Ideal Types

Claudio Gutierrez

The literature of social science methodology is rich in discussions on the nature of what are commonly called ideal types. In reviewing part of this literature I am not going to partake in the main front of that discussions, i.e., whether ideal types are "natural" or "artificial," whether they are "concepts" or "theory". I am going rather to confine myself within a more specific problem, being content with considering ideal types as artificial and as natural as any instrument of human thinking, and as "propositional" as any concept should be, as "conceptual" as any theory must be. The problem I am going to concern myself with is rather that of the relationships, and possible identity or opposition, between ideal types of two different kinds, i.e., "abstract models" on the one hand, and "assumptions," "fundamental propositions," or "basic postulates" on the other. What is relevant for my present purposes of analysis is again the crucial distinction between the "closed" and the "open," the formal and the non formal, ultimately between the objective and the subjective which could possibly be discerned in this matter. We have been discussing this distinction all along. What is going to be new in this chapter is the consideration of the two aspects within the "formal side" of theory, rather than one in the non formal and the other in the formal sides. The reason for this "repercussion" of the formal-informal polarity within the formal side is to be found in the nature of "residual categories" or "theoretical notions," as was shown before. In order to operate with theory one needs logical closure, and this implies that the whole of the non formal side be represented by some tokens within the formal side–these tokens being what we are going to call assumptions in most of what follows.

Milton Friedman states the main problem of economic methodology, as he sees it, in these terms. "Pure theory" is only an analytical filing system. Economics needs to be something more than theory in order to be as predictive as it should. So, we have the assumptions, which are useful devices, abstract and perforce unrealistic. Being unrealistic, hypotheses must be tested by their implications, not by the realism of their assumptions. (FRIEDMAN 53, pp. 7-15) NOTE 1 A hypothesis consists of two elements: the "abstract model" and some "rules" that both define the relevant interpretations which make the model valid and determine the correspondence between certain concepts in the model and certain empirically given properties or relations.

These two parts are very different in character. The model is abstract and complete; it is an "algebra" or "logic." . . .

The rules for using the model, on the other hand, cannot possibly be abstract and complete. . . .

In seeking to make a science as "objective" as possible, our aim should be to formulate the rules in so far as possible. . . . But, no matter how successful we may be in this attempt, there inevitably will remain room for judgment in applying the rules. Each occurrence has some features peculiarly its own, not covered by the explicit rules. The capacity to judge that these are or are not to be disregarded. . . [the capacity to judge] what observable phenomena are to be identified with what entities in the model, is something that cannot be taught, it can be learned but only by experience and exposure in the "right" scientific atmosphere, not by rote. It is at this point that the "amateur" is separated from the "professional" in all sciences. . . . (FRIEDMAN 53, pp. 24-25)

Let us take good heed of the last, very important remark. We most certainly can correlate this characteristic of the "rules," their being ultimately dependent upon professional judgment, with what has been said about the non-formal powers of thought necessary for the operation of formal processes. We can further enrich this concept with our notion of assumptions as residual categories which represent, as it were, in a token form the risk and heuristic commitment inherent in all assertions of theory (POLANYI 64, pp. 308-16). Equipped with this understanding, we can wonder now what to do with Friedman's thesis about assumptions. Should they be unrealistic or rather the "abstract models"? If "assumption" is identified with the non formal power of thought, or perhaps with the token formal version of it, then most surely the assumptions are our wide road to reality, and they must be realistic at least in this sense. But because informal thought is heuristic, most surely the assumptions may be also unrealistic, in the sense that heuristic anticipations can eventually be proven wrong. I do not think, though, that this is the meaning the author wants to convey. I feel more able to make sense of what he actually says by taking the alternative interpretation. Not the assumptions but the models which the investigator operates with under the assumptions, should be unrealistic. These models are at a lower level, so to speak, with respect to the assumptions, and they–the models–should be formal rather than non formal or unformalizable. Without making very much of this definition, let us say that a process or element is formal if the semantic and pragmatic dimensions of it, as a significant whole, are removed or put within parentheses so that the only remaining concern is the possibility of operation according to syntactical rules. In other words, we must not be concerned with what objects of the real world the formal element represents or what purposes the process serves, but only with what the element or process can produce of itself by the sole application of the (not necessarily formal) rules which govern it. Now, it is possible to see that it is to the benefit of the investigation that the scientist is conducting and its accurate results that the models be unrealistic–that is, formal–so that he can operate more easily with them and through them.

Another question regarding the correspondence of Friedman's terminology with ours arises. When he says that pure theory is an analytical filing system, is he talking about "abstract models" in our sense? Could we possibly say that an abstract model is part of a filing system? I think the answer is no. The best description of the way in which a set of abstract models operates is, to my mind, the one presented by Koopmans. For him, economic theory is neither entirely self-evident nor readily tested by experience. It is rather "a sequence of conceptual models that seeks to express in simplified form different aspects of an always more complicated reality" (KOOPMANS 57, p. 142) Perception of additional aspects of reality precedes their recognition in model formation. Rigor follows along to consolidate gains, "rigor" being presumably a change or refinement of models (KOOPMANS 57, p. 143). According to this description, then, models are not, in themselves, anything empirical, being rather akin to a mechanism, a symbolic medium, or a game. Their empirical relevance could only be explained by appealing to the concept of a "preestablished harmony" between the inner nature of the models and external reality, or to some other means of rendering the philosophical content of that important myth. The fact is that abstract or formal models are as closed as monads were thought to be. "They have no windows" to the world. We use them. But the use we make of them is external to them, even to the point of having to change the model altogether in order to alter its empirical significance. They cannot be "files" at all.

In summation: "pure theory" can be identified alternatively with either assumptions or models. If with the former, it must be realistic in the sense of heuristic anticipation. If with the latter, it must be unrealistic in the sense of formal, as such closed to reality but continually revisable and revised. The dialectical motion of theory creation surrounds the models, although they, in themselves, remain unmovable. In this respect we should carefully distinguish the mind as intellectual agent, so to speak, from the passive although equally necessary aspects of intelligence. To put it in an epigrammatic way, abstract or formal models cannot avoid being "stupid as a computer." In fact, to the extent that one has used formal procedures in thinking, one has been using "computers" all along, perhaps with the equivocated notion that they were intelligent (one thought that because one was unable to think of them as different from oneself!) But it is precisely here that we face the need of distinguishing between the model that we use and the assumption that we identify with. From this distinction intellectual efficiency cannot but benefit, as we have seen. I am unable to see that ill results may possibly come about from the professionally sound use of formal devices.

A different analysis of ideal types is provided by C. Hempel. For him there are two classes of ideal types: intuitive and theoretical ones. The former is only [sic] a heuristic category; the latter can be taken to be formal, more or less in our sense of the term. It is important to note that for this author intuitive ideal types are defined reductively, that is, saying what they are not: theoretical terms. Therefore, they form a "residual category" in approximately Parsons' sense. As for theoretical ideal types, they are characterized by two related requisites:

1. they are postulates deduced from broader principles, and
2. the area of their application is clearly specified by logically independent criteria. (HEMPEL 63, pp. 222-28)

It is apparent that Hempel's intuitive types do correspond to our "assumptions," notwithstanding the difference in appreciation of their methodological importance. A problem arises in this connection for our own view in the matter. In what sense can we maintain, in the light of Hempel's analysis, the dependence of abstract models (Hempel's theoretical types) on the assumptions (Hempel's intuitive types)? Are not the requisites (1) and (2) a restatement of the principle of the empirical control via direct verification of propositions? If so, am I objecting to that principle by the insistence on the priority of assumptions (intuitive types)? There is much to be said about this matter. For the time being, let us indicate that I am not objecting to the empirical principle itself, but only to the belief that the problem of verification is clearly separable from the problem of theoretical ideation. One verifies hypotheses which have a good chance of being true; so, the problem of empirical verification is not strictly distinct from the problem of theory formation in general (POLANYI 64, p. 30). We verify a hypothesis if we find it coherent with a broader theory to which, and for good reason, we are committed, while putting aside for later investigation whatever adverse evidence happens to occur (KUHN 62, pp. 52-65).

Besides this implication of separate verification, (1) seems to be saying only that the abstract model must be seen as systematically contextual, i.e., that every model is jointly affirmed with some other models. But apart from paradigmatic systematism, which Hempel is not maintaining, this is not at all important. Logical simplification can always serve to isolate a particular model from its context, i.e., from "p & q" one can always get "p" alone. Requisite (2) seems more interesting, since it opens the door for the discussion of the issue of what we may call "methodological gradualism". If "logically independent criteria" does not mean the same as the "systematic context" of requisite (1) then the only thing it can mean is the necessity of a non formal basis for formalism. Now, one can choose to say that the passage from formal to non formal is gradual, so that one can have models functioning as assumptions with respect to other models and assumptions functioning as models with respect to other assumption. In other words, there are types which are "more assumptions than models" and types that are "more models than assumptions." The gradation between formalism and non formal context is continuous, with no sharp distinction between the two aspects at any point. This, of course, is different from what Hempel envisions, i.e., a "hypothesis" on the one hand, and an "area of application" of the hypothesis on the other, a clear-cut dichotomy. That such an oversimplified view of the problem of knowledge is possible is due, I think, to the fact that we do in practice identify ourselves with the context of the model we are operating with; at least we identify with it for the time the investigation is in course. For obvious reasons, we always try to be "as close as possible" to the model we are manipulating; however, sometimes we cannot get "that close" and we have to reconcile ourselves with the unavoidable intervention of some context, e.g., a mathematical apparatus of some kind. NOTE 2 More often than not, though, we do get "that close," but only through a great, sometimes painful, change of ourselves, the act of affiliation to particular uses of the profession. We know that this change can be done. We all live informally a great deal of abstruse stuff of our profession. NOTE 3 In any case, if we identify with some context it is easy not to perceive the variegated nature of that context, especially if we are over interested in individual hypotheses rather than in the paradigmatic unity of a set of them. If, on the contrary, we are more interested in this organic unity, then we cannot miss the fact that a single piece of information can be used as the methodological presupposition for some inquiry, as well as be made itself the object of direct investigation (with the help of some other presuppositions). Witness, as an analogy, the case of a hammer; one can drive a nail with it, but also, if broken, it can be repaired with the help of other tools, perhaps another hammer. NOTE 4

Another view on the matter is furnished by T. W. Hutchison, pp. 30-31.For him, assumptions are mere definitions, although in the material mode (CARNAP 35, p. 68). Besides, they are arbitrary, their selection resting mostly on the availability of statistics . This way of posing the problem is of course naively positivist, sharing abundantly of the dogma that all terms must be definable into sense-data experience. One wonders how such an extreme position can be maintained in spite of the contradiction and total depletion of intellectual force that it ultimately entails. The answer might lie in the "arbitrariness" of definitions which is postulated by this type of reasoning: this concept acts as a back door through which all that the positivist approach excluded comes again into the picture. In fact, this arbitrariness is equivalent to what we have called heuristic aspect of theory-ideation. To select this rather than that definition is to identify oneself with some sort of assumption, however unclearly known its implications may as yet be. If these are made explicit and a contradiction appears, then one may drop the "definition" in the hope that something better is available to take its place.

Related to this position, but much more tolerant and interesting, is the way in which Felix Kaufmann attacks the problem. For him, methodology is the theory of scientific decisions, which are the acceptance or elimination of propositions in accordance with rules which state exemptions from the general prohibition to change the corpus of a science. He makes the distinction between "empirical laws" and "theoretical principles." The former are falsifiable by a single instance [sic]; the latter are governed by higher rules related to the whole theoretical framework of the sciences (KAUFMANN 58, pp. 48 and 213-14). The main objection to this approach has to do with the sharp dichotomy just stated. Why rule out the possibility of a thesis which in a certain context is an "empirical law," and in another functions as a "theoretical principle"? On the other hand, what are the grounds for the faith in the rejectability of hypotheses in the face of a single contradictory instance? (KUHN 62, pp. 52-65). I myself will tend to approach the problem exactly in an inverse manner. Suppose there is no difference between "laws" and "principles," but that we have one (homogeneous) paradigm capable of a gradualistic interpretation, as explained above. We can distinguish, if need be, an aspect or part of the paradigm that tends to function like an empirical law more than like a theoretical principle, although, according to context, it is generally capable of playing both roles. The problem of falsification can then be considered as the problem of the empirical depletion or qualitative exhaustion of the paradigm; it has to do with the requirement that under certain circumstances some hypotheses or the paradigm itself must be dropped. On the other hand, the problem of the necessity of certain assumptions NOTE 5 must be viewed as the complementary theme of the rational depletion or quantitative exhaustion of paradigms; this has to do with the requirement that under certain circumstances a given paradigm should be considered as the necessary one (since no other could possibly be available). In this light "assumption" or "theoretical principle" will be understood as the general and systematic assertion of the paradigm, inarticulate or non formal, and based in intellectual commitment. "Abstract model" or "empirical law" will be the formal elements of the paradigm, its positive aspects, closed to the world, but dialectically used and revisable according to the motion of scientific progress. We must now turn to closer scrutiny of these issues.