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To Improve Predicting In The Study of Living Systems



254 Kensington Place, Marion OH 43302



Department of English, Ohio State University at Marion,

1465 Mt. Vernon Avenue, Marion OH 43302



Department of Foreign Languages, Literatures and Linguistics

University of Rochester, Rochester NY 14627



The first author presented another version of this paper at the 97th Annual Meeting of the Ohio Academy of Science, Ohio State University at Newark, April 1988.





This paper addresses the generally acknowledged lack of rigor and predictability of the biological sciences. The authors claim that these problems stem from hidden, restricted and restrictive assumptions encoded in the various biological theories, which eliminate from consideration certain key relationships crucial to an adequate understanding of living systems. Most biologists fail to recognize that when they represent living systems in terms of the kind of "one-way causality" characteristic of non-living mechanisms, they not only build on but also ratify the neglect of these relationships. Without these key relationships, our biology cannot account for the kinds of "happenings" which we designate as human behaving/experiencing, self-reflexive relations, the structure of the transacting which occurs between organism and environment, etc. These remain among the least tractable topics in biology.


The authors have proposed an alternative theoretical system, one which discloses these hidden assumptions, disallows them, and so permits taking these neglected relationships into account with full mathematical rigor. This allows creating a much closer match between theoretical constructs and the actual observations observers wish to account for.


To illustrate the strengths of this theory, we have chosen to examine a sequence from the first author's behaving/experiencing, and interpret it in terms of several constructs from our theoretical system. We invite others to test our proposals by applying our terminology, models, etc., in some work already underway.



To Improve Predicting In The Study of Living Systems |-



254 Kensington Place, Marion OH 43302



Department of English, Ohio State University at Marion,

1465 Mt. Vernon Avenue, Marion OH 43302



Department of Foreign Languages, Literatures and Linguistics

University of Rochester, Rochester NY 14627





In discussing the topic of improving our predicting in the realm of living systems, I speak from the point of view of a comprehensive, and perhaps unexpected, theory -- a revised frame of reference (Hilgartner, 1968, 1974, 1976; Hilgartner & Randolph, 1969a,b,c).




This theory asks and answers the following fundamental question:


How does a dynamically changing organism, functioning within a dynamically changing environment, and operating from sensory information that remains intrinsically inaccurate, incomplete and self-referential, manage to keep itself intact-and-growing from moment to moment for a whole lifetime?


For the next few minutes, consider me as a biological specimen, of the species Homo sapiens, functioning as an-organism-as-a-whole-in-my-environment-at-a-date. As the topic of our scrutiny -- that aspect of my behaving/experiencing that needs explaining -- let's look at me participating in the 97th Annual Meeting of the Ohio Academy of Science.


In a self-referential theory, for me to select the topic of my own behaving/experiencing appears legitimate.




Over the millennia, humans have devised a number of versions of what I call the logic of opposites -- the schema which spells out the relations which obtain between a term C and its opposite or complement or contradictory, Not-C .


The standard Western Indo-European (WIE) version of the logic of opposites specifies no setting for its terms. Instead, it posits what we call an undelimited domain. In other words, it treats Not-C as made up of "everything else" outside of C . Thus, with respect to the term-pair organism and not-organism (environment), it treats "the environment" as made up of "everything else" outside of "the organism."


In contrast, our revised theory utilizes a non-standard version of the logic of opposites: It posits a specific, delimited setting on which to specify any term and its opposite. I could describe this setting in English as "a world inhabited by organisms (including humans) transacting with -- in contact with -- their environments." The Gestalt therapists, Perls, Hefferline & Goodman (1951), capture the sense of this specific delimited setting in a vivid phrase, where they say,


We speak of the organism contacting the environment, but it is the contact that is the first and simplest reality.

And from this "simplest and first reality," e.g. from some contacting specified on this setting, we humans INFER organism and environment, or I and it, or I and thou, etc.


I can designate this setting by means of a run-on phrase such as "The dealings of one particular organism-as-a-whole-with-her/his-environment-at-a-date"; or I can indicate it with a single term such as transacting or contacting.


Stated this another way: As polar opposites, the constructs of organism and environment remain mutually necessary, mutually-constitutive -- we cannot isolate them from one another, for we cannot define either one without the real or implied existence of the other.


Moreover, according to our revised theory, any behaving/experiencing sequence resembles a story: It has a beginning, a middle, and an end or outcome. The beginning consists of some 'disturbance' which affects both organism and environment. The middle, the response to this 'disturbance', consists of "doings" of the organism and "doings" of the environment -- both of which remain relentlessly dynamic. At the end, the "doings" of organism and environment mutually affect each other so as to produce the outcome.


Still further, a behaving/experiencing sequence involves an intimate dialogue or "dance" between organism and environment. As observers, we may have trouble seeing, and/or saying, this, but the two constructs have something in common: every phrase in the dialogue, every step in the dance, involves them both, contains a contribution from both.


The behaving/experiencing I have chosen to examine, my participating in the Ohio Academy meeting, started a week or so after I became a member of that organization, when I received a copy of the CALL FOR PAPERS. That led me to imagine an outcome, a potentially fulfilling situation -- namely, the possibility that I might successfully present a paper here and receive satisfying feedback (in the form of useful discussion with the audience -- instead of, say, their blank uncomprehending stares).


After an encounter or situation has gotten underway, and before it reaches an outcome, both the environment and the organism DO things.


1) In this situation, 'what the environment does' includes activities of the distant environment, e.g. those persons who handle the logistics of the meeting -- hiring the hall, enrolling the moderators, scheduling the presentations, providing overhead projectors, and a myriad other such details. Too, it includes the other participants, those who also intend to answer the CALL FOR PAPERS, preparing their own presentations; people coming to the meeting; attending "my" session, etc. By way of activities of the closer environment, it also includes what my collaborators do in working with me, the functioning of the word-processing equipment in my writing studio, etc.

2) On the other hand, 'what the organism does' includes my conferring with collaborators, writing the paper, producing fair copy, preparing the transparencies for the overhead projector, and in general, taking care of the myriad details required to get ready for the presentation. It also includes me getting myself to the proper location, in time to present the paper.


3) At the end, 'what the organism does' and 'what the environment does' interact. In this situation, that interacting takes place at the actual meeting of actual people for the actual presentation.


4) That interacting produces the outcome -- which (as judged by the stated criterion) will appear satisfactory from the point of view of the organism, or else not satisfactory. Since (as of the time I wrote this analysis) the present situation remained as yet still uncompleted, my self-reflexive analysis of my own situation slopped over into the realm of predicting: What will come to pass there? When I present this paper before a live audience, will the presentation, in this organism/environment situation, generate useful dialogue, or blank looks, from my audience? Surely, DISCUSSING the hypothetical audience's possible responses to this self-reflexive analysis, WITH an actual audience, will affect the outcome -- but HOW?


In fact, when I spoke before the Ohio Academy, my presentation elicited no direct questions from the floor. However, about a minute into the next presentation, the speaker stopped himself in mid-sentence and then revised the way he phrased his point, using the terminology I had just introduced; and he acknowledged me with a glance and a nod as he did so. I took this as indicating that he had picked up some part of my model and terminology, and used this in his own endeavors. That in turn means that my presentation elicited "useful dialogue" with at least one member of my audience -- which satisfies the condition of a successful outcome, from my point of view. Further, that transaction detectably altered ME; and now, in seeking publication of this paper, I show that the successful completion of one behaving/experiencing sequence can serve as the initiating condition for the next.




This way of describing my activities presupposes an explicit model, specifically a model of the apparently-purposive activities of living systems. Let me present this model with some care and rigor.


Whenever we look in detail at what living systems DO, we find that whatever we may examine seems "goal-directed" or apparently-purposive. In other words, we find that, all at the same time all together, a living system engages in activities of different relative sizes -- it concurrently participates in a geology and an ecology, shows morphology and anatomy, runs a physiology and a biochemistry, etc. We find that whatever we examine fits into place in the activities on the next higher level as if "on purpose," so as to make the higher level functions work. Furthermore, at least down to the level of biochemistry, in anything whatsoever we may examine, we find it has subsidiary details, occurring on the next lower level of activities, which fit in as if "on purpose," so as to make the details under examination also work.


Starting at the latest with Aristotle of Stagira (384-322 BC), biologists developed a way of describing living systems which treats this apparently "goal-directed" aspect as a manifestation in nature of some "ultimate purpose" (Greek, teleos). They developed a traditional lexicon of teleological terms, which posit this kind of "ultimate purpose." For over two thousand years, the doctrine of teleology seemed plausible and acceptable. But with the developments in logic, mathematics, physics, etc., of the last couple of centuries -- including increasingly strict standards of rigor -- teleology (and its later offshoot, vitalism) came to look increasingly implausible. Furthermore, efforts to make biological theory rigorous in its own terms consistently failed.


Faced with that failure, over the past century or so some biologists have sought to "reduce" biological theory, to borrow theoretical constructs from the physical scientists and express their biology in the terminology of physics and chemistry; others have used the teleological terminology anyway; and others, aware of the bankruptcy of the first two approaches but with no alternative to offer, have fought shy of dealing with the overall problem of life altogether.


As the anatomist and cyberneticist Gerd Sommerhoff (1950) puts it,


It is not difficult to see why exact science has been unable to cope with this purposive or goal-directed aspect of organic nature: science still lacks really exact concepts in terms of which it can even as much as describe it, let alone interpret it. Biologists have been too keen to explain things before they were able to state in exact terms what they wanted to explain and what objective system-properties they were studying. Instead of scientific theories about the exact spatio-temporal relations and types of order involved in the organization of living systems, we find but hazy descriptions of the various purposive aspects of life in terms of such vague and often anthropocentric concepts as 'adaptation', 'subservience', 'coordination', 'regulation', 'integration', 'organization', 'final causation', etc., none of which, as they stand, attain to that standard of exactness which modern mathematical theory has shown to be indispensable to a strict and deductive scientific system. The result is a welter of discordant opinions about the general nature of life, and that typical inability to reach agreement, which so often accompanies the use of philosophical concepts whose inherent vagueness allows of almost as many readings as there may chance to be readers. None of these traditional biological concepts tell us much more than that there is in nature something analogous to the purposive behavior of Man; but what this is biologists have so far been unable to say with precision. It is the main task of our analytical biology to remedy this failure

To describe HUMAN behaving/experiencing -- apply it to sequences like the one concerning me participating in this meeting -- we carry the absurdity to even more absurd lengths: We say, in effect, "There is in HUMAN behavior something analogous to the purposive behavior of Man."


Sommerhoff proposes a model for the apparently-purposive activities of living systems. He uses a specialized mathematical notation, with formalized "rules of inference," to do so. A specialized notation confers one great advantage: It restricts discussion to the topic at hand. Sommerhoff's mathematics makes it at least possible NOT to wander off the topic of the apparently purposive activities of living systems, or NOT unawarely to engage in sloppy reasoning. And where previous efforts to model that purposive domain have failed, his model, which he calls directive correlation, succeeds both logically and empirically (cf. Singer, 1946).


Sommerhoff explicitly states that he did not frame his construct as a full-fledged axiomatic system or a comprehensive theory; instead, he regards it as a kind of tool. In the revised axiomatic theory, we re-interpret Sommerhoff's construct, and then designate our version of it with a verb-phrase rather than a noun-phrase: directively correlated. Then we use this slightly modified construct as one hinge-pin of our entire theory.




To show how the construct of directively correlated works, let me express it first in words, then mathematically (in a set theory notation). To do this verbally, I'll need two main mathematical constructs: variable and function.

a) The term variable refers to a kind of mathematical "blank check," which can take 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 two variables and three functions.




i) Coenetic variables (CV), a kind of "initial conditions" affect both organism and environment. Let d (a 'disturbance') signify a particular value of CV .


ii) Focal conditions (FC), the criterion for a 'favorable' outcome, from the point of view of the organism. FC comprises a part (subset) of outcomes (OC). Let oc signify a particular value of OC , which might or might not satisfy this criterion and so belong to FC .






i) Interactions of the CV with the organism, which I can express as the function f . As a set, f signifies "What the organism does"; f(d) mathematically signifies "What the organism does with the disturbance d ."

ii) Interactions of the CV with the environment, which I can express as the function g . As a set, g signifies "What the environment does"; g(d) signifies "What the environment does with the disturbance d. "

iii) Interactions of f(d) with g(d) , which I can write as Psi . As a set, Psi signifies "How 'what the organism does' and 'what the environment does' interact." Psi(f(d),g(d)) leads to an outcome oc .


The outcome oc may or may not qualify as 'favorable' from the point of view of the organism. If it does so qualify, I say oc belongs to FC (satisfies the criterion of 'favorable' from the point of view of the organism) oc FC ; if not, oc / Fc .


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


At t0: d At t1: f(d) and g(d) At t2: Psi(f(d),g(d)) = oc




In describing the behaving/experiencing sequence which I called "my participating in this meeting," I used this terminology and this model.




By current standards of rigor, no one has to believe reasoning done only in words. If someone wants something taken seriously, he had better do the main reasoning for it in some mathematical notation. That makes things particularly easy for those who like mathematics, and harder on those of us who don't.


Let us present the construct of directively correlated as a definition and a set theory sentence.


DEFINITION: The function f qualifies as directively correlated with respect to d , g , and Psi if and only if, for all d that belong to CV , the outcome oc belongs to FC .


In a Bourbaki algebraic set theory notation (Ashby, 1962), I write this as:


Psi (f(d),g(d)) belongs to FC for each d that belongs to CV .


Figure 2 may help in visualizing this construct.





To summarize, then, this mathematical model keeps the promises made above, in the Introduction. Intrinsically, it presents a story, with a beginning, a middle and an end. And it shows organism and environment as if they remained in an intimate dialogue or dance.


So we've got a theory and a mathematical model which allegedly departs from the theory and model used by traditional biologists; and I seem very pleased with it. But -- so what? Does the revised theory confers any advantage(s) over the traditional theory?


In the remainder of this paper, I shall outline some implications of the two rival theories, which will give readers a basis for choosing between them.


For this discussion, I shall use both logical and empirical criteria to elaborate on how each theory handles the constructs of organism and environment.



Our traditional biological theories remain non-notational -- they do not utilize a specialized mathematical notation to state their key relationships. Consequently, no advocate of such a theory can back up claims that, in her/his theorizing, (s)he has NOT wandered off-topic, or NOT unawarely engaged in sloppy reasoning. Further, our traditional biological theories do not explicitly distinguish between the logical and empirical senses of a term; nor do they define or recognize the construct of polar term-pair. Instead, they treat the terms organism and environment as ordinary noun-phrases, related as a pair of contradictories; and handle these noun-phrases in accordance with tacit, non-formalized "rules of inference" -- namely, those incorporated into the grammar of the discursive language (in this instance, English) used in framing the theory.


Any language has to have some kind of grammatical structure, and that structure incorporates assumptions which, in effect, segment the world along linguistic lines. We who use the language

cut nature up, organize it into concepts, and ascribe significances as we do, largely because we are parties to an agreement to organize it in this way -- an agreement that holds throughout our speech community. The agreement is, of course, an implicit and unstated one, BUT ITS TERMS ARE ABSOLUTELY OBLIGATORY; we cannot talk at all, except by subscribing to this way of organizing and classifying data decreed by the grammar. (Whorf, 1956)


The assumptions built into the grammar common to the WIE discursive and mathematical languages (such as English or set theory) cut up what we experience into fixed "things" and more or less evanescent "relations". We signify these "things" by self-identical nouns or noun-phrases, and the "relations" by not-self-identical verbs or verb-phrases. Then to form a complete sentence, a speaker or writer combines at least one noun-phrase with at least one verb-phrase:


The cat grinned.


To form a well-formed formula, s/he combines one or more quantities or things (e.g. 3 or C ) and at least one relation (e.g. + or Not- ):


1 + 2 = 3 .


Not-C .


So far so good. But then we unawarely project this linguistic structure, this arbitrary grammar, onto our own experiencing, granting it some kind of "universal validity": We posit an "outside world" made up of static-and-unchanging thing(s) (exactly suitable for us to represent in terms of self-identical noun-phrase(s)), which enter(s) into transient relations (exactly suitable to represent in terms of not-self-identical verb-phrase(s)) (Hilgartner, 1977/78).


In other words, not only in our discursive languages but also in our logics, mathematics, sciences, etc., we WIE provincials tacitly posit that our linguistic, logical, mathematical and scientific "maps" qualify as identical with the "territories" they allegedly represent.


Granted, we exponents of WIE science conduct our scientific disciplines on self-correcting lines. But on a lower, more basic level, we tacitly claim to achieve "absolute certainty": We speak as if we know how "things" REALLY ARE. Even the greatest scientists, the most wary, the most skeptical, still frame their research questions, conduct their inquiries, interpret their results, and express their findings, in the WIE notational and discursive languages which, at the most fundamental level -- the level of grammar -- encode this claim to "absolute certainty."


That has serious consequences for our sciences in general. First, if my neuro-linguistic map actually did qualify as identical with the territory, that would mean that it satisfied a entirely accurate and exhaustively complete one-to-one relation, so that every point of my map represented one and only one point of the territory and no point of the territory went un-represented -- a fair approximation to "absolute certainty." But in that case, my map would in principle have no "room" in it for any kind of representation of the map-maker, the observer, the participant, the organism. It would qualify as "completely objective" -- metaphysically linear (characterized by "one-way causality," where A causes B, and B causes C, and C causes D, and  ...) rather than self-reflexive. And that, in turn, would mean that no observer/organism could legitimately select her/his own behaving/experiencing as a topic for study.


Second, that traditional pattern has a definite structure, the implications of which impose constraints on how we deal with pairs of opposites, such as organism and environment. It does not recognize the construct of polar opposites, specified on a delimited setting; rather, it treats such term-pairs as mutually-exclusive contradictories, specified on an undelimited setting, which have nothing in common except for their opposition. Since both terms qualify as noun-forms, we have no way to handle them in a WIE grammar except to treat them as static, self-identical "things" which enter into transient "relations" -- which means, treat these constructs as separable and separate, except in passing encounters.


As a case in point, take a look at the theme of the Ohio Academy meeting, which says, "Our World -- One Environment." This phrase implies a hypothesis: "To treat our world rigorously as a single comprehensive surround will yield predictions likely to survive testing." In effect, the organizers of this meeting invite commentators from the entire range of Western science -- from Anthropology to Zoology, or from the mathematical to the physical to the biological to the human psycho-social disciplines -- to support, and/or criticize, this implied assertion from the point of view of their own disciplines.


But the phrase in question invites us to consider the "one environment" in isolation. It does not explicitly mention any organism bounded by, in contact with, transacting with the unitary environment in question. Where it uses the pronoun our, it does imply human organisms. But this possessive form expresses the relation of owning. It represents the "world," the human environment, as a "thing" that humans 'possess' or 'own,' like a car or a toaster (which we could, after all, do without).


In sum, our traditional biological theories treat this way of handling the constructs of organism and environment as acceptable -- they bank on it.




Instead of discursive language, the revised theory utilizes a specialized, non-standard mathematical notation based on non-standard assumptions (Hilgartner, 1977/78, 1978a) to state its key relationships, e.g. to restrict discussion to the topic of the transacting between organism and environment; and it explicitly distinguishes between the logical and the empirical aspects of a construct.


A) Logically speaking, the terms organism and environment form a polar term-pair, which we cannot isolate from one another nor define except in terms of one another.


B) Empirically, we cannot separate what these terms refer to. For example: Any actual organism separated from even a part of its environment -- e.g. a grey squirrel deprived of suitable air for more than a few minutes -- dies.


But in order to deprive an organism of this part of its environment, we have to substitute an alternative environment -- that of a plastic bag over the nose and mouth, or a box or breathing mask supplied with gases free of breathable oxygen, or a vacuum chamber, etc.


In short, according to the revised theory, the construct of organism remains inseparable from that of environment, both logically and empirically. The present theory suggests that what we call organism and what we call environment OCCUR, within the experiencing of any observer, in the kind of intrinsic, transactional, constitutive relation/process that makes that which I call my environment into "the other side of my skin."


When I paraphrase the theme of the Ohio Academy meeting from the viewpoint of the revised theory, it comes out as follows:


"The Biosphere -- The Other Side Of My Skin; AND: Me -- The Other Side Of The Biosphere's Skin."


This contrasts with the traditional theory, in which we still SPEAK as if we could separate organism and environment. We treat them as noun-forms, independent and isolated from each other; or at best, we posit them as separable and separate, and then secondarily re-combine them. And then we wonder that the life sciences appear "lacking in rigor and predictability."


I invite readers to test these proposals on their own, by substituting the more rigorous language/standards into some work you already have in progress, and see what differences this makes.




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


Hilgartner, C. A. (1968). "General Semantics, Psychotherapy, and the Logic of Science." ETC.: A Review of General Semantics 25:315-324.


Hilgartner, C. A. (1977/78): "Some Traditional Assumings Underlying Western Indo-European Languages: Unstated, Unexamined, and Untenable." General Semantics Bulletin Nos. 44/45, pp. 132-153.


Hilgartner, C. A. (1978a). "The Method in the Madness of Western Man." Communication 3:143-242.


Hilgartner, C. A. (1978b). "A Human Studying the Sensing of Chemicals by Bacteria." Acta Biotheoretica 27:19-43.


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


-----, "B. The Structure of 'Unimpaired' Human Behavior." Journal of Theoretical Biology 23:347-374;


-----, "C. The Structure of Empathy." Journal of Theoretical Biology 24:1-29.


Singer, E. A. (1946). "Mechanism, vitalism, naturalism." Philosophy of Science 13:81-99. (Singer publicly formulated the logical structure for Sommerhoff's solution several years prior to Sommerhoff's publication.)


Sommerhoff, G. (1950). Analytical Biology. New York & London: Oxford University Press, p. 7. (Italics mine.)


Whorf, Benjamin Lee (1956). Language, Thought, and Reality: Selected Writings of Benjamin Lee Whorf. John B. Carroll (Ed.). Cambridge, MA: MIT/Wiley, pp. 213-4.



FIGURE 1. A directively correlated sequence.


FIGURE 2. The construct of directively correlated.

Given: Variables CV ("Initial conditions"),

X ("Organism component"),

Y ("Environment component"), and

Z ("Outcomes"),

with FC ("Favorable outcomes") a subset

of Z.

Functions f ("What the organism does")

g ("What the environment does")

Psi ("Interactions of f with g ").

Then f qualifies as directively correlated with respect to g , Psi, and FC if and only if, for each d which belongs to CV ,

Psi(f(d),g(d)) belongs to FC .