of tugging behavior, the bird straightens up with an earthworm grasped in his beak; he shakes it vigorously, mashes it with his beak and otherwise abuses it, and then swallows it.


In a short presentation, I cannot analyze every detail of the robin’s performance. Let me focus particularly on the moment, very shortly before he pecks, when our robin-organism cocks his head as if "listening". (I have heard that robins find their prey mainly by auditory cues.)


I take this postural display as the outward and visible sign that the robin has engaged in abstracting so as to generate an abstraction – which I could express in English as the assertion, "I HAVE LOCATED A WORM". That uses two more of my ring of five terms.


By acting on his abstraction – thrusting his (partly-opened) beak into the ground – our robin-organism treats his abstraction as a guess or behavioral hypothesis, and puts it to test. Then when he captures a worm, he must render it unable to crawl back out of his crop and escape, and must swallow it, or else he will derive no biological advantage from his capture. If he had come up with no worm, he would have to discard that behavioral hypothesis, and set about to generate another – which means, resume stalking earthworms.


By using these terms to describe what I observe, I indicate that I attribute to the robin (or to any other living organism) the ability (non-verbally) to abstract (to generate a ‘map’ of "what goes on in and around this organism"), and the ability (non-verbally) to distinguish between (non-verbal) map and (non-verbal) territory. I can state this point in more abstract terms as (i) the ability to generate a map, and (ii) the ability to generate an ordering on abstracting. That, then, completes the circle of five terms I started with.


In analyzing any other detail of the performance of our robin-organism transacting with his environment, I would again use all five members of this polar terms-cluster.


Figure VI gives a graphical representation of these relationings, analogous to the Venn diagrams of Figures IV and V.


Figure VI about here. (Step-diagram)


I invite you to regard this drawing as depicting the process of abstracting, in place within that ring of five polar terms.. Every visible and namable detail of this drawing represents some distinction (some non-identity) from within this Non-identity-based theoretical system (frame of reference), as viewed, by a designated observer ("I", the implied "speaker" of this paper).


The "steps" signify a hierarchical ordering (a series of adjacent "logical levels", which makes up one aspect of an ordering on abstracting). The arrows to the right of the two middle, complete "steps", labeled T1 and T2 , indicate that adjacent positionings in this hierarchical ordering (adjacent "steps") do not qualify as "synchronous" or "simultaneous", but rather "occur" or "exist" in such a way that they show a spatio-temporal ordering – it takes a while to get from one "up", or "down", to the next. (That forms another aspect of an ordering on abstracting.)


Given any pair of adjacent "steps", I can designate the "lower" one as ‘territory’ and the "higher" one as ‘map’.


On the "lower" (‘territory’) "step", the irregular circle labeled H signifies that part of the ‘territory’ which I call our ‘organism’. The irregular circle labeled Y signifies that part of the ‘territory’ I call her/his (‘external’) ‘environment’. The smaller internal circles signify that part (of ‘organism’ or ‘environment’) in principle detectable by the ‘organism’. The exterior rings signify that portion (of ‘organism’ or ‘environment’) in principle not detectable by the ‘organism’.


The arrow labeled s signifies that relationing I call self-referential abstracting; the one labeled r signifies hetero-referential abstracting. (That covers another of my ring of five terms.)


The irregular circle drawn on the "upper" ("map") "step", not labeled, signifies the organism’s ‘map’ (abstraction – the fifth member of the ring)) of the adjacent ‘territory’. Here I show it as divided into Self (Sf) and Other (Ot) "components". The inner half-circles signify those portions of the ‘map’ directly obtained by abstracting from the ‘territory’, whereas the outer half-rings signify those portions of the ‘map’, unavoidably present, which do not in any sense derive from the ‘territory’, but rather, which have to do with the ‘organism’ who does the abstracting.


In order to transform this graphical way of representing the construct of abstracting into an explicit version of the Logic of Opposites, I need only re-interpret the irregular circle on the top "step". On the configuration which expresses the structural biological issue of "Self" vs. "Other" or "organism" vs. "environment", superimpose a representation of a Gestalt, with a figure which focally interests our organism, against a (back)ground which (at present) does not.


When I transform the argument in my non-standard notation, my premises (a variant of the non-aristotelian premises of Korzybski) require me to make explicit how the abstraction arises, and where it occurs. When I approximate that notational argument in English, the fact that I use that ring of five terms appears merely arbitrary.


Then with reference to this modified step-diagram, I can approximate the non-identity-based version of the Logic of Opposites in English as:


1. Our incompletely informed and inaccurately-informed and self-referentially-informed (symbolic) ‘organism’,


2. Consists of spatio-temporally-ordered "doings" or "happenings" which occur within a (delimited) overall setting known as transacting.


3. By her/his abstracting, our ‘organism’ elaborates a ‘map’ framed as a ‘gestalt’ (abstraction) composed of

a) a ‘figure’ which focally interests the ‘organism’

b) specified against a ‘background’ which does not (at present) interest her/him.


4. Any ‘gestalt’ further consists of two ‘components’

a) one of which tells about one aspect of the territory, namely, the ‘external’ ‘environment’ and

b) the other tells about another aspect of the territory, namely, the ‘organism’ which elaborates the ‘gestalt’.


5. In negating a ‘gestalt’, our ‘organism’ interchanges the ‘figure’ and the ‘background’, and alters none of the other considerings listed here.


Since this frame of reference shows an intrinsic spatio-temporal ordering, when you negate and then re-negate a Gestalt, that does not bring you back to your starting-place.


If nothing else has already brought the point home, this last finding should make it palpable that this specific delimited version of the logic of opposites differs radically from either of the blank versions.


How do we get a sense of the magnitude of this difference?


To begin with, at the level of its most-fundamental premises, the frame of reference which includes this alternative version of the logic of opposites stems from the non-aristotelian premises of Korzybski, which, as their most fundamental premise, reject the logical construct of identity. In contrast, we express the Laws of Thought, or the modern logical axiom of identity, in languages whose grammar intrinsically depends on the construct of identity.


The alternative version makes a number of distinctions (non-identities) which neither Aristotle’s nor even Zermelo’s versions require. Furthermore, it demands that I regard any abstraction as "inaccurate, incomplete and self-referential". As a consequence, it utilizes the polar term-cluster presented above; it requires its users to make the map-territory distinction; etc. Since it stems from Korzybski’s premises, including the Postulate of Non-identity, our version of the logic of opposites conclusively depends on some other grammar, and dismisses and displaces the Law of Identity, and with it, the Law of Contradiction and Law of Excluded Middle.


Let me warn you that in this presentation I will have to pull out the rug that I currently stand on, namely, my continuing use of WIE languages (such as English and set theory) to express these constructs.


If, as I point out above, in an operational sense (e.g. the sense of what we DO rather than what we SAY) we generate our two main "parts of speech" by treating the NP’s as "identical with themselves" and the VP’s as "not identical with themselves", then the logical act of disallowing identity has an unexpected consequence: It renders us unable to distinguish the "nouns" from the "verbs." Consequently, the entire structure of the WIE grammar collapses, taking with it our logics, mathematics, sciences, philosophies, jurisprudences, religions, etc.


In order to present my proposals for biology in a thorough-going fashion, within the non-standard frame of reference, I would have to treat the other topics listed in Figure 2n in a similarly detailed and loving fashion.


In developing my alternative frame of reference, and using it as the basis for proposals in the domain of biological theory, I have upheld my own standards of rigor. I have done my investigating in at least two formalized notational languages: first, a traditional one (set theory); and later, a non-standard one (which I developed in collaboration with several associates, most notably the late Ronald V. Harrington). I have taught this non-standard language to several groups in courses with fifty or so contact hours. Members of those groups have told me, and/or showed me, that they found the material personally and professionally useful. We lack the time at this meeting to acquire fluency in such a language.


In undertaking this presentation, however, I promised myself that I would make what I have to say accessible to my fellow-humans, including those who do not have mathematical languages like set theory at their command. That means that from this point on, I must walk a tightrope – for the next topic on the agenda started out as a mathematical construct.







Figure 44



In 1950, the British anatomist and cyberneticist Gerd Sommerhoff performed a logical analysis of the traditional biological construct of the apparently-purposive activities of living organisms. He generated a mathematically-defined model of it, which he calls directive correlation. He used it to analyze the major teleological terms, and to provide logically and empirically satisfactory definitions for them.


In 1962,W. Ross Ashby provided a summary of a Bourbaki algebraic set theory notation, and translated Sommerhoff’s construct into that notation. Further, he provided a theorem which generalizes Sommerhoff’s definition.


In 1965, using Ashby’s notation, I incorporated Sommerhoff’s construct into my developing theoretical system. In order to do so, I had to reinterpret it in light of Korzybski’s premises in general, with special attention to the Postulate of Non-identity.


Let me return to the example of the robin and worm, discussed above, this predator/prey encounter which I observed. To describe this biological occurrence in terms of the modified construct of directively correlated, I must partition my picture of these "doings" or "happenings", and assign the various aspects of this setting to the relevant parts of the construct. (I began that process when I designated robin as organism and worm, etc., as environment.) Now, considering the various aspects separately and/or together in accord with this interpreted model, I must show what they do.


In order to do this, I'll resort to a mathematical vocabulary, but in a way that will allow persons with little mathematical background to follow the argument. In particular, I'll need two main mathematical constructs: variable and function.

a) The term variable refers to a kind of mathematical "blank check," to which you can assign various values.

b) The term function designates a kind of "logical machine" which, when you give it one value, returns you another value, according to some "rule."


Then to spell out the construct of directively correlated, I require at least two variables and three functions.



Figure 45


i) Coenetic variables (CV), a kind of "initial conditions" which, at the beginning of the purposive sequence, affect both organism and environment – in this case, the background factors consist of the lawn-worm-robin constellation, and the foreground factors consist of whatever interoceptive and/or sensory cues led the robin to start hunting ("hungry", "stalking"), and whatever sensory cues led him to peck into the ground at that spot ("detecting a worm"). Let d (a disturbance) signify a particular value of CV . (This term, introduced by Sommerhoff, intrinsically includes both the background and the foreground factors.) .


ii) Focal conditions (FC), the criterion for a favorable outcome, from the point of view of the organism – in this case, for the robin, obtaining a worm to eat. FC comprises a part (subset, designated Ì ) of outcomes (Oc). Let oc signify a particular value of Oc ("ending up obtaining a worm", or "ending up not-obtaining a worm"), which might or might not satisfy this criterion and so might or might not belong to FC .


The constructs of coenetic variable and focal condition function as another mutually-defining, polar term-pair. For example, an organism can develop or experience no valid "need" – such as for oxygen or food or the physiological aspects of sex – without the actual or potential existence within the environment of something that can satisfy the need, such as breathable air, edible foodstuffs, or at least potentially available sexual partners.


Figure 46



i) Effects of the CV on the organism, which I can express as the function f . As a set ("collection of the effects of various values of CV – e.g., effects of various sensory cues – on the organism"), f signifies "What the organism does" – which includes the making of maps and the process of guiding itself by these maps, or in other words, the activities which I call abstracting. Then f(d) mathematically signifies "What the organism does with the disturbance d " – e.g. generates some particular maps of or abstractions about what in particular goes on in and around our organism at the moment in question, such as "hungry", "stalking", and "detecting a worm".


ii) Effects of the CV on the environment, which I can express as the function g . As a set ("collection of the effects of these factors on the environment"), g signifies "What the environment does". Earthworms form a part of our robin's environment, so "what the environment does" will include what earthworms do. Then g(d) signifies "What the environment does with the disturbance d " – here, it includes what this particular earthworm does. .



Figure 47

iii) Mutual correlations between f(d) and g(d) , which I can write as Psi (Y).
As a set, Y signifies "How what the organism does and what the environment does articulate."

Y(g(d),f(d)) signifies "How what the robin does this time meshes with what the environment (including this earthworm) does this time."

Y(g(d),f(d)) leads to an outcome oc . The particular outcome oc may or may not qualify as favorable from the point of view of the organism. ("I caught this worm", vs. the unfavorable "I didn't catch this worm.") If it does so qualify, I say oc belongs to FC (satisfies the criterion of favorable from the point of view of the organism); if not, I say oc does not belong to FC (Alternatively, I might study a series consisting of a pre-determined number of such predator/prey encounters, and classify the outcome as favorable from the point of view of the organism if and only if it satisfies some statistical criterion, e.g. if the predator captures the prey more often than would happen if the predator guided his actions by chance alone.)



Figure 47 (lower half)

A directively correlated (apparently purposive) sequence, then, over the interval t0 to t2, involves the following "doings" or "happenings":




At t0: d lawn-robin-worm-etc. system ...

At t1: f(d) and g(d) robin detects earthworm,..., pecks...

At t2: Y (g(d),f(d)) = oc struggle,..., robin eats earthworm


So far, so good – when presented in this verbal fashion and deployed in some detail, the construct of directively correlated gives a convincing enough accounting for this predator/prey encounter. From this point on, those with scant background in "Let’s Keep Track of What We Say" types of mathematics will have to take my word for it to an increasing degree, while I translate this verbal presentation into a set theoretic definition and three theorems.



Figure 48

The construct of directively correlated, as defined in a Bourbaki algebraic set theory notation, goes as follows:


Given: Spaces O , E , CV Ì O × E , and Oc Ì O × E , together with an onto function g:CV® E and a function y :E × O® Oc ; then, with FC a subset of Oc, we have


DEFINITION: A function f:CV® O qualifies as directively correlated with respect to g , y and FC if and only if

" d Î CV : y (g(d),f(d)) Î FC. Sentence (1)


Figure 7 may help in visualizing this construct.


Figure 7 about here (Ashby/H&R)





Figure 49

The main point of describing a situation of interest in a mathematical language lies not in stopping there and resting on your laurels, but rather in the support for further developments which the mathematical language provides.


As presented, Sentence (1) refers to specific situations, such as a robin-and-worm encounter. As displayed, it shows both sets (e.g. CV , f , g , Y , etc.) and some of the elements of these sets (e.g. d , f(d) , g(d) , the ordered pair (g(d),f(d)) , etc.).




Element-Free Expression


The tools of set theory make it possible to rearrange a definition like Sentence 1 to bring any one of its constituent terms under scrutiny (in the process, concealing the elements). Here, I scrutinize the term f , "what the organism does (with d )". This entails generalizing Sentence 1 so as to describe not just the structure of specific predator/prey encounters, but rather, to specify the part played by the chosen key component of the construct of directively correlated in relation with the other components.



THEOREM: In the notation of sentence (1), f qualifies as directively correlated with respect to g , y , and FC if and only if


f Ì y -1(FC) o g . Sentence (2)


PROOF. A proof appears in the Appendix, and also in Hilgartner & Randolph (1969a), p. 336.




Figure 50


Biologically Integrated Relations between

Directively Correlated Activities


Sommerhoff defines the construct of integrated in the biological sense as follows:


A set of organic activities is integrated in the biological sense if the activities are directively correlated and if these correlations are again directively correlated inter se (e.g., if their respective focal conditions may in turn be regarded as a set of directively correlated variables). (Sommerhoff, 1950, p.195)


I display two systems, P and Q , each of which qualifies as directively correlated in this notation. I define P Ì O × E so that (1) and (2) hold, while Q Ì O × E involves a space

J Ì O × E , an onto function n:J® E , a function m:J® O , and a function g :E × O® Z , with

H Ì Z . Then m qualifies as directively correlated with respect to n , H and g if and only if


" j Î J : g (n(j),m(j)) Î H . Sentence (3)


Then by reasoning like that displayed for theorem (2),


m Ì g -1(H) o n . Sentence (4)


Simplest case: Let us suppose that the set of ‘favorable outcomes’ (focal conditions) for P consists of the same elements as does the set of ‘disturbances’ (coenetic variables) for Q , or in other words, FC = J .


Then, given a mapping, the projection onto the O axis PjO: E ´ O ® O , then the relation between P and Q qualifies as ‘integrated’ (a ‘directively correlated’ relation between two ‘directively correlated systems’) if and only if


f Ì y -1(m-1 o PjO o g -1(H)) o g . Sentence (5)


PROOF: A proof appears in the Appendix; and first got published in A Non-aristotelian "Rosetta Stone" (Hilgartner, 1971).



Figure 51


Living System


Sommerhoff defines the term living organism (for which I substitute living system, (LS)) in terms of integrated relations between directively correlated systems.


A living organism may be described as a compact physical system of mechanically connected parts whose states and activities are related by an integrated set of directive correlations which, over and above any proximate focal condition, have the continued existence of the system as an ultimate focal condition. Death may be described as the breakdown of these directive correlations. (Sommerhoff (1950), pp. 195-6; cf. also 161 ff.)


Here, besides the multiordinal usages of directively correlated, Sommerhoff also specifies multiordinal usages of focal condition (and thus, by polar relations, multiordinal usages of coenetic variable as well).


In the notation of directively correlated systems and of integrated relations between directively correlated systems, I can express the sense of Sommerhoff’s formulation by using Sentence (5a) to define the set of living systems, (LS). I make this explicit in Sentence 6 below.


Given a system which I shall call our (supposed) organism O , which contains a finite set of parts (sub-systems which involve the states or activities of our organism), namely,

P1, P2, P3,..., Pn , for each of which sentences (1) and (2) hold, and where

FC1 È FC2 È FC3 ... È FCn Ì Z ; and given that our supposed organism contains another sub-system Q for which sentences (3) and (4) hold and for which J = FC × FC2 × FC3 × ... × FCn ; and finally, given that the focal condition H which figures in Q refers to what Sommerhoff calls "the continued existence of the system (as an ultimate focal condition)", which I have rendered as the ultimate focal condition of all organisms ... the preservation-and-growth of the organism (Pr) throughout some finite time-interval (Hilgartner & Randolph, 1969a, p. 312):

Then, in notation.,


O Î LS Û [fi Ì y -1(m-1 o PjO o g -1(Pr)) o gi]i Sentence (6)


Proof. A logical proof of (6) would closely follow the lines of the proof of (5).


That completes the description of the mathematical construct of directively correlated.

(End of Figure 51)





With these mathematically-defined biological constructs in hand, I performed a number of studies which I cannot present in detail today, but can only mention.


1. I have re-worked enzyme chemistry, treating any enzymic reaction as an apparently-purposive system and potentially part of one or more integrated systems, e.g. the systems

which ‘control’ the rate of key reactions or of whole metabolic pathways in the intermediary metabolism of an actual living organism.


In extending the scope of "enzyme chemistry" in these ways, I did not have to sacrifice the chemical, physical-chemical, kinetic, thermodynamic, energetic, etc., insights achieved by earlier workers. Furthermore, in line with my proposals, if experimentalists should find evidence for integrated directively correlated activities in a particular system, they then generate empirical ground for classifying this system as living.


2. I combined data from two otherwise unconnected studies, both concerned with simulating early conditions on planet Earth, presumably prior to the appearance of the first living organisms. Sillén (1967) studied the physical chemistry of three-phase systems, providing a model for the physical chemistry of an abiotic planet with an ocean and an atmosphere. Miller (1953) set up an experimental system in which abiotic genesis of amino acids and other organic chemicals occurred.


When I examined the data from these experiments, I found that both systems appeared to operate in a directively correlated fashion. I proposed the possibility that, if someone should combine these two experiments, performing both concurrently within one experimental system, s/he might find that the two systems demonstrably functioned in a biologically integrated fashion. If they did, that would suggest that an "abiotic" planet with an ocean of liquid water and an atmosphere already satisfies the criteria for classification as living.


Such a finding, and conclusion, would cast a vastly altered light on the otherwise as yet unanswered question of how "living" organisms came into existence on Planet Earth. At present, biologists face the incomprehensible mystery of how LIVING organisms could arise on and from a NON-LIVING planet. My proposal shifts the grounds of the inquiry. The question of how cellular organisms arose on and from a planet which already has at least one integrated directively correlated system comes to appear isomorphic with the question of how further evolution of the "first" organisms came to pass – presumably, by the development of more numerous, more extensive, and more highly inter-related directively correlated activities.






In this presentation, I have demonstrated many features of a novel way of addressing biological theory in the light of general semantics. I trust that it may empower other workers to extend its implications beyond the start I have offered here.


I have presented a synthesis of Korzybski’s frame of reference, as adapted by me and several associates over the past thirty-plus years, with the constructs of other workers, including the anatomist and cyberneticist Gerd Sommerhoff. This synthesis advances Korzybski’s program in the domain of biology. By using the notion of polar term-pairs to clarify our understanding of the postulate of non-identity, and by generalizing it as polar term-cluster in the context of abstracting in general and biological abstracting in particular, this alternative frame of reference takes another of Korzybski’s breakthroughs to its next level. I can even hope that this work may facilitate others to approach these breakthroughs on the level of lived theory.



Figure 52

As a major implication of the arguments presented here, I point out that constructs such as life or living function in a self-reflexive manner. After all, we regard OURSELVES as living. Therefore, the way we define these terms becomes part of our "self-image" - part of our own functioning, part of US. The definitions offered here, backed up with mathematical logic, offer us opportunities to build our lives more to our own liking, and more in line with the constraints for living sustainably within the ecosphere.






American Heritage Dictionary, Second College Edition (1982). American Heritage Publishing Co. Inc., & Boston/New York/etc. : Houghton Mifflin Company.


Ashby, W. Ross (1962). "The Set Theory of Mechanism and Homeostasis." Technical Report No. 7, Electrical Engineering Research Laboratory, University of Illinois, Urbana, IL 61803 (cf. Hilgartner & Randolph (1969a), p. 336ff).


Dewey, John & Arthur F. Bentley (1949). Knowing and the Known. Boston: Beacon Press.


Hilgartner, C. Andrew (1970). "Metabolic 'Control' in Mature Erythrocytes." (Submitted for publication.)


Hilgartner, C. Andrew (1971). "A Non-Aristotelian ‘Rosetta Stone’." Privately printed for the Institute for Contemporary Education, Inc., 1510-16 East 87th Street, Chicago, Illinois 60619. pp. 49-52 & 52-3.


Hilgartner, C. Andrew (1972). "The Notions of 'Living System', 'Abstracting', and the 'Map'-'Territory' Analogy." (Submitted for publication.)


Hilgartner, C. Andrew, Ronald Harrington & Martha Bartter (1989). "Anomolies Generated by Contemporary Physics." Bulletin of Science, Technology, and Society 9, 129-43.


Hilgartner, C. Andrew, Ronald Harrington & Martha Bartter (1991). "The Conventions for Symbolizing" ETC.: A Review of General Semantics 18(2), 2-19.


Hilgartner, C. Andrew, & Theodore L. Miller, 1992 "How to Foster Innovating." Presented at the annual meeting of the Ohio Academy of Science, 3 May 1992.


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


Korzybski, Alfred (1921). Manhood of Humanity: The Science and Art of Human Engineering. E. P. Dutton, 1921. 2nd Ed., (1950), (M. Kendig, ed.), Institute of General Semantics, Lakeville CT.


Korzybski, Alfred (1933). Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics. International Non-Aristotelian Library Publishing Co., Chicago. 4th edition, Institute of General Semantics, Lakeville CT. 1958.


Korzybski, Alfred (1941). "General Semantics, Psychiatry, Psychotherapy, and Prevention." in Collected Writings, 1920 - 1950, pp. 297-308. (M. Kendig, ed.), Institute of General Semantics, Englewood, N. J. 1990.


Mayr, Ernst (1982). The Growth of Biological Thought Diversity, Evolution, and Inheritance. Cambridge MA: The Belknap Press of Harvard University Press.


Miller, S. (1953). Science N. Y. 117, 258.


Perls, Frederick M., Ralph Hefferline & Paul Goodman (1951). Gestalt Therapy: Excitement and Growth in the Human Personality. New York: Julian Press.


Sillén, L. S. (1967). Science N. Y. 156, 1189.


Sommerhoff, Gerd (1950). Analytical Biology. London: Oxford University Press.


Stanley, Wendell M., quoted in White, Handler, Smith & Stetten, see below (1954), pp. 7-8. These authors attribute this quote to Stanley (1948), American Scientist 36: 59-68. However, I do not find this passage in that review article.


Turbayne, Colin (1962). The Myth of Metaphor. New Haven & London: Yale University Press.


White, Abraham, Philip Handler, Emil L. Smith & DeWitt Stetten (1954). Principles of Biochemistry. New York: McGraw Hill.

Whyte, Lancelot Law (1969). "On the Frontiers of Science: This Heirarchical Universe" Korzybski Memorial Lecture, 18 April, 1969. Printed in General Semantics Bulletin, No. 36,

7-14, p. 12b.












DEFINITION: (cf. ms pp. 21-2 (Figure 48)) Given: Spaces O , E , CV Ì O × E , and Oc Ì O × E , together with an onto function g:CV® E and a function y :E × O® Oc ; then, with FC a subset of Oc, we have


DEFINITION: A function f:CV® O qualifies as directively correlated with respect to g , y and FC if and only if


" d Î CV : y (g(d),f(d)) Î FC. Sentence (1)





THEOREM: In the notation of sentence (1), f qualifies as directively correlated with respect to g , y , and FC if and only if


f Ì y -1(FC) o g . Sentence (2)


Proof: First let f qualify as directively correlated. I define a set A by


A = {(e,o)| $ d Î D: e = g(d), o = f(d)} .


That makes A a subset of the domain of y and, from (1), y (A) Ì FC . Also


A = {(e,o)| $ d Î D: (d,e) Î g, (d,o) Î f}

= {(e,o)| $ d Î D: (e,d) Î g-1, (d,o) Î f}

= f o g-1 Ì E × O by Definition 4.1 of Appendix 3: Notation.


Thus y (f o g-1) = y (A) Ì FC , so that, from (5.5) of Appendix 3,


f o g-1 Ì y -1(FC) ,




f o g-1 o g Ì y -1(FC) o g .


Since g:D® E comprises an onto function, then g-1 o g (superset) ID , so that


f o g-1 o g É f o ID = f .


From that, (2) follows.


Conversely, assume an f such that (2) holds. Then


f o g-1 Ì y -1(FC) o g o g-1 .


This time I use the fact that g o g-1 = IE to obtain first


f o g-1 Ì y -1(FC) and then y (f o g-1) Ì FC .


Select any d Î D . Then (d,g(d)) Î g, (d,f(d)) Î f and thus


(g(d),d) Î g-1 , (d,f(d)) Î f . Consequently,

(g(d),f(d)) Î f o g-1 , so that

y (g(d),f(d)) Î y (f o g-1) Ì FC


for each d Î D ,which by (1) means that f qualifies as directively correlated with respect to g , y and FC .







I display two systems, P and Q , each of which qualifies as directively correlated in this notation. I define P Ì O × E so that (1) and (2) hold, while Q Ì O × E involves a space J Ì O × E , an onto function n:J® E , a function m:J® O , and a function g :E × O® Z , with H Ì Z . Then m qualifies as directively correlated with respect to n , H and g if and only if


" j Î J : g (n(j),m(j)) Î H . Sentence (3)


Then by reasoning like that displayed for theorem (2),


m Ì g -1(H) o n . Sentence (4)


Simplest case: Let us suppose that the set of ‘favorable outcomes’ (focal conditions) for P consists of the same elements as does the set of ‘disturbances’ (coenetic variables) for Q , or in other words, FC = J.


Then, given a mapping PjO: E ´ O® O , the relation between P and Q qualifies as ‘integrated’ (a ‘directively correlated’ relation between two ‘directively correlated systems’) if and only if


f Ì y -1(m-1 o PjO o g -1(H)) o g . Sentence (5)


Proof. First let P and Q qualify as ‘directively correlated’ systems, with FC = J , and let the relation between P and Q qualify as ‘integrated’. I define a set R by


R = {(e,o)| $ j Î J: e = n(j), o = m(j)} .


Hence R comprises a subset of the domain of g and, from (3), g Ì H or


R Ì g -1 (H) Ì E × O . Then

PjO Ì PjO o g -1(H) Ì O ,


and since m-1 Ì O × J ,


m-1 o PjO Ì m-1 o PjO o g -1(H) Ì J .


As I show for (2),


f o g-1 Ì y -1(FC) ;


but since J = FC , then


f o g-1 Ì y -1(m-1 o PjO o g -1(H)) ,


from which (5) follows.


Conversely, assume a P and a Q such that if J = FC , then (5) holds. Then


f o g-1 Ì y -1(m-1 o PjO o g -1(H)) o g o g-1 .


Again I use g o g-1 = IE to obtain


f o g-1 Ì y -1(m-1 o PjO o g -1(H))


I have already demonstrated that m-1 o PjO o g -1(H) Ì J.


If J = FC , then


y -1(m-1 o PjO o g -1(H)) = y -1(FC) ,


and so f o g-1 Ì y -1(FC) .


But I have already demonstrated that given an expression of that form, then f qualifies as directively correlated with respect to g , FC and y .




j Î m-1 o PjO o g -1(H) Û m(j) = o Î PjO o g -1(H) Ì O ,




o Î PjO o g -1(H) Û PjO-1(o) = (e,o) Î g -1(H) Ì E × O ,


where e = n(j) . Then from the set R defined by


R = {(e,o)| $ j Î J : (e,j) Î n-1 , (j,o) Î m}


we can see that


R = m o n-1 Ì E × O ,


and thus


m o n-1 Ì g -1(H) .


But as I demonstrate for theorem (2), given an expression of that form, then m qualifies as ‘directively correlated’, with respect to n , H and g .


Thus if (5) holds, then both P and Q quality as directively correlated systems.

But 5 holds if and only if FC = J , where FC designates the set of focal conditions for P and J designates the set of coenetic variables for Q .


And by Sommerhoff’s definition of "’integrated’ in the biological sense", if (5) holds and J = FC , then the relations between P and Q qualify as integrated. That completes the proof.






Given a system which I shall call our (supposed) organism O , which contains a finite set of parts (sub-systems which involve the states or activities of our organism), namely,

P1, P2, P3,..., Pn , for each of which sentences (1) and (2) hold, and where FC1 È FC2 È FC3 ... È FCn Ì Z ; and given that our supposed organism contains another sub-system Q for which sentences (3) and (4) hold and for which J = FC × FC2 × FC3 × ... × FCn ; and finally, given that the focal condition H which figures in Q refers to what Sommerhoff calls "the continued existence of the system (as an ultimate focal condition)", which I have rendered as "the ultimate focal condition of all organisms ... the preservation-and-growth of the organism (Pr) throughout some finite time-interval (Hilgartner & Randolph, 1969a, p. 312):

Then, in notation.,


O Î LS Û [fi Ì y -1(m-1 o PjO o g -1(Pr)) o g i]i Sentence (6)


Proof. A logical proof of (6) would closely follow the lines of the proof of (5).