The first model is the Rescorla-Wagner model, which uses as a foundation the assumption drawn from Leo Kamin's experiments in blocking. This basically states that expectation can lead to an inhibition, or breakdown, in the classical conditioning patterns where contiguity and contingency were held to reign supreme. Robert Rescorla and Allan Wagner further refined this idea by stating the actual "amount of conditioning depended on the extent of the subject's surprise." (Lieberman, 1990, p.117.) Without coming right out and saying so, they appear to be attempting to model novelty.
The mathematical formula Rescorla and Wagner proposed is:
Vn = aB(L - Vc)
where the change in learning or extinction, Vn, is a function of the maximum or asymptotic value of L, determined by the US; minus the cumulative, or current strength of association given by Vc; multiplied by the constants a, the CS, and B, the US, which are used to represent their relative effects in a particular association.
This is a simplified exponential function of the type used by C. L. Hull in showing that the strength of a habit depends on the number of times the habit is repeated, and modeled by:
H(N) = 1000(1 - e-kN) (Lial & Miller, 1989, p.752.)
where H(N) is the strength of the habit, N is the number of repetitions, and k is a constant. What needs to be remembered in using these exponential functions, however, is that they are only approximations valid only in certain conditions (p.761), and depend heavily on the constants, or parameters, chosen. In the Rescorla-Wagner model, these constants are arbitrarily chosen after the experiments to make the resultant graphs match the data, and predictions using these models are then said to explain ". . . why conditioning, extinction, and blocking occur . . ."
(Lieberman, 1990, p.134.) However, the use of totally arbitrary values should set off warning bells in the head of anyone who is serious about making a science out of psychology.
The assumptions used in determining associative strengths seem to beg the question of why, and do not show the causes, but only the effects or outcomes. The limitations of the RescorlaWagner model are shown in experiments of configural learning, where compound stimuli do not show the associative strength of the sum of the components the model predicts, and in latent inhibition, where the model predicts that no conditioning would occur without the presentation of a US in preconditioning trials of a CS only. These results seem to show that reliance on underdetermined models to predict behavior are only useful in limited domains, and this limited power makes one wonder if we are really getting closer to a complete understanding of human behavior.
Going now from classical to instrumental conditioning, which deals with response reinforcement and suppression by feedback loops to the stimulus, we have Capaldi's Sequential Model. Formulated by E. J. Capaldi, this model adds another symbol, SN, to the litany of the S->R->R school of psychology. The meaning of this symbol is non-reinforced memory stimulus, and is a culmination of hypotheses dealing with interference in experimental control and prediction.
In noticing that contingency delays sometimes lead to disastrous results, it is postulated that there are almost innumerable responses (head turning, sniffing, running) taking place in the attainment of reinforcement, and just as many stimuli that could become secondary reinforcers (motivation, exteroceptive and interoceptive stimuli.) The problem of discrimination, on both the subjects and experimenters part, leads to schedules of reinforcement and attempts at stimulus control to increase the probability of a correct response to the proper stimuli with appropriate reinforcement.
Capaldi's Sequential Model is an offshoot of the discrimination hypothesis that is used to explain the partial reinforcement effect. A subset of the stimuli present is assumed to control the reinforced response, and "the level of responding in any situation is determined by the similarity of the stimuli present to those that prevailed during training." (Lieberman, 1990, p.238.) It is further assumed that nonreinforcement during training is a distinct stimulus event, and thus, according to Capaldi, responding during extinction trials depends on the similarity between the stimuli present in extinction to those present during conditioning. One of the major stimuli is Capaldi's SN, the memory of the nonreinforced event.
The amount of control SN has is influenced by the number of N-R transitions, which are the times reinforcement follows nonreinforcement, and N length, which is the number of nonreinforced trials that sequentially precede a reinforced trial. In the case of a rat running down an alley to obtain food, an association is said to be formed with SN that strengthens the running response when nonreinforcement is followed by reinforcement. These variables are then used to explain the length of extinction to operantly conditioned behavior, with larger values of SN indicating longer periods of responding.
I'm not arguing so much with Capaldi's results, as with the necessity of the methodology. The number of problems that need explaining away, and the apparent convolution of the resulting explanations, by failing to consider cognitive and biological factors, seem to assume much and prove little. It seems the above rat could simply be remembering that the expectation of food was not always fulfilled in its explorations, but that perseverance often paid off. Are we perhaps overlooking something with the assumption that behavior can be reduced to constants and variables in mathematical formulas?
In an attempt to take operant conditioning techniques out of the laboratory, Keller Breland and Marian Breland have shown that associative learning through operant conditioning can be extrapolated across most of the phylogenetic scale to a non-laboratory environment. However, as they became further removed from the precise control allowed by a Skinner box, they "have run afoul of a persistent pattern of discomforting failures . . . [that] all represent breakdowns of conditioned operant behavior." (Breland & Breland, 1961, p.681.)
In one case reported by Breland and Breland (p.683) where they had conditioned pigs to pick up a wooden coin and drop it in a slot, the animals starting developing problem behaviors after a period ranging from a few weeks to a few months. Instead of taking the coins to the slot the pigs would drop it on the ground, root it along, toss it up in the air, and root it some more. When reinforcement schedules were changed in an attempt to increase drive, the problem behaviors became worse, until the pigs were not getting enough to eat during the day.
This phenomenon of the complete breakdown of conditioning theory was called "instinctive drift" by Breland and Breland (p.684.) It seems that conditioned behaviors that are close to instinctive behaviors cannot take a long term hold on an animals behavior, and are "a demonstration that there are definite weaknesses in the philosophy underlying these techniques. . . . When behaviorism tossed out instinct, it is our feeling that some of its power of prediction and control were lost with it." (p.684.)
In addition to instinctive drift, it seems just as likely that boredom was setting in due to lack of novelty or loss of purpose in what had basically become an impoverished environment, or that they were witnessing the onset of neurosis by keeping animals in a forced, unnatural environment. This would seem to be in keeping with Konrad Lorenz's view on the possible total conditioning of humans when he says, "I strongly doubt whether you can condition man so that he does not become nervous and neurotic when he is crowded." (Evans, 1974.) Breland and Breland then conclude ". . . that the behavior of any species cannot be adequately understood, predicted, or controlled without knowledge of its instinctive patterns, evolutionary history, and ecological niche." (p.684.)
When it was discovered that control was possible, and could be generalized and manipulated with a fairly high repeatability, it was a major triumph of empiricism in the science of psychology. However, everything this new psychology of behaviorism was based on was then thrown out the window as no longer relevant. By then denying the pertinent information that can be derived from and the effects of cognitively caused and/or transformed behavior, and biologically innate behaviors and patterns, radical behaviorism looses its ability to predict and control with the accuracy and completeness necessary to assume law-like status or to become the epistemology of the science of psychology.
When we try to reduce behavior to the strict one-to-one functions of the stimulus-response paradigm, we forget the warning of the cognitive scientists ". . . that any theory of mind that fails to talk about the intervening mental processes that link these stimuli and responses will be unacceptably incomplete." (Flanagan, 1991, p.177.) As E. C. Tolman pointed out, incoming stimuli are "worked over and elaborated . . . into a tentative cognitivelike map of the environment. And it is this tentative map, indicating routes and paths and environmental relationships, which finally determines what responses, if any, the animal will finally release." (Tolman, 1948.)
The proofs used in statistics and probability theory are based on number and set theory. What they show are that distributions of number, under the guidelines of certain axioms, can be shown to follow predictable patterns. Now, if you hold that humans are mere numbers, and behavior is mechanisticdeterministic, you'll probably see nothing wrong in this strong linkage with mathematics in psychological theories. However, they leave me feeling slightly unfulfilled.
The fact that a constant or critical value can be selected to take the place of variables in algorithms, and arrive at a resultant value or create a graph does not mean that a problem solution or law of psychology has been found. It still begs the question of why in causal chains, and totally ignores whether the other problem variables had any relevance to each other whatsoever, and if so, to what degree.
When examining behavioristic models of the stimulus-response-reinforcement school, and all the possible permutations of these three concepts and their various feedback linkages, we find ourselves on shaky ground in the conclusions, extrapolations, and predictions that are allowed by what can at best be described as an incomplete epistemology. The one thing the models do show is that there is a remarkably constant amount of uncertainty and outright failure in experimental results. This happens irregardless of mathematical formulas advanced in support of the power of the model, and especially outside of the artificially contrived and controlled research laboratory.
I agree wholeheartedly with Abraham Maslow that the most realistic way of formulating a theory of human nature and behavior is through the study of healthy human beings in the normal environment and culture we have created. (Hall, 1968.) This does not mean that models and theories that have been derived from interspecies studies or mathematical models are totally useless. These theories and models provide useful guides for our insights into behavior, as long as we remember they are only descriptive generalizations and not necessarily complete and genuine causal explanations. By turning them into laws that disallow or ignore other concepts and explanations, we are implying too much from simple correlation.
By even partially ignoring both intelligent and innate biological behavior in natural environments, we give up the possibility of establishing a complete science of psychology. We seem to be presently insisting on underdetermining the field by basing it on the incorrect view that science is more concerned with prediction and control than on explanation and understanding. Could it be that for the radical behaviorists asking why admits to cognitive processes and the possibility of intelligent self-control that is not totally controlled by the environment? And does not fit neat little mathematical formulas? I think so.
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