Home Cybeneticians Anatol Rapoport Symbolic generalizations
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Anatol Rapoport

Symbolic generalizations
Definitions of Definitions

Definition by synonym is useful only if the synonym is closer to our experiences than the word defined Sometimes this is the case...If you have used pocket dictionaries a great deal, where words are defined by synonyms, you must have experienced the disappointment of finding a synonym that means no more to you than the word you have looked up...Definitions by classification are more often useful than definitions by synonym. Their usefulness depends on the familiarity of the person who asks for the definition with the "class" of things into which the word defined is placed.... Definitions by enumeration are useful in defining classes of things if the names of the members of the class defined are closer to experience than the class itself...A great advantage in making definitions by exhibiting an example is that one cannot define fictions that way. Just try to define "Jabberwock" or the "First Cause" by pointing to something and see how sticking to definition by exhibiting an example protects you from believing in ghosts. . . The operational definition succeeds most effectively in connecting abstract words with experience. Practically all operational definitions say in fact "Do so-and-so, and you will find. . ." They predict an experience. They may also be called definitions by prediction. ( 1, pp. 53-54)


A definition of "system" must be such that other than physical entities (perhaps language) are included. At the same time, the definition must exclude entities whose principles of organization cannot be at least partially specified Therefore, I accept the definition of a system as (1) something consisting of a set (finite or infinite) of entities (2) among which a set of relations is specified, so that (3) deductions are possible from some relations to others or from the relations among the entities to the behavior or the history of the system.

The notion of "environment" suggests a partition of a portion of the world into two regions, an inside and an outsides The environment constitutes the outside. The inside, that which is immersed in the environment, will be called a system. In the mind of someone who defines an environment, it is usually the system that is the object of interest. The environment is of interest to the extent that it has a bearing on what goes on in the system and what happens to it. Sometimes a system and its environment occupy different regions of space. At other times, however, the system and its environment are "diffused" through each other. (C, p. 453 and 10, p. 15)

Aspects of a Theory

Three different aspects of theory are emphasized in different senses of the term. One is the logical or "deductive" component of a theory (as in mathematics). One is the "predictive" content of a theory (as in natural sciences). One is the Heuristic aspect of a theory, its ability to provide intellectual points of leverage for investigations. (E, p. 17)


A "function" means a rule, whereby elements of one set are made to correspond respectively to elements of another. The most familiar functions assign correspondences between numbers. For example, y=X2 denotes a function which assigns to every number its square. In more general contexts, the elements need not be numbers. For example, the relation 'fathers can be viewed as a function which assigns to every individual a unique other individual, his father In the so-called Characteristic functions of N-person game theory, a number (the value) is assigned to each subset of the N players. This function was first defined by von Neumann. (3, p. 372)


Three fundamental properties of an organism appear in all organism-like systems. Each has a structure. That is, it consists of inter-related parts. If it is a material system, it maintains a short-term steady state. That is to say, it reacts to changes in the environment in whatever way is required to maintain its identity. It functions. It undergoes slow, long term changes. It grows, developes or evolves. Or it degenerates, disintegrates, dies. (E, p. 22)


Every system (except isolated ones) is in a physical environment. The events of this environment that impinge on the system are changes in the physical states, such as temperature, in concentrations of substances in the surrounding medium, etc. Correspondingly, within living systems there are physical and chemical mechanisms that respond to such changes, both external and internal. These mechanisms are inherent in the physical and chemical properties of the material constituents of the living system. Their operation depends on these properties alone.

Organisms endowed with nervous systems respond also to a Signal environment Certain events that would not by themselves elicit adjustments by virtue of the system's physical and chemical responses do elicit adjustments by virtue of being external stimuli to which the nervous system responds. . . The crucial circumstance is that the signal has been properly coded to be "accepted".

Man lives in a symbolic environment fashioned entirely by himself. Symbols, like signals, elicit responses that depend not on penetration of matter nor on the quality of energy inputs, but on configurations of events. The symbols of language differ from signals in that they can elicit "appropriate" responses even if no specific connection had ever been established between them and the responses elicited. (10, pp. 52-53)

Learning Experiment

In a learning experiement, the typical formulation is a specification of a set of clearly recognizable events (recognizable by the experimenter, that is) called "stimuli", another set of such events called "responses", and still another set called "the outcome of responses". (5, p. 4)


Cybernetics has been defined as the science of communication and control. It first developed in the context of problems associated with the development of complex weapons systems equipped with automatic guidance and control devices. Similar problems arose also in the design of communication systems and of high speed computers. Almost simultaneously, Wiener, a pioneer in cybernetics, and Claude E. Shannon, who first formulated rigorously the foundations underlying the mathematical theory of communication, recognized the cardinal principle involved in all of these problems, namely that of "amount of information." The concept of information is as central in cybernetics and communication engineering as the concept of energy is in classical physics. (F, p. 5)

Stochastic Process

A stochastic process is a mathematical model of a system that passes from state to state in accordance with some "law" governed by probabilities. (10, p. 259)

Hypothetico-deductive Method

The idealized methodology of the physical sciences is the so-called hypothetico-deductive method, essentially a strategy for arriving at new truths in a systematic, cumulative way. Given that certain very general laws have been empirically established, by means of the deductive apparatus (mathematics) we deduce other regularities to be observed. If the assumed laws are true, the predictions must be true. (D, p. 179)

Positive and Negative Feedback

A feedback in a system is an arrangement whereby the systemes output (performance) becomes part of the input (i.e., is included in the stimuli impinging on the system). Positive feedback is self-enhancing on the output; negative feedback is self-restraining, hence a balancing or corrective influence. (3, p. 366)

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