MATHEMATICAL RESEARCHES FOR ELEMENTARY BEHAVIORISTICS

Abstract

The object of this paper is to construct a sufficiently comp ehensive framework of reference with which we can formulate theories of human behavior. The elementary behavioristics is directed on its first step to find a universal mode of description with which we establish general laws of human behavior. From this point of view, we will begin our work with logico-operational analysis about terminology such as behavior, valence, path, etc. used by Lewin, and will try to replace them by mathematically well-defined terms.Although any kind of behavior always comprises some change of human state, it never means that every change of human state is attributed to behavior. In the region of physics human being is also a kind of matter which changes its state in accordance with physical laws. Similarly in the region of physiology the state of human being as a kind of physiological system changes under the laws of physiology. Such a change shall never be called a behavior. On account of these conditions, we will classify all changes of human state into two groups, one behavioral and the other natural which is under the control of so-called natural laws.Now we may take such a mathematical space that every point contained in it has one-to-one correspondence to every mutually distinguishable human state, and that any continuous change of human state should be represented by continuous curved line in the space. We call this the “state space” of human being. There may be infinite number of lines in the space, most of which can never be traced by behaving. The rest traceable by behaving is called the “path” in the state space. Now, let us suppose that an individual traces a path and reaches a split-point. Since he can not stop even for a moment in the state space-for we regard the time as one of the coordinates of the space-he is bound to select instantly one of the alternatives and to continue tracing this path. Then, what may be the standard for this selection? In view of the conditions that the selection should be carried out at the location of a split-point, we are compelled to recognize the existence of a uni-dimensional quantity whose value is the standard measure of selection. And the path having the maximum value of this quantity should be always selected among others. We call this quantity “Behavior-function” or briefly “B-function” of path. Next question is to determine the form of this function in terms of components of path.In the space we may have the so-called desirable state. Putting it in our terminology, there exists such a state that any path passing it has a tendency to be easily selected at the split-point among others. As to undesirable state, it goes by contrary. This fact means that each point in the space has its particular cantribution to the B-function of the paths passing it. We name this contribution the “valence” of state, and the state which has a valence, “effecta.” B-function must be additive about valences.It is necessary, however, to account for one more function as a constituent of B-function. Suppose that there is one effecta and several paths connecting an individual with it. In this case, what path is the best one? Let us call to our minds that natural changes are also members of human state change as well as behavioral ones. While an individual is going on a path by a sequence of behavioral changes, some natural changes might occur which separate his state from the effecta so that he can no longer find a new path connected with the effecta. We might not be certain whether such occasion does or does not takes place on each path, but there may be a difference for each path about the quantity named by the “degree of certainty” for occurance. And it is clear in such a case that one selects the path which has the naximam probability for the connection between the effecta and him. Such a path, we distinguish

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 3 citations exist upstream.