DYNAMIC CAUSAL STATE THEORIES OF PEOPLE

Let us start by considering the conditional properties of a communicating individual or a linkage. These are the properties that change, with an individual or linkage either having the property or not in a binary representation. A conditional property is the value of the related categorial property. It can be represented as zero or one, for the individual either having the condition or not at any given time. For example, an individual’s condition of having the turn in conversation at a certain moment will be represented by a value of one for one of the properties, and not having the turn will be represented by a value of zero.

An individual or linkage will be characterized at any given instant of time by a zero or one for each of the many conditional properties. The total set of zeros and ones representing the conditional properties at any given instant is the state of the system at that instant.

Changes in the state of a system take place whenever any one or more of the properties change from zero to one or from one to zero. Since conditional properties are discrete values, any change in value is discontinuous, values intermediate between zero and one being ruled out in a binary representation. When one or more properties change at a given instant, the system is said to have undergone a transition at that instant from an initial state to a final state. The initial state can then be represented as one set of zeros and ones and the final state as a different set of zeros and ones. Transitions occur in sequence. The final state of one transition becomes the initial state of the next transition. The state does not change between transitions, but remains constant for some interval of time. The intervals of time between transitions may vary.

Some of the conditional properties represent externally observable changes of a person during communicative behavior, such as the movements of the lungs and vocal tract resulting in speech sounds, or the movements of the body seen as gestures and facial expressions. These properties then serve as outputs from the system. Thus the verbal and nonverbal behavior of asking a question would be represented in the theory as the changes of many conditional properties in a carefully controlled time sequence.

There are also many properties that are hidden: They do not directly represent observable characteristics of the person. Such properties are postulated on the basis of indirect evidence from communicative behavior, and sometimes from associated noncommunicative behavior as well. For example, when a person has been asked a question, he is on the spot to provide an answer or some other appropriate response. Being on the spot could be represented by a one value of a hidden property that would only become zero when the person had answered the question or got himself off the spot in some other way. The evidence for the property of being on the spot or not comes from observations of similarities and differences of people related to their observable question-and-answer behavior. As another example, a hostess may ask her guests whether they would prefer coffee or tea. Her subsequent nonlinguistic behavior of bringing each guest the desired beverage is evidence of hidden properties involved with her understanding what they had replied.

What could cause the state of an individual to change? The causes of a transition could only be internal to the individual or external to the individual. Causes in this sense are theoretical entities postulated to reflect the real-world causes of the relevant changes in the person.

The internal causes are to be found among the conditional properties of the initial state of the transition. This initial state set contains conditional properties resulting from earlier transitions; thus they constitute the relevant history of the individual brought forward to the instant before the transition takes place.

The external causes all act across the boundary of the individual.

Some external causes arise in the external environment, reflecting input energies to the person from his surroundings. Examples of these would be the incoming sound waves of speech or the incoming light waves from a smile, a raised eyebrow, or a gesture.

Other external causes arise in properties of the person that are external to the communicating individual and influence the individual across the internal boundary between the individual and the rest of the person. An example would be Jill’s decision to ask Jack to get her an apple, which could be represented as a nonlinguistic property of Jill.

The external causes are treated in the same way as the internal causes. Those that are properties of the person external to the individual are already properties, and those that represent the detection of input energies can be treated as causes in the same way as properties.

Thus the causes of any transition are completely contained in the initial state set of properties and the initial set of external causes. A transition, therefore, is characterized or described by these two initial sets, by the final state set of properties, and by the interval of time since the last transition.

We now postulate that the relation between possible sets of causes and possible final sets is mathematically a functional relation: When a transition takes place the final state set is uniquely determined by its causes, which are the initial state set and the set of external causes. This conforms to the ordinary assumption of causality in science that has been so successful in the conduct of scientific research.

Since there are more combinations of possible initial state sets and sets of external causes than there are final state sets, the function is many to one— the same final set may be caused by any one of many different sets of causes.

The interval of time between the previous transition and the current one is the time delay associated with the transition. This time delay is also determined uniquely by the initial sets.

We have arrived at a characterization of an individual or a linkage in terms of a very large list of the possible transitions of the system and a list of the associated time delays. Each transition is characterized by its initial set of causes, its final set of conditional properties, and the time delay.

It should now be pointed out that when an individual or a linkage is characterized in this way, it is being characterized by means of a dynamic causal state theory, a type of theory that is well known in science, going back more than 300 years, and is widely used today in many scientific and engineering disciplines.

However, the theory at this stage is quite intractable. No state set will ever be the same as any other state set if no two individuals are ever the same, or any one individual twice the same. Therefore no one transition will ever be the same as any other transition. And since the number of properties is very large, the number of different state sets is astronomical, as is the number of different possible transitions. Thus as the theory now stands, we do not have any generalizations regarding transitions that could provide specific predictions about communicative behavior that could be tested against the evidence.

What is needed are valid generalizations regarding specific transitions or sets of transitions for particular individuals and linkages. These would constitute specific dynamic causal laws of communicative behavior that would provide predictive power and insight. The way to obtain these is to consider first some further lines of evidence and try to develop further general laws that will reduce the number of possible states and transitions given by the theory.

THE LAW OF SMALL CHANGES

There is considerable observational evidence for the predictability, consistency, and long-term stability of people from the point of view of how they communicate. Relative stability is observed in a person’s vocabulary, regional dialect features, and long-term memory for people, objects, and events of communicative significance. People can carry on a coherent conversation, which means that certain of their properties relevant to the conversation remain stable for appropriate lengths of time during the conversation. Stability of properties is also found in the phenomena traditionally analyzed in terms of grammatical or syntactic restrictions between different parts of a sentence. Such evidence for the consistency and predictability of people is widespread and incontrovertible.

In view of this evidence, we are led to a second observationally based general law of communicative behavior, the law of small changes:

Most of the properties of an individual remain stable and unchanged over considerable periods of time; thus only a few properties are changed during each transition.

This important law recognizes that individuals are highly structured in terms of stable groups of properties. Individuals do not suffer extreme fluctuations in their properties. Any large changes must be gradual, the result of the changes of only a few properties at a time. It also appears that properties are graded in terms of their frequency of change. A few may change fairly rapidly, for example the properties at the phonetic and phonological level during ongoing speech. Those that reflect sentence production or understanding would change a bit more slowly. Others reflecting the course of a conversation would change more slowly still. And properties reflecting vocabulary or dialect features would be the slowest to change. Thus there is a possibility of a level structure of properties. At each level there would be properties that change relatively rapidly against a background of more slowly changing properties.

THE PRINCIPLE OF CONTINUITY OF COMPONENT
PROPERTIES

The law of small changes leads to the possibility of studying the changes of only one property at a time.

Let us consider a particular conditional component property p_k and what happens to p_k when a transition takes place. With this limitation we will speak of component transitions, that is, transitions only from the point of view of what happens to p_k.

Now consider how p_k changes during a component transition. There are only four possibilities. Either p_k changes from zero to one during the component transition or from one to zero, or it does not change, remaining zero or remaining one.

Since according to the law of small changes only a few properties change during each transition, we expect that most of the component transitions are of the sort where p_k does not change. It would thus be a great simplification if while studying p_k we could ignore all the component transitions where p_k does not change. We can do this by introducing a principle of continuity of component properties:

A component property will remain the same unless caused to change from time to time by transitions occurring at those times.

This is simply a notational convention by which we agree that when studying a given component property p_k, we will remove from consideration all those transitions where p_k in fact does not change. Since on the law of small changes we expect that p_k does not change during most transitions, the remaining set of component transitions forms only a small subset of the original set of component transitions for p_k, and this brings a great simplification in the theory. Under the principle of continuity, then, when we speak of component transitions we will be speaking only of members of this small subset where p_k does change.

Adopting the principle of continuity of component properties brings the obligation that we try to find and consider all of the component transitions for p_k, for it is assumed that p_k does not change if no corresponding component transition is listed. We hope that the component transitions will be few enough that we will eventually be able to find them all.

The principle of continuity of component properties can be considered as a particularly simple means of formalizing the memory properties of the individual. A property will remain stable unless changed. That is, once the value of a property has been set by a transition, that value will be retained or remembered until it is caused to change again by a transition at some later time.

THE LAW OF RESTRICTED CAUSATION

Let us now look at the component transitions, those transitions where p_k changes. So far there are no restrictions on the causes of component transitions—as far as we now know the causes could include every component property and every external cause. There is evidence, however, that the causes of component transitions are far fewer than this.

We can set up an experiment to elicit the same small segment of communicative behavior from a number of different people and from the same person on multiple occasions. Since this can easily be done, we can conclude that most of the properties where the different people differ and where the same person differs on different occasions are probably irrelevant as causes for the component transitions associated with this small segment of behavior. We can also eliminate as causes for the component transitions all those external causes reflecting irrelevant parts of the surroundings like background noise, different objects in the vicinity, different other people in the group, and so on.

There is also evidence from limitations on the focus of attention. A person concentrating on or attending to a certain topic often does not simulatneously consider other topics, or if he is attending to certain inputs he does not respond to other inputs, as if they were not there.

It is also relevant that it is often rather easy to elicit a given facet of communicative behavior from a person. Because the law of small changes holds, the easy elicitation probably requires the change of only a few properties. However, more permanent cultural factors may also be involved as causes, but the number of these that are directly relevant as causes is also probably small if the facet of behavior elicited is as small as the change of a single property.

Such evidence leads to the third general law, the law of restricted causation:

Although the number of component properties is very large, the number involved as causes in the changes of any given component property is small.

This means that when we represent the set of component transitions for any component property we will not have to consider most of the component properties of the individual; only a small number will ever be involved. This law therefore makes possible a considerable further simplification in the theory: component transitions for p_k involve only a small number of properties in their causes.

SPECIFIC DYNAMIC CAUSAL LAWS OF
COMMUNICATIVE BEHAVIOR

But much more can be achieved: These three general laws—the law of componential partitioning, the law of small changes, and the law of restricted causation—make possible the development of the specific causal laws of communicative behavior that we have been seeking.

It is a direct implication of the law of restricted causation that in the list of component transitions for p_k most or all of the transitions listed cannot be distinguished from others in the list because they have identical causes. That is, the list contains subsets of identically represented component transitions which come from original transitions only differing from each other elsewhere in their causes.

For each of these subsets of identically represented component transitions we need represent only one. This vastly reduces the number of component transitions represented for p_k.

Furthermore, according to the law of restricted causation only a small number of causes will be involved. This means that there will be only a small number of remaining differently represented component transitions. With a binary representation, 10 causes will allow no more than 1024 different component transitions, 6 causes will allow no more than 64, and 4 causes will allow no more than 16. However it is not yet clear how many causes there will actually turn out to be when we start to analyze data relevant to the changes of specific properties.

The time delays associated with component transitions also need to be adjusted, but this does not drastically alter the conclusions.

Starting with thousands or millions of properties and an astronomical number of transitions, we have found that we can reduce the scope of our consideration to the changes of only one property at a time, and that there will be only a few causes for its component transitions. There is thus the possibility that the differently represented component transitions will be few enough in number that we can find them all. There actually is a chance, then, of achieving a complete representation of the causes for the changes of each component property we study.

It can now be pointed out that:

Each representation of a component transition in this final form is tantamount to a specific dynamic causal law of communicative behavior.

Each such representation says that every time the indicated properties and external causes in an individual reach the values specified, a component transition will take place, changing the property p_k appropriately. Such a representation is a true generalization because there are many ways in which this can happen—the irrelevant properties may take many different sets of values. It has predictive power since it records what will happen under specific repeatable circumstances. It is thus a specific law that can be tested. It is a dynamic law because it deals with the changes of the property p_k. And it is a causal law because it connects the specified change of p_k to its causes.

It turns out that the same considerations hold for linkage properties, and linkages can also be treated in terms of specific causal laws such as these.

THE REPRESENTATION OF CAUSAL LAWS

What remains to be done with these specific dynamic causal laws is purely notational. But notational matters are not unimportant, for they can make a considerable difference in the facility with which research can be carried out and the clarity with which the results can be presented.

Instead of using zero and one as values for the properties in the state set, we can adopt a truth-functional notation in which p_a means that it is true that the property p_a has the value one, and –p_a (not p_a) means that it is not true that p_a has the value one; i.e., it has the value zero.

Suppose we have a dynamic causal law that says that p_k changes to the value zero whenever it is the case that the properties p_a, p_b, and p_c in the state set of the individual take the values of one, zero, and one respectively. Then, since these values must simultaneously hold, we can combine them with the truth-functional and, which we write as x.

Using this notation borrowed from logic, and adding the nonlogical notation :: (which we read as sets), we can write the causal law as

which we read as p_a and not p_b and p_c sets not p_k, or in full, the logic expression “p_a and not p_b and p_c” becoming true sets p_k to the value zero (false). We call this a setting expression.

Suppose this is the only dynamic causal law that sets p_k to zero. But in general there will be a number of causal laws that are equivalent in that they all set p_k to the same value. For instance, we may have the following causal laws for setting p_k to the value one:

Since these are equivalent causes for the same thing, they can be combined by the logical (inclusive) or, which we symbolize as v. This gives

For any property p_k there are two equivalence classes of causal laws: one where p_k changes to the value zero and one where it changes to the value one. Thus if the above causal laws cover all the cases, we can express all the changes in p_k by means of the two setting expressions:

This is called a setting procedure.

Other notations are also available for setting procedures, but this notation will be sufficient for carrying the argument forward at this point.¹

We may need to consider also the time delays in the changes of the property p_k. There are straightforward notational means available to do this. The choice of notation will be influenced strongly by what observation reveals about how the time delays depend on the causes. Since such data are not yet available, we will not consider the matter further at this point.

One of the advantages of borrowing a notation from logic for the causes in setting procedures is that we can make use of the known methods of simplification of logic expressions. In the case at hand, the second setting expression can be simplified, so that the setting procedure can be written

Another advantage of using the notation of logic is that we can explicitly show by symbolic manipulation whether alternative formulations are equivalent or not. This should help to forestall meaningless arguments.

It is clear that this formulation is completely general. A setting procedure, when correctly formulated on the basis of the evidence, provides a complete and compact representation of the causes for the property to change, and the properties and changes in properties of a communicating individual or linkage can be completely characterized in terms of setting procedures.²

In comparing this formulation of linguistic theory with others, whether grammatical or not, it should be kept in mind that this formulation does not rest on any special or a priori assumptions such as Bloomfield’s assumption. It does not assume language. It has been proposed in the light of, and justified completely on the basis of, readily available and incontrovertible observational evidence that has been assessed and interpreted with the help of only the most general assumptions of science, which have withstood the test of several centuries of successful application in the physical and biological sciences.

LINGUISTIC PROPERTIES

The introduction of setting procedures introduces into human linguistics what are called procedural properties, which stand as a third type of property beside the conditional and categorial properties already discussed.

There is also a fourth type of property. If an individual or a linkage has conditional, categorial, and procedural properties, then the individual or linkage must also have the properties of having such properties. Thus there must also be what we will call foundational properties. Foundational properties are required as a foundation on which the other properties are built.

In this picture, then, individuals and linkages are modeled in terms of four types of properties: conditional properties, categorial properties, procedural properties, and foundational properties.

We have seen that the conditional properties or conditions are the changing state properties of the individual or the linkage. Specific configurations of conditional properties selectively trigger or activate any given procedure whenever they match the triggering conditions required for that particular procedure. Then when the procedure executes, it changes one or more of the conditional properties. Conditional properties, when they are changed by the executing of procedures, will stay in their changed state until changed again by the executing of other procedures. Thus they constitute memory properties that record or remember the changing context of situation or changing state of the individual or linkage at every level from phonology to pragmatics—and even, if necessary, the state of the tasks being coordinated by the communicative behavior.

The categorial properties or categories are the dimensions along which the conditional properties vary. They provide the possibilities of change, the categories according to which situations can be represented. Categories are related to conditions as gender is related to feminine, case to dative, or number to plural in the linguistics of language. Categories are not necessarily binary. There may be a number of possible values or conditions, or some may even be represented as continuous variables if that is needed for modeling certain changeable communicative aspects of a person.

The procedural properties consist of procedures, which to some may seem reminiscent of grammar rules. It is important, however, not to confuse them with rules in grammatical theories. Unlike grammar rules, they are not part of a theory of language; they are part of a communicative theory of a person or of a group. They specify the context of conditions under which something will happen, and how what happens then changes this context of conditions. Unlike grammar rules, they are applied or executed on occasion—or better they trigger or activate and execute whenever the stated conditions obtain. They are unordered: All triggering conditions are explicit. And unlike grammar rules, the conditions and changes do not take place in an assumed abstract grammatical or logical domain of a “derivation,” or “representation,” rather they are part of a dynamic theory that models what takes place in people as they communicate.

The foundational properties contrast with the conditional, categorial, and procedural properties, which together are called informational properties. They provide the foundation or support on which the informational properties rest, and constitute the underlying mechanism that makes these properties possible.

Within this framework, specific properties of communicating individuals and linkages are postulated on the basis of observational evidence about specific persons or groups. Since the properties are postulated as parts of theories of real objects, there is the possibility of testing them against further evidence from the real objects. And as we shall see, the properties of communicating individuals and linkages are highly structured, which provides further possibilities for testing postulated interrelations between the various properties.

It is probably worth pointing out that human linguistics does not offer a theory of performance in connection with an assumed competence-performance distinction, since it does not operate with a concept of competence, or indeed of grammar at all. Properties in human linguistics are structured in ways sometimes resembling constructs familiar in grammar, but they are enough different that intuitions about them derived from familiarity with grammatical theories are frequently wrong on account of the psychological reality of grammar fallacy.

Linguistic or communicative behavior is not seen as rule-governed behavior but as lawful behavior. This is just the difference between the logical domain and the physical domain. Our analysis is not reminiscent of the school child laboriously constructing a sentence of Latin by following a rule book, but rather of his practiced, unthinking, and automatic handling of his native language. It has to do with finding the constraints on actual behavior, of accountability to the evidence, not to some ideal or norm. The behavior is seen as being lawful in that it would be exceptionless if we had enough knowledge of contextual factors and of the relevant laws governing their effects. Cases that would be seen as free variation in the linguistics of language would be seen as cases where the relevant constraints are not yet completely known— an invitation to do further research. Similarly, “slips of the tongue” or “mistakes” would eventually have to be accounted for, since we are dealing with a theory of a reality. There is no evidence that people are not subject to the laws of nature. It is up to science to find the laws.