METABOLIC 'CONTROL’ IN MATURE ERYTHROCYTES

 

THE NOTIONS OF 'LIVING SYSTEM', 'ABSTRACTING',

AND THE 'MAP'

'TERRITORY' ANALOGY

 

C. A. Hilgartner

 

INTRODUCTION

 

By about 1950, the main outlines of the major metabolic pathways of plant and animal organisms seemed well known. Since then, those mechanisms which determine the concentrations of metabolic intermediates under self

stabilizing conditions, or determine the overall rates of the various metabolic pathways, have received increasing study. But although we seem to understand more and more of the minute details which make up what I might call 'living systems', we still appear not to comprehend the overall relations which constitute a 'living system'.

Many workers in the past and even today unabashedly use the usual terminology of 'teleology', e.g. , terms such as 'adaptation', 'coordination', 'integration', 'control', 'regulation', etc. But as I have pointed out elsewhere (Hilgartner & Randolph, 1969a, pp. 297

9), those terms presume-and-express the notion of 'the rational soul', as propounded by Aristotle (384

322 BC). Impolitely paraphrased, that means this traditional terminology stands equivalent to assuming that a little demon does the organism's 'regulating' or 'adapting' for it; or in other words, stands equivalent to gratuitously assuming that the "happenings" designated by those traditional terms remain not only unspecified but also unspecifiable. Moreover, so far as I know, no one has yet succeeded in rigorously defining those as primary terms. Thus as judged by the standards of modern logic, 'teleology' comprises a logically inadequate 'theory of biology'.

 

And although in the last two decades we have accumulated a literature concerning mathematical models of 'adaptation', still, no fundamental revision of that archaic terminology has yet become generally accepted.

 

Similarly, many workers have used the constructs of physical chemistry, e.g., reaction kinetics, or of thermodynamics, in attempting to define and describe 'living systems'. But the

theoretical constructs of our physical sciences fail to make several crucial distinctions

; and thus, without stating them directly, these constructs imply

assume certain parochial and untenable premisings fundamentally incompatible with the notion of ‘living system'.

 

I shall take pains to show what I mean by so asserting, first informally, in words, and in the next paper of this series, in notation.

 

Here, in order to bring out the contradiction(s) inherent in any accounting for 'living systems' which neglects these crucial distinctions, I go through three steps: a) I explore the topic of the 'map'

'territory' analogy; b) I offer examples of traditional constructs which fail to make these crucial but usually neglected distinctions, and contrasting examples of non

traditional constructs which insist upon them; and c) I examine these two contrasting constructs in light of the criterion proposed by Oliver & Landfield (1963):

 

The point is simple in the extreme: what is to be accounted for must be accounted for, else the venture is a failure; a any psychological venture is a failure if in its accounting it fails, or refuses, to take into account its own accounting. (Oliver & Landfield, 1963, p. 199)

 

ABSTRACTING: THE 'MAP'

'TERRITORY' ANALOGY

 

I can briefly outline some of these crucial but usually neglected distinctions by reference to the notion of 'abstracting' ' and to the so

called 'map'-'territory' analogy, which taken together provide a specific and definable version of the old notion of 'irritability'. In this view, the primary "responding" of an 'organism' to its 'environment' at any instant qualifies as some kind of 'map' of it. By using this analogy I contrast the abstracting ("'map'

making") of human and infra

human 'organisms'.

 

A. Order of abstraction

 

In writing this paper, I can do no more and no less than to put on paper markings which somehow, in my opinion, represent those "happenings" I might designate by terms such as "words, phrases, sentences, paragraphs, sections, etc. ". For example, I can include groupings of markings such as

clapping my hands ,

but I cannot literally include examples of those "happenings to which my words, phrases, etc., refer, e.g., examples of those "happenings" or "doings" which I might describe by some phrase such as "non

verbally" non

symbolically, clapping my hands".

 

At first glance, the above paragraph may appear to make the traditional "use

mention" distinction which, after Frege, modern logicians (e.g., Mates (1965), p. 19) insist on. But please note that, unlike the traditional distinction, my version explicitly involves distinguishing between "happenings" on at least three "levels" (orders of abstraction), viz. , between 'markings' and 'words' and 'non

verbal "doings"’; and further, it implies at least two other "levels", e.g., 'what I want to say by means of written markings', and 'my "detecting" my own non

verbal "doings"’. Moreover, any one of these "levels" can, at times, function as 'territory', and any one of these "levels" can, in appropriate context, function as 'map'. For example, the markings I make and (after revising) let stand qualify as a 'map' of that 'territory' I might designate by means of the phrase, "what I wanted to say by means of written markings"; or those non

verbal "happenings" I might designate by the phrase, "my "detecting" my own non

verbal "doings" qualify as a 'map' of that 'territory' I might designate by means of the phrase "non

verbally clapping my hands"; etc.

 

Thus the usual "use

mention" notion qualifies as at best a special case of the distinguishing I intend.

 

B. The abstracting of infra

human 'organisms'

 

According to the 'map'

'territory' analogy, the primary "responding" of an 'organism' to his 'environment' at any instant qualifies as a 'map' of it. But there exists a fundamental asymmetry in the relationing between 'map' and 'territory', betokened by the criterion of 'similar in structure'. For example, given a particular wildebeest which at sunset has come to a particular water

hole to slake his thirst: the fact that he actually arrives at the water

hole implies that, after looking, sniffing, etc. , he has formed a 'map' which I could represent by the phrase "No lions here

now", or by the predicting, "I won't have to run for it just yet." If, however, there actually exists a lioness concealing herself at that water

hole at that moment, which the wildebeest has failed to detect, then at best the unfortunate ungulate will have to run for his life and at worst he may end up as the evening meal for a pride of lions. And in any case, in terms of the 'map'

'territory' analogy, we would have to conclude that the wildebeest's 'map' qualifies as not similar in structure to the actual 'territory'.

 

In this context, the term 'map' refers to one particular (hypostatized) example of the inarticulate "responding" of a (hypothetical) member of an (inferred) class of 'living systems' incapable of linguistic behaving (viz., 'living systems' incapable of speaking, writing, reading, etc. ( cf. Korzybski (1921)). But even in this context, we can see that for any 'organism' the primary 'territory' to which he "responds" ( the so

called "event

level" ( remains fundamentally unknown, by which I mean, 'known' only by inferring, e.g., from the 'map', and therefore 'known' at best incompletely and inaccurately.

 

C. Specifically human abstracting

 

The abstracting of a particular human organism likewise involves particular "happenings" which I might regard as 'maps' on orders of abstraction similar to those of the wildebeest, viz., 'symbolic' but 'non

verbal' ('maps' on the so

called "silent levels"). But specifically human abstracting also involves 'maps' on specifically "verbal levels", which I might designate by hierarchically

ordered terms such as "label, description, lower

order inference, higher

order inference, still higher

order inference, etc.", or such as "comment, reply, reply to the first reply, reply to the second reply, etc."

 

Now in order to present my view of specifically human abstracting, I hypostatize a specific 'situation' which I could describe by some phrase such as "a physical scientist (experimenter

observer) performing an experiment concerning the topic of the trajectories of objects freely falling over distances small compared to the diameter of the earth." I indicate the crucial distinctions between "event

level" 'territory' and "silent

level" and/or "verbal

level" 'maps' and 'maps of maps', etc., by italicizing those terms I use to signify what I might call "(inferred) non

verbal, observable event

level happenings" (e g., the experimenter

observer, or his particular experimental system), and by enclosing between two number

signs the terms I use to signify 'maps', such as those "happenings" which I might call "one's #picture# of some observable event

level happenings" (e g., one's #picture# of an experimental system, viz., an #experimental system#, or a #theoretical system# which can encompass many #experimental systems#, and which thus occupies a higher order of abstraction than does any one of these subsumed #experimental systems#).

 

I point out that the theoretical constructs (viz., equations) of our traditional 'logics', 'mathematics', 'sciences', etc.-- for example, classical thermodynamics, or Newtonian mechanics -- do not in any way explicitly distinguish between two very different kinds of "happenings", viz., between the symbolic #theoretical system# (which our "physical scientist" (experimenter

observer) has elaborated, and which encompasses the specific #experimental system# in question), and the specific, non

symbolic, non

verbal (but still inferred) experimental system (which the experimenter

observer has brought together to test the predictings of his #theoretical system#). Nor do the constructs of our traditional 'logics', 'mathematics', 'sciences', etc.

e.g.,

classical thermodynamics, or Newtonian mechanics

specify the intricate relationings between the experimenter

observer, the #theoretical system# he elaborates, and the experimental system he brings together to test the predictings of his #theoretical system#. Finally, our traditional constructs fail to distinguish between the (inferred) non

verbal experimenter

observer and our (explicit and/or implicit) #picture# of the "role" of the experimenter

observer, viz., the #experimenter

observer#.

 

To neglect to distinguish between any two of these classes of "happenings", or, having distinguished, to neglect to specify the relationings between them, seems to provide, in human abstracting, as clear an invitation to disaster as, in infra

human abstracting, the wildebeest could provide by somehow assuming that his 'map' of the water

hole qualifies as "accurate" and "complete". For example, to neglect to distinguish between experimenter

observer and #experimenter

observer# implies one or the other of two absurd assumings, which in the end appear equivalent: this neglecting implies that the experimenter

observer remains otiose, that he has no part whatsoever in his own abstracting and that, therefore, the conclusions he arrives at (e.g., the #theoretical system# he elaborates) somehow "exist" utterly apart from and independent of "him"; or it implies the assuming that the experimenter

observer does a "perfect" job of abstracting, viz., that in his designing, setting up, executing, recording the results of, analyzing, and inferring from the "experiment", his abstracting remains 100% "accurate" and "complete". In either case, he and we could then safely neglect to distinguish between experimenter

observer and #experimenter

observer#.

 

CONTRASTING FORMULATIONS

 

In the symbolism of Newtonian mechanics, we describe the trajectories si of particular observable objects oi which we have ourselves observed freely falling by means of the equation

 

si = ( gi ti 2 .

 

Likewise, we predict the #trajectories# sj of observable objects or even hypothetical #objects# oj , which we have not ourselves observed freely falling but which will or might do so, by means of the equation

 

sj = ( gj tj2 .

 

Clearly, the formulations of Newtonian mechanics do not explicitly contain any trace of the distinction between "event

level" and ''verbal

level" "happenings". It even seems a little silly to go to so much trouble to distinguish between oi and oj or between si and sj .

 

Similarly, no equation from any one of our physical sciences contains even one term signifying "the experimenter

observer" on any level of abstraction whatsoever3. And in fact, if we take modern science as beginning with the lifetime of Sir Isaac Newton (1642

1727), modern scientists pursued their studies for about two centuries before Peirce (1839

1914) first studied "what scientists do" in practicing science and "how they do it".

 

To contrast to these conventional formulations, I presume a specific situation: Our experimenter

observer watches a particular object, stone1 , fall freely during a particular interval tli . Polanyi (1958) describes how we "appreciate the externality of objects lying outside our body" (or in my terminology, "form an 'awareness"; or, substituting a verb

form for the noun

verb phrase, how we go about awaring) as follows:

 

Our appreciation of the externality of objects lying outside our body, in contrast to parts of our own body, relies on our subsidiary awareness of processes within our body. Externality is completely defined only if we can examine an external object deliberately, localizing it clearly in space outside. But when I look at something, I rely for my localization of it in space on a slight difference between the two images thrown on my retina, on the accommodation of the eyes, on the convergence of their axis, and the effort of muscular contraction controlling the eye motion, supplemented by impulses received from the labyrinth, which vary according to the position of my head in space. Of all these I become aware only in terms of my localization of the object I am gazing at; and in this sense I may be said to be subsidiarily aware of them. (Polanyi, 1958, p. 59)

 

(Also, Polanyi does not explicitly mention the slight "jitter" of the eyes, which I consider one kind of visual scanning, and without which the rods and cones of the retina quickly cease responding to the unmoving visual image, producing a functional "blindness" to all stationary objects in the visual field.)

 

ence, in the notation of the set theory calculus of behavior of Hilgartner & Randolph (1969a,b,c), I can represent any moment of visual awaring Aw vi as composed of ('organized' by means of) some combination of these processes. That makes each Awv a unique structuring. For example, in the visual awaring of stone1 falling freely during times tli , I can represent the actual values of the binocular differences of projecting, the accommodating, the converging of ocular axes, the eye

movings involved in tracking the object, whatever postural chargings the tracking involves, the labyrinthine impulsings, and whatever visual field scanning occurs during this Aw i , etc., as some transform of the Newtonian equation twice quoted above.

 

In order to wax specific, I specify this transform for one of the variables mentioned, the direction of gaze of a single eye, as the organism tracks a freely falling object whose trajectory has no horizontal component of velocity.For the sake of simplicity, I make the horizontal (OH) distance from the anterior aspect of the cornea (O) to the trajectory EH of the falling body E measure 10 meters. The body starts its fall from a point 10 m above this horizontal line, and the object has a size such that its image on the retina has about the same diameter as does the fovea centralis, that sector of the retina which corresponds to the region of greatest visual acuity of the visual field. Further, I assume that the organism can track a falling object accurately enough so that the midpoint of the image never deviates from the midpoint of the fovea centralis by more than the radius of the fovea centralis. Finally, I fix the head of the organism in a "neutral" position, with neither a side

side tilt nor an up

down inclination, and during the tracking I allow no postural change. Hence the extra

ocular muscles power the entire tracking.

 

Under these conditions, the tracking will consist of the extra

ocular muscles moving the eye so that the angle ( = HOE varies, on the average, as a function of t . Within these limitations, the actual eye

movings involved in the tracking could comprise anything from a smooth, continuous moving to a series of stepwise movings similar to what we do while reading I could describe a smooth moving by the expression

 

d(/dt =

1/10 g t cos 2 ( (

k 2t ,

 

where k serves as a constant. Similarly, I could describe the less likely "jerky" moving in terms of a series of stepwise movings, in which the angles covered by the salutatory eye

movings themselves would define an increasing series.

 

Similarly, I could work out a mathematical expression which describes each of the other processes mentioned above, e.g., accommodating, converging the ocular axes, etc. Then the overall expression which describes the visual awaring of the falling of stone1 during the interval tli would consist of the conjunction of these various component expressions. And this overall expression would then describe the "happenings" which (we infer) "take place" in the specific situation I posit, in which our experimenter

observer watches stone1 freely falling.

 

THE CRITERION OF 'REFLEXIVITY' AND THE NOTION OF 'LIVING SYSTEMS'

 

At this juncture, the criterion of reflexivity proposed by Oliver & Landfield (1963) brings into high relief a pervasive finding in biology, which seems so fundamentally important that it forms the basis for one postulate of the premisings which underlie the present viewpoint: The "doings" which make up 'living systems', e.g., the non

verbal 'maps' which 'organisms' elaborate as primary "respondings" to those 'territories' which make up their "event

level" 'environments', support two kinds inferrings: inferrings about the "happenings" which make up the 'environment', and inferrings about the "happenings" which make up the 'organism'. In my example, from the extended expression for Aw vi we could infer the structure of the 'territory', viz., the free falling of some specific "object", and also we could infer the structure of the 'organism', viz., able to track a falling object, and since it did in fact track this particular object, therefore somehow interested in this falling object; etc.

 

In the terminology of the criterion, then, those 'maps' which make up what I have variously called "abstracting or awaring", or here, "tracking", both "account for" the 'territory' they supposedly refer to and also "account for their own accounting".

 

Otherwise stated, any 'map' of a particular 'territory' unavoidably consists of two components, one of which I could label 'hetero

referential', in that it "tells" about the 'territory', and the other 'self

referential', in that it "tells" about the 'organism'. Conversely, any 'map' which appears to consist of only one component then implies that a 'non

living system' "elaborated" it. (And the notion of a 'non

living system' "elaborating" a 'map' stands as a contradiction in terms.)

 

Moreover, the above concludings about the structure of "silent

level" 'maps' (primary "respondings") themselves qualify as ("verbal

level") 'maps'. And as such, they show a very peculiar structuring: These concludings briefly #account# for at least some of the ways #humans# #account# for human accounting. For I could describe the 'hetero

referential' referent of these 'maps' (concludings) by some phrase such as "the abstracting of human and infra

human 'organisms"'. Hence both components of these 'maps' refer (in different ways) to the "happenings" which make up the 'organism', and so these ‘maps’ qualify as "entirely self

referential". Therefore, demonstrably, they too meet the criterion of reflexivity proposed by Oliver & Landfield (1963).

 

But in contrast to these formulations derived from the set theory calculus of behaving of Hilgartner & Randolph (1969a,b,c), the formulations of our physical sciences, e.g., the Newtonian "law of universal gravitation" quoted above, will NOT support these two kinds of inferrings. Referring back to the specific situation I posit, the formulations of Newtonian mechanics give no clues concerning the "physical scientist" who, given some awaring or observings and/or recorded observings (#observings#), arrives at that 'map' of the 'territory' which he specifies, viz., his #theoretical system#. Instead, as I showed above, by neglecting the crucial distinctions I discuss, the formulations of our physical sciences tacitly represent the experimenter

observer as "otiose" and/or "perfect"; or otherwise stated, our physical scientists present their formulations as if they consisted of only one component.

 

But that implies that a 'non

living system' "elaborates" the "laws of physics, chemistry, etc. " In other words, our physical scientists tacitly posit a #‘Universe'# devoid of #'living systems'#.

 

However, I regard our physical scientists as themselves qualifying as 'living systems'. And for a 'living system' to elaborate a #theoretical system# which posits a #'Universe'# devoid of #'living systems'# presents what Oliver & Landfield (1963) call a "paradox of self

reference". With reference to paradoxes of self

reference in psychology, they write:

 

If, from a presented body of evidence, a conclusion is drawn about the nature of thought, and if, taking thought as what this conclusion asserts it to be, this very conclusion could not have been drawn from this evidence by a process of thought, the paradox of self

reference is evident. Or, if a theory of the nature of perception is urged upon evidence which by this theory could not have been observed, the paradox is again evident. This form of argument is graphically described by the phrase, "sawing off the limb one is sitting on." (Oliver & Landfield, 1963, p. 189)

 

In conclusion, therefore, no currently

existing #theoretical system# from our physical sciences succeeds in "accounting for its own accounting".

 

Since the #theoretical systems# known as 'thermodynamics', 'reaction kinetics', etc. , demonstrably neglect the crucial distinctions I discuss, therefore any exponent of 'thermodynamics', etc., by ratifying this neglecting, gratuitously and on an a priori basis posits a 'lifeless' #'physical Universe'#.

 

Hence any accounting for #'living systems'# based solely, or even principally, on the 'lifeless' constructs of our physical sciences appears intrinsically self

contradictory.

 

These destructive criticizings have the effect of dismissing as inadequate most of the accountings for those "happenings" which make up 'living systems' so far elaborated.

 

ALTERNATIVES TO INADEQUACY

 

By way of constructive suggesting, I opine that in order adequately to specify the abstract structuring of 'living systems' we must invent an economical notation whose constructs satisfy the conjunction of many kinds of constraints.

 

This series of papers serves to present a new theory of 'living systems', one for which it seems reasonable to hope that it does not share the major failings of its older rivals. Framed as an axiomatic system stated in a set theory notation, this theoretical system starts from a novel and interesting set of premisings, the so

called non

Aristotelian postulates of Korzybski (1933, 1943), as rendered in notation by Hilgartner & Randolph (1969a, pp. 295

7; 1969b, pp. 354

6). As their central point, traditionally defined, these assumings forbid

(disallow) the notion of ‘identity’ (the binary relation of ‘identical with’) in any guise or form, explicit or tacit.

 

HISTORICAL

 

Singer (19460 and Sommerhoff (1950, 1969) deserve the credit for first showing how, in ways which meet modern logical and scientific standards of adequacy, to deal with the topic of the apparently 'purposive' or 'goal

directed' activities of 'living systems'. Sommerhoff's (1950) version, the relation of directively correlated, stands as a kind of joint

causation involving an intrinsically temporally

ordered sequence: coenetic variables ('initial conditions' coenetic variables which affect both 'organism' and 'environment' ), followed by respondings of 'organism' and of 'environment' to the coenetic variables; and these respondings in turn interact so as to arrive at (or in the negative case, not arrive at) the organism's focal conditions ('goals', viz., outcomes which prove somehow 'favorable' from the point of view of the organism).

 

But as Sommerhoff (1950) takes pains to point out, the new construct he proposes does not itself qualify as an entire theoretical system:

 

In the present volume we are only concerned with critical analysis and not with the construction of axiom systems. (Sommerhoff , 1950, p. 36)

 

In another context (Hilgartner & Randolph, 1969a,b,c,d), the notion of 'directively correlated' has undergone and survived extensive scrutiny: In the process of performing a logical analysis of a new theory of the structure of human psycho

dynamics (Hilgartner, 1963, 1965), we incorporated this notion into the logical superstructure of the axiomatic system mentioned above. Consequently, we treat what I might call human behaving

experiencing ('behaving' as seen by others, 'experiencing' as seen by oneself) as a special case of the apparently 'purposive' "doings" of 'living systems'.

 

Recently, it seemed worthwhile to try to obtain some estimate of the degree of adequacy of the notion of 'directively correlated' itself, in some context more or less independent of human behaving. To do this, I have utilized this construct to account for the structuring of, and the inter

relations between, the mechanisms of 'control' of carbohydrate metabolizing in the ''minimal" living system presented by mature mammalian red blood cells. This series of papers presents some of the findings of that study.

 

THE PRESENT STUDY: A COMPROMISE

 

The results of these explorings already appear so interesting as to warrant presenting them, even in a demonstrably provisional form. However, by now a fundamental difficulty with the set theory version of the theoretical system, suspected from the beginning, has become unavoidably apparent: The non

Aristotelian postulates of Korzybski forbid the notion of 'Identity', whereas traditional logic and set theory admit 'Identity'. Thus there exists a possible contradiction between the findings of the set theory version of this theoretical system and the notation used to state these findings.

 

Furthermore, as I have convinced myself the hard way, no one can convincingly back up the claim that he has ''subtracted" the notion of 'Identity' from traditional logic and set theory.

 

There exists no way to rule out the above

mentioned possible contradiction short of elaborating a new relational languaging, which re

works the domains of symbolic logic and set theory, but which starts ab initio from the non

Aristotelian postulates of Korzybski.

 

But as yet no relational language which meets that description exists; has seen publication.

 

Furthermore, even provided that it proves feasible to elaborate a new relational languaging which meets that description, it will predictably take months or years to do so. So, faced with the choice between waiting to present my findings until after the ideal language in which to present them stands completed, or presenting them in at best a provisional form, I have chosen the latter proceeding.

 

THE COURSE OF THE ARGUMENT

 

II. In the next installment, I develop the preliminaries of a new non

Aristotelian languaging, define the 'undefined terms' of traditional set theory in terms of the 'undefined terms' of this new system, and assume, perhaps hazardously, that the 'logical machinery' I have specified leads (directly, or perhaps with supplementary assumings) to an array of mathematical constructs such as that displayed in Appendix II.

 

(Alternatively stated,, I take the theorems of "naive set theory" (e.g., those displayed in Appendix II) as "received doctrine", but with the perhaps brash proviso that I have succeeded in defining the 'undefined terms' of "naive set theory" in terms of my non

Aristotelian framework, and so (implicitly at least) have specified the relationings between my premises and the theorems of "naive set theory".)

 

Then I use this 'logical machinery' to state the premises and the counter

premises of a non

Aristotelian system.

 

Thereby I cover in notation the considerations covered in words alone in the present installment.

 

In the third installment, I begin reinterpreting the empty form composed of (empty) set

theory symbols based on these premises (devised originally to represent the transactional relationings of a man with himself

environment) so as to make it refer to the transactional relationings of a unicellular organism with itself

environment. Specifically, I use this mathematical languaging to represent the chemical dynamics of generalized reactions in ways which meet the constraints of physical chemistry. And in Appendix III, I present a formal definition for the relationing of 'directively correlated', along with relevant theorems and their proofs.

 

IV. In the fourth installment I use this mathematical languaging to represent enzyme

catalyzed reactions and to represent modifier

sensitive enzymic reactions. At that point I make the claim that the logical machinery I have specified suffices to represent the known "metabolic machinery" of mature mammalian red blood cells. Furthermore, I show that any enzymic reaction, as represented in this notation, qualifies as 'directively correlated'. This demonstrating shows that the topic of the 'control' of glucose metabolizing does in fact provide a suitable test case against which to examine the question of the adequacy of the construct of 'directively correlated' as a model or 'map' of the structuring of the apparently 'purposive' activities of 'living systems'.

 

V. In the fifth installment, I take actual quantitative data from the biochemical literature, findings concerning the 'mechanisms' by which mature mammalian red blood cells 'control' their own glucose metabolizing, and use the modified theoretical system as a "computing machine" to process these data. It turns out that, given these data and given the starting conditions specified by the experimenters, this transformed system ''predicts" that the theoretical #red blood cells# will #do# the symbolic equivalents of those things the experimenters report that their actual, non

verbal red blood cells in fact do.

And since these theoretical #operations# take place in a mathematical notation, I can draw inferences from them: I demonstrate that this 'logical machinery" makes of the term 'living system' (or 'organism') a rigorously

defined set theory operator, so that on formal grounds alone I can show that a non

verbal example of what we might call a "mature mammalian red blood cell" qualifies as an element of the set of 'living systems' ( a degree of rigor in biology not previously attained, to the best of my knowing.

 

VI. In the sixth installment, I summarize the results of my attempts to elaborate a specific realization of this theoretical system in the form of a computer program, stated in FORTRAN IV, which simulates the 'behaving" of mature mammalian red blood cells as manifested in the Embden

Meyerhof pathway of anaerobic glycolyzing.

 

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201 (1963), Reprinted from the Journal of Individual Psychology.

 

Polanyi, Michael (1958): Personal Knowledge: Towards a Post

Critical Philosophy. Chicago: University of Chicago Press Torchbook Edition (1964), New York: Harper & Row.

 

Russell, Bertrand (1903): Principles of Mathematics. Second edition, undated, New York: W. W. Norton.

 

Singer, E. A. (1946): Mechanism, vitalism, naturalism. Philosophy of Science 13: 81

99.

 

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

 

Sommerhoff, G. (1969): The Abstract Characteristics of Living Systems. In F. E. Emery, editor. Systems Thinking. Baltimore: Penguin Books, pp. 147

202.

 

Swanson, Marjorie (1958): On Four

Dimensionality: A Psycho

Physiological Analysis. General Semantics Bulletin Nos. 22 & 23, 1958, pp. 35

40.

 

Tarski, Alfred (1965): Introduction to Logic and to the Methodology of Deductive Sciences. New York. Oxford University Press.

 

Webster's (Second) New International Dictionary of the English Language Unabridged, 2nd Edition (1961). Springfield, Massachusetts: G. & C. Marriam.

 

Webster's Third New International Dictionary of the English Language Unabridged, (1961), Springfield, Massachusetts: G & C. Marriam.

 

Whorf, Benjamin Lee (1956): Language, Thought, and Reality: Selected Writings of Benjamin Lee Whorf. John B Carroll, editor. New York: John Wiley & Sons.

 

In Appendix I, I list certain linguistic conventions I adhere to, and certain orthographic devices I use, e.g., special usages of single and double quotes, hyphens, etc.

 

As I may as well acknowledge in passing, the destructive criticizings I offer apply beyond the domain of 'biology', however we choose to delimit it. For although here I focus on the topic of our 'theories of biology', the untenable premisings I criticize turn out to underlie each of the various 'philosophies', 'logics', 'mathematics', 'sciences', etc., so far elaborated by those who write (and perhaps speak) in at least one of the western Indo

European languagings, e.g. , English, French, German, Greek, Latin, Russian, etc.

 

However much these various writings may differ in detail, they demonstrably share certain (usually unstated) assumings codified in (viz., inferable from) the linguistic structuring of these closely

related languagings in which they get expressed. These usually unstated center about four notions, any one of which I can define in terms of the other three: a) the distinction between 'nouns' and 'verbs'; b) the notion of 'identity' (the binary relation of 'identical with', defined in Webster's (Second) New International Dictionary (2nd edition, 1961, p. 1236) as "entire and absolute agreement or negation of difference"); c) the copula (in English, the verb 'to be'); and d) the "Laws of Thought" attributed to Aristotle.

 

When examined, the assumings hidden behind these four topics appear untenable, as judged by any standards whatsoever (except the "standard" provided by presupposing these four notions).

 

I refer to any theoretical structure which uses these four notions, and thus ratifies the untenable assumings which underlie them, as "an expressing of a traditional Indo

European 'World

View'.

 

3 The general theory of relativity does use different coordinate systems as a metaphor for the "frames of reference" of different "observers". But by making use of the tensors calculus, general relativity proceeds to eliminate from consideration the ways that different coordinate systems differ. And by specifying the relations between the anatomy and physiology of a human organism and the abstract structure of Cartesian coordinates, Swanson (1958) has in effect showed how poor a metaphor for the functioning of an 'organism' a coordinate system provides.

 

 

 

Hilgartner

 

PAGE

d above.

 

In order to wax specific, I specify this transform for one of the variables mentioned, the direction of gaze of a single eye, as the organism tracks a freely falling object whose trajectory has no horizontal component of velocity For the sake of simplicity, I make the horizontal (OH) distance

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+METABOLIC 'CONTROL’ IN MATURE ERYTHROCYTES

Martha Bartter

Martha Bartter

Aristotelian postulates of Korzybski forbid the notion of 'Identity', whereas traditional logic and set theory admit 'Identity'. Thus there exists a possible contradiction between the findings of the set theory version of this th

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METABOLIC 'CONTROL’ IN MATURE ERYTHROCYTES

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METABOLIC 'CONTROL’ IN MATURE ERYTHROCYTES

catalyzed reactions and to represent modifier

sensitive enzymic reactions, At that point I make the claim that the logical machinery I have specified suffices to represent the known "metabolic machinery" of mature mammalian red blood cells, Furthermore, I show that any enzymic reaction, as represented in this notation, qualifies as 'directively correlated'. This demonstrating shows that the topic of the 'control' of glucose metabolizing does in fact provide a suitable test case against which to examine the question of the adequacy of the construct of 'directively correlated' as a model or 'map' of the structuring of the apparently 'purposive' activities of 'living systems'.

 

V. In the fifth installment, I take actual quantitative data from the biochemical literature, findings concerning the 'mechanisms' by which mature mammalian red blood cells 'control' their own glucose metabolizing, and use the modified theoretical system as a "computing machine" to process these data. It turns out that, given these data and given the starting conditions specified by the experimenters, this transformed system ''predicts" that the theoretical #red blood cells# will #do# the symbolic equivalents of those things the experimenters report that their actual, non

verbal red blood cells in fact do.

And since these theoretical #operations# take place in a mathematical notation, I can draw inferences from them: I demonstrate that this 'logical machinery" makes of the term 'living system' (or 'organism') a rigorously

defined set theory operator, so that on formal grounds alone I can show that a non

verbal example of what we might call a "mature mammalian red blood cell" qualifies as an element of the set of 'living systems' ( a degree of rigor in biology not previously attained, to the best of my knowing.

 

VI. In the sixth installment, I summarize the results of my attempts to elaborate a specific realization of this theoretical system in the form of a computer program, stated in FORTRAN IV, which simulates the 'behaving" of mature mammalian red blood cells as manifested in the Embden

Meyerhof pathway of anaerobic glycolyzing.

 

REFERENCES

 

 

Bourland, D. David Jr. (1965/66): A Linguistic Note: Writing in E

Prime. General Semantics Bulletin Nos. 32 & 33, pp. 111

114.

 

Halmos, Paul R (1960): Naive Set Theory. Princeton: Van Nostrand.

 

Hilgartner, C. A.(1963): General Semantics, Psychotherapy, and the Logic of Science. Unpublished manuscript; revised 1967. Truncated version, ETC.: A Review of General Semantics 25: 315

32 (1968).

 

Hilgartner, C. A. (1965): Feelings, Orientation, and Survival: The Psychological Dimension of the Current Human Crisis. Presented at the Ninth International Conference on General Semantics, San Francisco State College, August 1965.

 

Hilgartner, C. A. & John F. Randolph (1969): Psycho

Logics: Human Behavior in the (Organism ( Environment) Field.

1. A Logical Calculus of Behavior. Journal of Theoretical Biology 23: 285

338 (1969a).

 

2. The Structure of 'Unimpaired' Behavior. Journal of Theoretical Biology 23: 347

374 (1969b).

 

3. The Structure of Empathy. Journal of Theoretical Biology 24: 1

29 (1969c).

 

4. The Structure of 'Impaired' Behavior. (1969d, submitted for publication)

 

Korzybski, Alfred (1921): Manhood of Humanity. New YMicrosoft Word for Windows 95

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