Nature and use of assumptions

The inability strictly to disconfirm economic laws has raised the issue of the status and the function of assumptions in economic reasoning. Although a history of such propositions as the so-called “rational principle,” or the principle of profit maximization, transcends the scope of this work, it should be noted that these and similar propositions were originally thought to have immediate empirical content and thus to be “realistic.” Certainly, Bentham did not think of his felicific calculus as a mere formal postulate but rather as a set of propositions about some aspect of the real world. Adam Smith viewed the basic behavioral propositions used in The Wealth of Nations similarly — although he certainly considered the propositions as relevant only to certain aspects of human behavior. The same attitudes would seem to apply to the first formulations of the model of perfect competition.

In the course of the development of economics, the basic behavioral propositions met with increasing dissatisfaction. In recent years they have come under heavy attack because of the lack of empirical content. Now, it is a familiar occurrence in science that concepts that at first are thought to have immediate empirical content (to refer to observables) are later found to have no such content. Normally such concepts are simply eliminated when they are no longer useful. If they appear in higher-level laws, they are replaced by  other concepts more satisfactory in the explanation of lower-level laws. This procedure, of course, requires the constant control of empirical verification. Economics, however, is still essentially based on “intended empirical laws.”

The role of assumptions in the physical sciences is nothing like their role in economics. Almost any law may be treated as an assumption if this is convenient for the purpose at hand, but there are no laws that occupy the position of “basic assumptions.” There are, of course, laws that explain other laws, but these remain subject to constant control through the process of verification of their empirical implications.

In physics, too, the issue of the “realism” of propositions has been debated. What was involved, however, was the operational nature of theoretical concepts. On the other hand, in economics, what is meant by “lack of realism” is inconsistency of propositions with observables. This problem, of course, is one of substantive economics, which must be solved by empirical research. The fact that it could become a basic methodological problem is surprising.

A brief review of Friedman’s argument may help to clarify the main issues. Friedman argues that “assumptions” need not be “realistic.” They are judged exclusively by the predictive success of their implications. Thus, he concludes that criticism of assumptions as unrealistic is ill-founded and, indeed, that the search for more realistic assumptions is illicit.

Friedman himself is well aware of the ambiguity of the term “assumption.” He offers three interpretations: “(a) they are often an economical mode of describing or presenting a theory; (b) they sometimes facilitate an indirect test of the hypothesis by its implications; and (c)…they are sometimes a convenient means of specifying the conditions under which the theory is expected to be valid.”

As an example of the first interpretation he offers the case of the leaves of trees, which behave as if they were maximizing the amount of sunshine to which they are exposed. He defends this form of expression essentially by asserting that the alternative to it would be to enumerate each tree. Rotwein has pointed out that this is false since Friedman’s formulation simply amounts to saying that the density of leaves on trees is a positive function of the amount of sunshine (a consequence of heliotropism). Even if, within the narrow limitation of a reference to the density of leaves on tree trunks, the two statements may be accepted as equivalent, the question remains as to why the unrealistic statement, couched in anthropomorphic terms, should be used in preference to the other. Although it seems to have no advantage, it does have a serious disadvantage. Since the statement does not fit into the existing theoretical structure of plant biology and chemistry, it would seriously impede explanation. Friedman himself realizes this and gives up his formulation in preference to those more realistic. Thus, in the end it would seem that in some cases crude generalizations are better than exhaustive enumeration, and no one would dispute this.

Friedman’s second interpretation is not concerned with the nature of assumptions at all but with experimental design. The specific example offered by Friedman is a good design and is used routinely. Again, what is involved is no special type of proposition that is an “assumption” but simply general hypotheses to be verified by routine procedures.

What is meant by an “assumption” as a convenient way to state the conditions under which a theory is expected to be valid is not quite clear. Obviously these conditions must always be stated. They are, in fact, normally incorporated into the general hypothesis: a general law, after all, must state to what it applies. More likely, what Friedman has in mind is the state description rather than lawlike statements. In the terms of Hempel-Oppenheim, this means that Friedman refers to C -statements and not at all to L -statements.

For example, consider “perfect competition.” This is a state description; from it alone nothing follows. In order to obtain an explanatory model L -statements must be supplied. Here these L -statements may be, for example, the hypothesis of profit- maximizing behavior, the law of variable proportions, and the Marshallian demand curve. The usual “results of perfect competition” now follow from this model.

If E is given (that is, has been observed) and the C ‘s and L ‘s are provided afterwards, then we have explanation. If E is deduced from the C ‘s and L’s before it occurs, then we have prediction. Thus the requirements for explanation are also appropriate for prediction.

Whether such a state description is realistic is a question of substantive economics or, in general, an empirical question. As a matter of fact, the particular state description of perfect competition is believed to be unrealistic. It is normally introduced by such words as: “Let it be assumed ….” Here we seem at last to have come across the generally accepted usage of the term “assumption”: a state description (a set of C -statements). Normally, such a state description is called an “assumption” when the C -statements of which it consists are known to be all or in part untrue -and, in fact, are chosen because they are untrue. In this sense assumptions are part of an experimental design. They are used primarily when it is not feasible to produce actually desired conditions (as can be done where laboratory experiments are possible). The desired state is then imagined (assumed) and the consequences of a hypothesis under these conditions are explored. Whether a particular set of assumptions is adequate for the purpose at hand is not a question of general methodology.

In the end, it becomes clear that Friedman uses the term “assumption” in reference to quite different things: (crude) generalizations — especially those actually known to be unrealistic, the uses of hypotheses in certain experimental designs, and the counterfactual state description used again for purposes of experimental design.

It is submitted that the last-mentioned usage is the most legitimate and seems to correspond with general usage. In this sense “assumptions” refer to what is usually called a “mental experiment.” It would be helpful for methodological discussion if the term “assumption” were used only in the context of mental experiment.

Friedman’s interpretation of the term “assumption” as a hypothesis known to be unrealistic raises the question as to whether there ever is any justification for the use of such propositions. This question leads to the heart of the matter. Consider his example of the expert billiard player whose shots are predicted on the basis of the assumption that, before each shot, he solves the mathematical problems involved. What has occurred here is the following: after having observed the successful play of an expert billiard player, we ask how he goes about making the billiard balls go where he wants them to go. The hypothesis is offered that he may with lightning rapidity solve the mathematical problem of the path of the balls required for success. This hypothesis may be borne out by the correct prediction of further shots.

Now the first difficulty arises from the fact that the hypothesis will not yield consistently correct predictions; we do know that even the most expert billiard player makes bad shots, loses games, and may even have days on which he plays poorly. Thus, the hypothesis may not yield completely correct predictions. However, it may be argued that perhaps the illustration is poorly chosen and that some other illustration might serve us better. Therefore, let us simply assume that the hypothesis actually does yield consistently correct predictions.Another, more significant, difficulty now arises: it is actually known that billiard players, expert or otherwise, do not solve the relevant mathematical problems before making their shots. This is easily proved by testing expert billiard players for their mathematical knowledge. The mathematics required for the purpose is complex and quite beyond the grasp of all but well-trained mathematicians. In other words, the hypothesis that expert billiard players solve their problems by the use of higher mathematics can easily and unambiguously be disconfirmed. We may, indeed, safely consider it to be actually disconfirmed. Friedman’s whole argument rests on the assertion that an assumption -which now we know to be a lawlike statement — is verified exclusively by its predictive power. In fact, he defines the “truth” of such a statement as its power to yield correct predictions. This is the generally accepted definition of the “truth” of a law. It follows from Friedman’s argument that the hypothesis that billiard players solve  the problems encountered in the game by the use of higher mathematics must be considered to be true. It is not even permissible to speak of it as unrealistic — even though we positively know most billiard players to be ignorant of the required mathematical techniques. The point is that, although the hypothesis may yield consistently correct predictions of the shots made by expert billiard players, it yields consistently wrong predictions of the solutions obtained by the same players when confronted with the mathematical formulation of the problem of making a good shot. Three possibilities emerge:

The hypothesis that expert billiard players make their shots by solving mathematical problems is considered to be disconfirmed and is, therefore, discarded.

The hypothesis is known to be strictly disconfirmed. Since, however, it yields correct predictions in a given class of events  (for unknown reasons), it is retained in the theoretical structure until a better hypothesis can be formulated. The situation is considered to call for a search for a more  satisfactory hypothesis. In this context the fact that the disconfirmed hypothesis yields correct predictions for a given class of events must also be considered as a problem that requires solution. This is, of course, the situation that prevails in all areas of the scientific enterprise, as long as we are not omniscient, and, therefore, the solution of each problem raises new problems. Mutually inconsistent hypotheses and hypotheses yielding correct predictions in one area, whereas failing in another, are routinely retained in a theory.

Finally, the hypothesis may, as it were, be split in two: a hypothesis b 1 (expert billiard players solve the relevant mathematical problems before making a shot) and b 2 (expert billiard players have mathematical training to solve the mathematical problems presented by the game). Whereas b 2 is now considered to be strictly disconfirmed, b 1 is considered to be true.

Friedman chooses the third alternative. Such a choice means that in the process of verification only those implications of a hypothesis that yield correct predictions are considered. Now, although the retention of a hypothesis in spite of its failure in one or more classes is heuristically defensible, it may not be established as a methodological principle or rule. It would, indeed, lead to a complete fragmentation of science and make impossible the subsumption of apparently quite different events or attributes under one general theoretical structure. That is, it would prevent explanation beyond the lowest-level laws. Since its inception, however, science has considered as its major task the explanation of observable regularities by ever more general laws.

The fundamental difference between laws containing references to observables and laws that no longer contain references to immediately observable entities or attributes must be recognized. Although not all higher-level laws are free from references to observables, only higher-level laws can be of this kind.

Laws that thus do not contain references to observables can, in the way Friedman indicates, be verified only by deriving from them L -statements that do contain such references. These L -statements, in combination with C -statements, are then used in predictive models. Hypothetical constructs of this high level are obtained finally by successively asking why things are behaving in the observably regular way in which they actually do behave. Such hypotheses can be neither “realistic” nor “unrealistic” -the terms do not apply here.

On the other hand, if lawlike statements do contain terms purporting to refer directly to observables, there must be actual observations corresponding to these terms. Otherwise, the lawlike statement is obviously falsified. This proposition follows from the fact that any reference to direct observables implies predictions. To say, for instance, that billiard players solve mathematical problems implies the prediction that if a billiard player is confronted with a mathematical problem, he will in due time be observed either to state or write down an arrangement of symbols  that constitutes the correct solution to the problem. If it is now said that the L -statement about the mathematical abilities of billiard players is “unrealistic,” this means that the players in the situation described above will either say or write nothing at all or will produce symbols that do not constitute the solution of the problem. According to Friedman’s own argument, the hypothesis that billiard players solve complex mathematical problems is thereby disconfirmed and should be discarded. If no more satisfactory hypothesis can be found at the time, the disconfirmed hypothesis will remain in use for those classes of events for which it has been found to lead to correct predictions. In fact, additional applications of the hypothesis may be found. All of this, however, means only that the hypothesis will be used until a more satisfactory hypothesis can be formulated. If some hypothesis yields correct predictions for one class of events and fails to do so for another class of events to which it is claimed to apply, then it follows that there must exist at least one more satisfactory hypothesis. This may turn out to be a single hypothesis yielding correct predictions in all cases to which the old hypothesis has been applied; it may also be found that the cases in which the old hypothesis held are really special cases. That is, an explanation will be found as to why the old hypothesis has failed in some cases to which it had erroneously been believed to apply. The fact that a hypothesis is found to be “unrealistic” indicates the need to search for better hypotheses. Our disagreement with Friedman is not over his refusal to discard unrealistic hypotheses. This procedure, as we have seen, is legitimate as long as nothing better is at hand. Our disagreement is over the fact that his position seems to imply that an unrealistic hypothesis, because it seems to yield correct predictions in some cases, is beyond the principle of permanent control  (any accepted proposition can be dropped at some later stage of investigation) and must be accepted. His argument, if followed literally by economists, would prohibit further research in a number of areas.

Source: Skyttner Lars (2006), General Systems Theory: Problems, Perspectives, Practice, Wspc, 2nd Edition.

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