CONTROL SYSTEMS AND TELEOLOGICAL SYSTEMS

by Thomas W . Simon'

University of Florida

A cybernetic systems framework i s constructed within which a distinction between teleological, i.e., purposive, and nonteleological systems is drawn on empirical grounds. The following provide conjunctively sufficient and disjunctively necessary tests of the teleological: (1) applicability of cybernetic specification; (2) perturbation test; and (3) independent testability of component relations. This analysis avoids the problem of pin- pointing the defining characteristics of the teleological and at least provides the groundwork for a complete analysis of purposive behavior. Teleological systems are found to cut across a broad array of system types, including living and nonliving machine systems, regulatory and servosystems, as well as various system levels ranging from intracellular to organiza- lional. Finally, a cybernetic systems framework is claimed to be adequate for teleological phenomena in that it is capable of accounting for human purposive behavior.

N

N ARRAY of problems falls under the ru- A bric teleological problems. At the core of these problems lies the seemingly for- midable task of providing explications for key teleological notions such as function, purpose, goal, and expectancy. Certain programs such as reducing teleology to mechanism, constructing a synonymous, nonteleological translation schema, and reducing mcntalistic discourse to non- mentalistic discourse, often are mistakenly taken to providc solutions to the problems of teleology. Although some of these stratc- gies have intrinsic merit, they frequently serve more to obfuscate than to resolve teleological problems. Here, an attempt is made to redress this situation by developing a cybernetic framework within which the more relevant and more significant distinc- tion between teleological and nonteleological systems is drawn not on a priori but on empirical grounds. By adopting this cyber- netic systems approach the pitfalls of mentalism arc avoided and the temptation to treat the notion of systems as ubiquitous is resisted.

A further way in which many analyses of teleology fail is due to the overly stringent demands placed on a successful analysis. One such demand is to seek the condition

1 This study is based on my doctoral disserta- tion, completed at Washington University. I most gratefully acknowledge the assistance of my dissertation director, Professor Richard Rudner, but he is in no way responsible for any of my

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which is to be taken as definitive of the teleological. I n the inquiry below no one feature is found to be definitive of teleo- logical phenomena. Instead, a set of symp- toms of teleological phenomena is developed. Goodman (1968, pp. 252-255) confronts a similar methodological problem in attempt- ing to define aesthetic experience. He lists a set of four symptoms of the aesthetic experi- ence which are respectively neither sufficient nor necessary but may be conjunctively sufficient and disjunctively necessary. Good- man's approach seems equally applicable to the attempts to devise a neat formula for distinguishing the nonteleological from the teleological. The list of teleological charac- teristics that is constructed in this paper may not provide a crisp criterion for this demar- cation, but it does provide a useful and sig- nificant set of symptoms or aspects of the teleological.

CYBERNETIC SPECIFICATION

Let us proceed by a series of refinements to a standard description or canonical de- scription form of a cybernetic or control sys- tem. The description is constructed in terms of the appropriate variables and mathemati- cal operations of a feedback control system. These designations are derived from a num- ber of sources (McFarland, 1972, pp. 26-27; errors. I would also like to thank the referee of this journal for helpful comments. A version of this paper was presented to the Fourth Annual Conference of the Far West Region of the Society for General Systems Research.

326 THOMAS W. SIMON

Milhorn, 1966, pp. 97-98; DiStefano, Stub- berud, & Williams, 1967, pp. 13-15). As might be expected, specific characterizations do vary from one another depending on the source in the literature, but these variations do not affect the present analysis.

A rudimentary characterization of a con- trol system might be: The numerical varia- bles are either environment or system varia- bles. Environment variables consist in one or more disturbance variables. The system vari- ables are: (1) error variable, e ; (2) controlled output variable, c ; (3) primary feedback variable, b; and (4) input reference variable, r . The values of these system variables are related in terms of the following mathemati- cal operations:

(1) Direct transfer function, g, which pairs particular values of the error variable with particular values of the controlled out- put variables.

(2) Feedback transfer function, h, which pairs particular values of the controlled out- put variable with particular values of the primary feedback variable.

(3) Mixing point relation, which pairs particular values of the primary feedback variable with particular values of the input reference variable.

The behavior of these variables can be computed by means of classical calculus, but control engineers employ a more powerful method based on the Laplace operator. By means of a Laplace transform a linear differ- ential equation is changed into an algebraic equation. The Laplace transform permits the representation of the output-input relation- ships of linear devices and systems by trans- fer functions, the standard form of which is Output/Input.

When one Laplace transforms a variable, the convention of replacing the lower-case variable letters with capital letters is fol- lowed. G is now more properly termed a direct transfer function, and H, a feedback transfer function. The variables and func- tions listed above constitute the canonical constituents of a feedback control system, and the following important equation is de- rived from it:

This equation is the general equation of a feedback control system. All such systems can be reduced to this form. In this equation a - indicates a positive feedback system and a +, a negative feedback system. I n the terminology used previously, in a positive feedback control system the mixing point relation adds some value of the primary feedback variable to a value of the input reference variable. In negative feedback sys- tems it acts as a subtractor.

PERTURBATION TEST

Let us examine some general principles of negative feedback systems which will, in turn, provide more features of teleological systems. The analysis closely follows that of Ashby (1960, 1956). Negative feedback sys- tems are basically a type of equilibrium sys- tem. There are three standard kinds of equilibrium systems: unstable, neutral, and stable. These three cases are usefully repre- sented by the analogy of a marble rolling on different surfaces (Milsum, 1968, p. 47). The (a) unstable case is where the marble is posi- tioned on top of a convex curve. An instance of (b) neutral stability is a marble on a level plane. The (c) stable case is the marble situ- ated in the bottom of a concave curve or trough. A parallel set of examples is pro- vided by Ashby (1956, p. 77): (a) a cone exactly balanced on its point; (b) a billiard ball on a table; (c) a cube resting on its face.

In Ashby's analysis, these three cases are differentiated along the following lines. The variables are measurable quantities, i.e., variable quantities, and functions of time such that at any given time, t , the variables, x and y, have definite numerical values. A transformation is an operation performed on one or more of these variables. The state of a system is a set of ordered n-tuples of nu- merical values which the variables have a t time t . A state of equilibrium occurs during time t when a certain designated set of trans- formations on the system variables fails to change the state of the system during t.

Ashby (1956, p. 77) defines stability as being relative to a specified set of disturb- ances :

. . .we start with a state of equilibrium a, displace the system to state D(a) , and

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CONTROL SYSTEMS AND TELEOLOGICAL SYSTEMS 327

then find TD(a) , T2D(a) , T3D(a), and so on; and we notice whether this succession of states does or does not finish as a, a, a, . . More compactly: the state of equilibrium a in the system with transformation T is stable under displacement D if and only if:

TND(a) = a.

Applying this formulation to Milsum’s three examples, one finds that in (a), where the marble is being displaced from the top of the hill, the system is unstable; for, whatever the limit of applying the transformation is, it will not return thesystem to theinitial stateof equilibrium. System (b), however, is neutral for i t retains the displacement D(a), neither annulling it nor exaggerating it; but the transformation will not bring it back to a state a after the displacement. Finally, sys- tem (c) is stable because the transformation will return the system to its initial resting state of equilibrium. The same analysis ap- plies to Ashby’s examples.

A system is a stable equilibrium system and, in the general sense we are now pro- posing, a teleological system relative to a specified set of actual or potential disturb- ances. To paraphrase Ashby (1956, p. 79), a system is said to be teleological only if some sufficiently definite set of disturbances D is specified. A system is teleological if the fol- lowing counterfactual conditional is well- confirmed:

If a t t a disturbance D would be intro- duced on a system S , then if X were in equilibrium state a before the disturbance, DS would be either in state a or in a state approaching a a t a specified later time. I t is an empirical question whether a sys-

tem is teleological or nonteleological. Fur- thermore, there are degrees to which a system is teleological relative to the D-specifications, e.g., the extent of the disturbance and the length of time allowed for the system to re- turn to state of equilibrium a. S may be highly stable for DI , . . . , D, , but less so for D,+l .

of values to another variable and vice versa. The rate of inflow and outflow of water into a bathtub with an overflow drain is taken by McFarland (1972, pp. 20-23) to be an ex- ample of this passive control. This seems to be a unity feedback system for which the overall transferfunction,C/R = G / l + G - H , may be calculated with the value of the feed- back transfer function, H , being unity.

If the test for a teleological system is simply the applicability of this characterized mathematical formulation, i.c., the overall transfer function, then i t appears that any system whatsoever qualifies as teleological in that the values of both the input reference variable, R , and the feedback transfer func- tion, H , can be set a t unity. But the test for a teleological system is rather the material or empirical one of introducing a disturbance into the given system. Yet, the bath system seems to meet all of the empirical tests for a negative feedback system, including the con- firmation of our counterfactual. If at t a dis- turbance D, e.g., increasing the rate of inflow, would be introduced on the bath system S, then if S were in equilibrium state a, i.e., the height of the water in the tub within a specified range, before the disturbance, DS would again be either in state a or in a state approaching a at a specified later time. Of course, the system is not stable if the rate of inflow is made to increase so that the water overflows the top of the tub. Furthermore, the bath system oscillates within a value range which might be the range of values on the height of the drain.

Given the bath example, the notion of feedback as formulated in terms of the over- all transfer function may appear to be rela- tively useless. In other words, the behavior of the bath teleological system can be ade- quately accounted for in nonteleological or noncybernetic terms. Yet, the plausibility, relevancy, and utility of the cybernetic ac- count is reestablished by the following con- siderations. The mathematical formulation of negative feedback systems is not sufficient; what is required is an interpretation of rele-

INDEPENDENT TESTABILITY Mathematically, it srrms that feedback

rxists whenwrr the assignment of values to one variable deprinds upon thc assignment

vant mathematical variables in a material Way. Similarly, Hempel (1952, P. 71) argurs that:

. . . the rules for the fundamental meas-

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328 THOMAS W. SIMON

urement of a quantity S do not completely define S, i.e., they do not determine the value of S for every possible case of its theoretically meaningful application. To give an interpretation to S outside the domain D, an extension of those rules is called for.

The cybernetic description is not a syntac- tical formulation but rather a mathematical interpretation of an underlying syntax. How- ever, this mathematical interpretation does not completely define the terms. Every ap- plication of the mathematical formulation gives a new physical theory of a realizable physical system which will be an alternative to, or model of, the mathematical interpre- tation. The teleological/nonteleological sys- tem distinction is not made by recourse to the mathematical interpretation. A material condition of adequacy for a teleological ac- count is an empirical interpretation and an assessment of that interpretation.

It is not that the bath system is a teleo- logical or feedback system but rather that an adequate empirical interpretation of the cy- bernetic terms, particularly feedback trans- fer function, has not been provided. This is done by noting that there are not independ- ent empirical tests relating changes in the rate of outflow to changes in the rate of in- flow, because whatever tests relate inflow to outflow also do the same for outflow to inflow. The independent testability criterion simply requires an empirically discernible relation- ship between the output and input of a sys- tem as well as an empirically discernible relationship between the input and output. The bath system does not meet this criterion and is only misleadingly termed a feedback system because changes in the rate of outflow do not effect changes in the rate of inflow. In other words, an adequate teleological ac- count must give an empirical interpretation in the formulation, C / R = G / 1 + G - H , to both G , the direct transfer function, and H , the feedback transfer function. SCOPE OF TELEOLOGICAL AND CONTROL

SYSTEMS These tests, viz., cybernetic specification,

perturbation, and independent testability, clearly enable one to distinguish teleological from nonteleological systems. It should be

noted, however, that some adaptive, in the broad sense, systems are nonteleological in the sense that is being proposed here. An open loop system could be adaptive. For example, in controlling the indoor tempera- ture of a house, one could calibrate the out- door temperature so as to increase or decrease the fuel supply to the furnace as appropri- ate. In cybernetic terminology this would be a system which cannot control input but must adjust or adapt its direct transfer func- tion. This system wouId fail, for example, the perturbation test. If one were to perturb only the indoor temperature, the system would not make the appropriate adjustments.

The range of teleological system, them- selves, is rather extensive. Teleology en- compases certain types of living and non- living systems. Teleological systems are found at a variety of subsystem levels of living systems. These include: the intercellu- lar level such as the neuronal reflex arc, the organ level such as the pupil control system, the organism in goal-directed behavior, the group level in ecology, and even the organi- zation level. At all of these levels the same basic feedback mechanism can be seen operating. In other words, control systems are found at all these levels.

Control systems in living system or ma- chines are of two basic kinds: regulatory and servosystems. This distinction is expressed in terms of the temporal variation of the in- put reference variable quantity. I n a regula- tory system the values of the input reference variable quantity remain relatively constant over a period of time commensurat,e with the temporal scale of the process in question. In servosystems these values vary. A regulatory system is a type of function system found extensively in biology as, for example, the system which controls internal body tem- perature. Regulatory systems maintain the controlled output at a constant value regard- less of any of a wide range of fluctuations that may occur a9 a result of external perturba- tions. In servosystems, such as may be con- stituted by a predator pursuing a prey, the controlled output follows rather rapid fluc- tuations in the input over a fairly wide range. The range of values assigned to an input reference variable fluctuates more when that

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CONTROL SYSTEMS AND TELEOLOGICAL SYSTEMS 329

variable is a constituent of a regulatory sys- tem. Hence, the difference between these two types of control systems is actually one of degree.

As should be evident from the discussion so far, the scope of a cybernetic systems framework is quite broad, but the question arises whether or not this framework can en- compass all teleological phenomena. Ackoff and Emery (1972, p. 14) claim this approach has a useful but limited application because cybernetic concepts do not “capture all the meanings of purpose in human or even ma- chine behavior.” A truly purposive system, according to Ackoff and Emery, is not only able to maintain different courses of action in attaining a given end, and to exhibit out- comes which have different functions, but also it, “. . . can change its goal in constant environmental conditions ; it selects goals as well as the means by which to pursue them (p. 31).” In fact, this ability to select goals has been claimed by many to provide the differentia between human and animal sys- tems. Hawkins (1969, p. 172), for example, claims that “we alone in the animal kingdom are able to set purposes and not just seek t,hem.” Cybernetic systems seem, a t least prima facie, to be quite removed from pur- posive behavior when characterized in this manner.

Yet, this does not seem to present any formidable difficulties for a cybernetic sys- tems program. Admittedly, the symptoms expounded upon in this paper only enable us to draw the line between nonteleological and teleological systems. But there are no a priori grounds which bar extending this list of features so as to include all types of human purposive systems. For example, given the way we have specified a cybernetic system, the system can change its own mixing point relation by modifying the value range of the input reference value. A system manifesting this symptom would be one which selects its own goals, i.e., the input reference, as well as pursues them. Hence, internal changes of ends and goals can occur in cybernetic sys- tems without the necessity of external changes of the environment. Contrary to the Ackoff and Emery position, one does not need a new, noncybernetic analysis. A new

set of systems concepts is not needed when a perfectly adequate set of cybernetic ones are well-entrenched and available. This is not t o be taken as a rejection of the program that Ackoff and Emery develop. Rather, it is simply meant to show that a great deal more mileage can be obtained from a cybernetic systems framework than Ackoff and Emery seem willing to grant.

CONCLUSION

An attempt has been made to show that the distinction between teleological and non- teleological systems is empirical and that a system must meet a number of requirements in order to qualify as teleological. First, the system must be characterizable in terms of the environmental or disturbance variables, and the three mathematical operations as set forth above. This characterization can be represented by the equation for the overall transfer function. Second, a system is teleo- logical if the counterfactual condition pre- sented above is well-confirmed. A system is teleological relative to a specified set of disturbances. Finally, this empirical char- acter is further amplified by the requirement that its mathematical formulation be em- pirically interpreted and consequently that the direct transfer function and feedback transfer function be independently testable. The notion of purpose is then empirically characterized and no attempt is made to de- fine it in terms of some synonymous notions. Hence, what is indicative of a teleological system and thus of purposive behavior is the presence of certain symptoms. By under- taking our analysis in this fashion, we avoid the seemingly insurmountable difficulty of deciphering the defining characteristics of the teleological. These features are minimal in the sense that they are the least that can be taken as conjunctively sufficient and dis- junctively necessary for the teleological.

By assimilating teleological with control systems, a powerful empirical account of teleological phenomena becomes available. Teleological systems were seen to cover a wide spectrum of system types: living and nonliving, regulatory and servo, and from intracellular to organizational. A cybernetic systems framework was then claimed to be

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330 THOMAB W. SIMON

an extensive one, extending its scope to even human purposive behavior.

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systems. Chicago: Aldine Atherton, 1972. Ashby, W. R. A n introduction to cybernetics.

London: Chapman & Hall, 1956. Ashby, W. R. Design for a brain. (2nd ed.) London:

Chapman & Hall, 1960. DiStefano, J. J., Stubberud, A. R., & Williams,

I. J. Theory and problems of feedback and control systems. New York: McGraw-Hill, 1967.

Goodman, N. Languages of art. Indianapolis: Bobbs-Merrill, 1968.

Hawkins, D. The nature of purpose. I n H. von

Foerster, et. al. (Eds.), Purposive systems: Proceedings of the jirst annual symposium of the America.n society for cybernetics. New York: Sparton Books, 1969.

Hempel, C. G. Fundamentals of concept forma- tion in empirical sciences. Vol. 2, No. 7. International encyclopedia of unified science. Chicago: Univ. Chicago Press, 1952.

McFarland, D. J. Feedback mechanisms in animal behatiior. New York: Academic Press, 1972.

Milhorn, H. T. The application of control theory to physiological systems. London: W. B. Saunders, 1966.

Milsum, J. H. General systems dynamics. In J. H. Milsum (Ed.), Positive feedback. Oxford: Pergamon. 1968.

(Manuscript received March 27, 1975)

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