Within the framework of a formal model of the subject (Lefebvre, 1995), mathematical analysis of a function representing the subject's behavior allows us to find another function corresponding to an "image of the self." In this way we successfully obtain information about the subject's inner domain without relying on introspective methods.
"Lefebvre's contribution to a theory of the mind was the
development of formalism to serve as framework in which to
cast a mathematically rigorous theory of introspection."
(Rapoport, 1995, par. 7)
2. The term "introspection" has in two different meanings in psychology. The first meaning refers to the natural human ability to turn mental activity back on itself. Insofar as I am concerned with this particular ability of human beings, it is true that I construct "a theory of introspection."
3. There is another meaning of the word "introspection." It is connected with a special method of studying the human psyche in which self-observation is used as a technique for receiving information about the structure and dynamics of mental phenomena. The introspective method reached its apogee in Wundt's school, but later was found to be non-productive. It has not offered theoretical schemes allowing us to systematize information related to the inner domain and to make predictions regarding that domain. Moreover, the very fact of observing a mental phenomenon may change its dynamics. In constructing a formal model of the subject (Lefebvre, 1995; 1992), I have not used this introspective method at all.
4. The question naturally arises of how we can receive information about the mental sphere without relying on introspective observation. My answer is that we can try to obtain information about subjective states by analyzing a function related to human behavior. I describe this method below.
5. When we state that the subject is aware of his behavior, we assume that he has "an image of the self" which is, to a certain degree, correct and that there is an external world influencing the subject which he is also aware of.
6. Now let us translate the content of the above paragraph into the language of functions. We put a subject into correspondence with function
X1=F(x1,X2), (1)
defined on the set of real numbers. Variable X1 represents the subject's behavior, x1 the influence of the external world, and X2 the subject's behavior from his own point of view. This is the core of a model of the subject who is aware of his behavior.
7. Expression (1), however, does not reflect the correctness of the subject's image of the self. The first thing that comes to mind is to declare that X1=X2, but this is only a particular case of the more general assumption that variable X2 is represented by the same function as variable X1:
X2=F(x2,x3), (2)
where x2 is the influence of the world on the image of the self and x3 is an image of the self which belongs to the image of the self.
8. It follows from equations (1) and (2) that the subject can be represented as follows:
X1=F(x1,F(x2,x3)). (3)
9. Imagine now that we have managed, independently of the considerations given above, to find the function
X1=f(x1,x2,x3) (4)
related to the subject's behavior, where x1 corresponds to the objective influence of the world, x2 to its subjective reflection, and x3 to the subject's consciousness. Then, if we succeed in representing f(x1,x2,x3) as composition (3), we will obtain information about the subject's "image of the self."
10. It was demonstrated in my paper (Lefebvre, 1995) that the function
X1=x1+(1-x1)(1-x2)x3, (5)
where x1, x2, and x3 belong to [0,1], reflects human behavior in the situations of choice and that it can be deduced from very general assumptions. Earlier (Lefebvre, 1992), I proved that function (5) can be represented as (3), where
F(x,y)=1-y+xy, (6)
and that such representation is unique. Therefore, within the framework of this model, an "image of the self" corresponds to function (6).
11. Thus we have succeeded in obtaining information about the subject's mental domain from a function related to his behavior, without reliance on introspective observation.
Rapoport, A. (1995) Human Reflexion and the Anthropic Principle. PSYCOLOQUY (6)37 human-choice.3.rapoport
Lefebvre, V. A. (1995) The Anthropic Principle and Human Choice. PSYCOLOQUY (6)29 human-choice.1.lefebvre.
Lefebvre, V. A. (1992) A Psychological Theory of Bipolarity and Reflexivity. Lewiston: The Edwin Mellen Press.