Anatol Rapoport (1996) Probabilistic Choice and Lefebvre's Model of Human Reflexion. Psycoloquy: 7(27) Human Choice (8)

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Psycoloquy 7(27): Probabilistic Choice and Lefebvre's Model of Human Reflexion

Commentary on Lefebvre on Human-Choice

Anatol Rapoport
University College
University of Toronto
Toronto, Canada


Some points raised by commentators on Lefebvre (1995) are examined. It is argued that Lefebvre's efforts are an important contribution to injecting rigorous deductive reasoning into intuitive approaches to human reflexive cognition.


choice; computation; decision theory; ethical cognition; mathematical psychology; model building; parameter estimation; probability; rationality.
1. In reading Adams-Webber's (1995) and Kampis's (1995) comments on Lefebvre's discussion of human reflexion and the anthropic principle, I tried to imagine a discussion between them on that subject and found it difficult. Kampis seemed to be interested mainly in the logical structure of Lefebvre's thought processes and found it deficient. Adams-Webber wrote about the content of Lefebvre's arguments and found it to be rich. Both showed an interest in the anthropic principle and evaluated Lefebvre's ideas about it, Kampis negatively, Adams-Webber positively. I found no common ground.

2. In re-reading my own remarks (Rapoport, 1995), I realized that they barely touched upon the anthropic principle, which was supposed to be central in the discussion. It became clear to me that I was only mildly interested in the question posed and answered by the principle and consequently I contributed next to nothing to the central theme of the discussion. What I am intensely interested in is the phenomenon of human cognition and its place in ethics and in the philosophy of science. Specifically, I am interested in a science of human cognition rooted in its most directly perceived aspect (introspective consciousness) but developed according to strict principles of rigor and operational criteria of meanings. It is primarily for these reasons that I joined the discussion. And it is in this spirit that I continue it.

3. In replying to Kampis's comments, Lefebvre (1996a) points out that he does not regard the irreducibly probabilistic model of physical reality underlying quantum mechanics as evidence supporting the existence of freedom of will. I interpret this reply to mean that "probability" is a multi-level concept.

4. To take a simple example, consider the probability p that a tossed coin shows heads. In a way, p is a parameter representing one of the physical properties of the coin. In attempting to "determine" p, we initially assign to it a "prior density distribution." For example, to express our initial total ignorance about p, this prior density may be one with maximal entropy, that is, f(p)=1(0<=p<=1). This density is a particular "beta function," namely B(1,1). To get a better estimate, we toss the coin several times. The recorded outcomes modify the parameters of the prior density, whereby the "posterior" density B(m,n) with m>1, n>1 exhibits a maximum on the interval [0,1] and its variance (or entropy) decreases. Our confidence in the "true" value of p increases but never reaches certainty. We can now speak of the "probability that p lies within certain limits", that is of a "probability of a probability." This concept can be clearly extended to higher levels, thus reducing indeterminacy on one level to determinacy on another: we say "the probability that the value of p lies within such and such limits 'is' so and so." And so on.

5. I believe it is in order to avoid infinite regression that Lefebvre essentially treats "freedom of the will" as a primitive (hence undefined) term in his model. In this context then, the postulate of the existence of free will cannot be falsified. In fact, I am inclined to express a mild criticism of Lefebvre's emphasis on the unfalsifiability of his initial assumption (which nevertheless leads to empirically corroborated predictions). Actually unfalsifiability of initial assumptions, as well as undefinability of primitive terms pervades the most rigorous "hard" sciences, and there is no need to emphasize them.

6. In the context of hard science methodology, it is also held axiomatic that only theorems devoid of empirical content can be "proved". Empirically testable hypotheses can be only corroborated or refuted. For this reason, Kampis's dismissal of Lefebvre's allegedly attempted "proof" of the free will hypothesis misses the mark. The corroborations of consequences derived from Lefebvre's introspection model constitute not a "proof" that it is true but only evidence that it is theoretically fruitful. Construction of fruitful models is, after all standard practice in all development of theories.

7. This brings me to Lefebvre's distinction between two meanings of "introspection" (Lefebvre, 1996b). In one sense, the term refers to the human ability to "turn mental ability back on itself." In this sense, Lefebvre agrees, introspection plays a central part in his researches. In another sense, introspection refers to studying the human psyche through self-observation, a path pursued by Wundt and his followers. This method, Lefebvre points out, led to a dead end and was subsequently abandoned.

8. It seems to me that the main reason for abandoning introspection as a method of scientific psychology was the appearance of a strongly seductive rival, namely behaviorism, which offered much broader opportunities for designing theoretically fertile mathematical models and well controlled experiments, particularly on animals (whose "inner world" is inaccessible to us). In turning away from self observation and from concepts in which mental phenomena play an important part, the behaviorists believed that they were putting psychology on a more solid "objective" basis. Yet their conceptual schemes also rested on undefined terms and unverifiable (and unfalsifiable) assumptions, although not explicitly recognized as such.

9. Consider a standard experiment in instrumental conditioning. The experimenter's notebook contains a number of check marks indicating instances when a rat, after a signal was given, "pressed a lever, in consequence of which a mechanism delivered a food pellet, which the rat ate." Apparently this statement is a model of clarity and objectivity. Yet consider the tacit assumption on which it rests, namely, that all the events mentioned can be subsumed under well defined classes. In the same way, in recording the results of coin tosses, the experimenter tacitly assumes that every toss is like every other. This is manifestly false: every toss is different. The angle at which the coin is thrown, the number of times it turns over while falling, how it is caught all differ from toss to toss. Nevertheless all these variations are ignored for a very good reason, namely, that those differences really don't make a difference.

10. Let us return to the experiment with the rat learning to get a pellet by pressing a lever. While the pellet-delivering mechanism may act in more or less exactly the same way from trial to trial, the same cannot be said of the rat. It may use entirely different muscles in different sequence pressing the lever and eating the pellet. Yet all these events are also lumped into one observed event marked by checking a column in the experimenter's notebook. The only thing that varies and matters is the number of these check marks under various experimental conditions.

11. Now what is the faculty of human cognition that makes possible the act of classification, that is, lumping together innumerable events into a single "recognized" event? The word "recognized" identifies the faculty -- recognition. Of course we share it with other living beings, and take it for granted that it is "natural" for a dog or a cat to distinguish between a dog and a cat. But aside from identification of a few key stimuli, we know very little about the mechanism of recognition in higher animals. Witness the persistent and thus far only vaguely fruitful efforts to build artificial intelligence devices that possess really impressive faculties of recognition, say of the sort that we exhibit when we recognize the bee alighting on a flower and a man sending flowers to a woman as steps in the same process, namely, sexual reproduction.

12. Possibly introspection in Lefebvre's sense, that is, "turning mental ability back on itself" is a faculty unique to humans, something that in view of the inaccessibility of the inner worlds of non-humans cannot be verified. However the fact that we possess it can be verified, namely, by introspection in Wundt's sense. If only for this reason, it seems not advisable to abandon introspection (in Wundt's sense) as a method of cognitive science. To be sure the problem of integrating it into the highly disciplined process of scientific cognition remains. It seems to me that Lefebvre undertook that very task, and it is for this reason that I regard his work in this area of prime importance.

13. Lefebvre's attack on the problem is presented in his monograph, A PSYCHOLOGICAL THEORY OF BIPOLARITY AND REFLEXIVITY (1992). He introduces the function X1=f(x1,x2,X3), where the arguments xi(0<=x<=1, i=1,2,3) represent respectively pressure on the subject toward a positive pole (of behavior), proximity of the of the subject's image of the world to the positive pole, and intention to perform a choice, while their complements 1-x, represent pressures toward the opposite pole. Assuming X1 to be a linear function of each of the three arguments separately, Lefebvre derives an expression for X1 as a function of two variables: X1=F[x1,F(x2,X3)], where F(x,y)=1-y+xy. Moreover, he has shown that this representation of X1=f(x1,x2,X3) is unique. In his discussion in PSYCOLOQUY, Lefebvre writes:

    "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" (Lefebvre, 1996b).

We have here an example of how Wundt's method can be "hardened" so as to satisfy the criteria usually associated with scientific cognition.

14. Finally a word is in order concerning the relevance of the anthropic principle to cognitive science. As it is usually stated, the anthropic principle asserts that any theory of cosmic evolution must contain an assumption that its supposed course should incorporate the coming into existence of an observer, actually of an observer capable of self-observation, because we (who are convinced that we exist) are such observers. If however, modern philosophy of science admits the possibility of irreducible uncertainty in the course of events (of the sort underlying, say, quantum mechanics), then the anthropic principle cannot be stated in a categorical mode. The most that can be attributed to it is that it should provide for a finite probability that a self observing observer appears in the course of cosmic evolution. This interpretation suggests that the course of cosmic evolution may have spawned several universes some with self-observing observers, some without. Of the latter, we can, of course know nothing. All we know is that we have been "lucky" to have appeared.


Adams-Webber, J. (1995). A Pragmatic Constructivist Gambit for Cognitive Scientists. PSYCOLOQUY 6(34) human-choice.2.adams-webber.

Kampis, G. (1995). The Anthropic Principle of What? PSYCOLOQUY 6(38) human-choice.4.kampis.

Lefebvre, V. A. (1992). A Psychological Theory of Bipolarity and Reflexivity. Lewiston: The Edwin Mellen Press.

Lefebvre, V. A. (1995). The Anthropic Principle in Psychology and Human Choice. PSYCOLOQUY 6(29) human-choice.1.lefebvre.

Lefebvre, V. A. (1996a). Extracting Information about Subjective States from a Function Describing Human Behavior. PSYCOLOQUY 7(08) human-choice.6.lefebvre.

Lefebvre, V. A. (1996b). The Inexplicable Effectiveness of Metaphysical Reasoning in the Construction of Mathematical Models. PSYCOLOQUY 7(09) human-choice.7.lefebvre.

Rapoport, A. (1995). Human Reflexion and the Anthropic Principle. PSYCOLOQUY 6(37) human-choice.3.rapoport.

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