On 'Modeling,' Models, and Theories

Extract From: Frolov, I. (1984). Dictionary of Philosophy. Moscow: Progress Publishers.

"Modelling, [is the] reproduction of an object's [known] characteristics in its analog, specially constructed for their study. This other object is called a model [and is isomorphic in some appropriate way to the object under indirect investigation]. The need for M. arises where it is impossible, difficult or expensive to study real objects directly, or where this process requires too much time, etc. There must be some analogy between the model and the object that evokes the researcher's interest. It may be expressed either in the similarity of the physical properties of the model and the object or in the similarity of functions, performed by the model and the object, or in the identical mathematical description of the behaviour of the object and its model. In each concrete case the model may perform its role if the degree of its correspondence to the object is defined strictly enough. Today M. is in wide use in computers and electronic simulation devices. The principle merits of this type of model are their ... convenient use, [for] quick and cheap research. .... In a scientific-technical investigation M. is only one of the methods of scientific cognition as a whole [(i.e., 'theory and practice are very important' too)]...." (p. 273).

Extract From: Kaplan, A. (1964). "Chapter VII: Models" (pp. 258-291). In The Conduct of Inquiry: Methodology for Behavioral Science. San Francisco, CA: Chandler.

MODELS AND THEORIES

The term "model" is often used loosely to refer to any scientific theory couched in the symbolic, postulational, or formal styles. I believe, however, that it is most appropriately applied only in connection with the last, or at most, with the last two. Broadly speaking, we may say that any system A is a model of system B if the study of A is useful for the understanding of B without regard to any direct or indirect causal connection between A and B. For in that case, A must be like B in some respects: if we wanted to infer that because A has the property p when B has some other property q we would need to know that A and B are somehow connected, according to the specific relation between p and q, while to conclude that B also has the property p, we need only know that A and B are similar in appropriate ways even though in fact they have nothing to do with one another. On the other hand, just which ways are appropriate is already limited by the condition that no conditions are imposed on the physical relations between the two systems. The systems must therefore resemble one another as systems, that is, in ways which do not depend on the particular elements of which each consists, or else we would need to know just how elements of these particular kinds effect one another. The resemblance is in terms of the pattern or order exhibited in each system, the information which each contains, in the current idiom, rather than in terms of the configuration of mass and energy in which the information is embodied. In a word, when one system is a model of another they resemble one another in form and not in content.

More specifically, models are isomorphs of one another. Both systems have the same structure, in the sense that whenever a relation holds between two elements of one system a corresponding relation holds between the corresponding elements of the other system. The systems need not stand in any causal connection, for what is required is only that the relations correspond, and to satisfy this requirement it is enough that we can put them into correspondence, that is, think of them as corresponding. Then, whether a system does or does not show a certain pattern in its own internal relations is plainly quite independent of what the other system shows. If there is an isomorphism, the systems significantly resemble one another only in their structural properties, additional resemblances, if any, being irrelevant.

The structural properties of a system are by definition those which would be shared by any other system isomorphic to the given one. Such [shared] properties are often called the "logical" properties of a system, in contrast to its [more particular] "descriptive" properties, but this is a misleading usage. They are, to be sure, very abstract[ed] properties, for they concern only those [isomorphic] features of relations which are wholly independent of what particular [concrete] things [p. 264] stand in those relations. But structural properties are not "logical" as contrasted with "empirical" [(i.e., ontological)]. What structure a particular system has is a matter of fact [whether known or unknown], unless, to be sure, the system [itself (e.g., "General Intelligence" or even a given "I.Q. Factor")] has been tacitly defined by reference to such properties [existing in another system (e.g., academic or vocational test performance)]. [In which case that supposed (tacitly agreed upon) 'system' would just as likely turn out to be a convenient fiction as something which exists in point of fact, or which is indicative of or actually isomorphic to that which it is attempting to model (e.g., human intellect) -P.B.]. Thus the cardinal number of a class [of existing systems or subsystems] might be regarded as the structure of the relation of diversity (nonidentity) in the class, and how many members a class has is, in general, an empirical question. Similarly, it is an empirical question whether say, the inheritance of [a particular] property in a given society has the structure of a mathematical progression, like the sequence of [additive] positive integers [or some other structure].

We can now understand why the term "model" is sometimes used as a synonym for "theory", especially one which is couched in the postulational style. The model is conceived as a structure of symbols [or measures] interpreted in certain ways, and what it is a model of is the subject-matter specified by the interpretation. Relations among the symbols are presumed to exhibit corresponding relations among the elements of the subject-matter. The theory is more or less abstract -that is, it neglects certain variables [(e.g., it treats them as unlawful error variance or noise in the data)]- and what it describes are certain more or less "ideal" entities, having an existence only in the context of the theory itself. What is hoped is that the system of such entities will be isomorphic, in appropriate respects, to the real system which provides the subject-matter for the theory. Some contemporary psychologists take the view that their subject-matter as a whole has a hopelessly complex structure, and so concentrate on the construction of "miniature systems" or "theorettes" [(e.g., the three-factor "model" of human intelligence; or the Big-Five "model" of personality)].

In my opinion, this sort of usage of the term "model" is of dubious worth, methodologically speaking. If "model" is coextensive with "theory, why not just say "theory", or if need be, "theory in postulational form"? In a strict sense, not all theories are in fact models: in general, we learn something about the subject-matter from the theory, but not by investigating properties of the theory. The theory states that the subject-matter has a certain [ontological] structure, but the theory does not therefore necessarily exhibit that structure in itself. All theories make abstractions, to be sure, in the sense of treating as irrelevant some properties of their subject-matter. But not all of them abstract to the point of treating as relevant only the structural properties. Consider, for instance, the difference between the theory of evolution [(which is not only strucutural and functional but also historical)] and a model which a geneticist might construct to study mathematically the [measurable] rate of diffusion in a hypothetical population of a characteristic with a specified survival value. I think that at bottom the tendency to view all theories as models stems from an old-fashioned semantics, according to which a true proposition must have the same structure as the fact it affirms (the early Wittgenstein and Russell)....

*Abraham Kaplan (1964) suggests that a model is not a theory even though some theories might function as exemplars of the way theories should be constructed. Let's attempt to illustrate these points with respect to a few psychological examples.

Under Kaplan's analysis, the so-called Triarctic model of human intelligence or Big-Five model of personality are not properly called models at all because that would at once assume too much about their isomorphism to the ontological subject matter to which they refer and be too modest at the same time about their empirical rigor or descriptive generality. More specifically, to call them models would assume that we already know how they correspond to human intellect and personality (respectively), yet they are not properly called explanatory theories because they are at one and the same time too close to the empirical data (which constitute their "tacit" definitional structure) and too removed from the subject-matter under investigation to be called theories. What a predicament! What then should we call them?

Kaplan seems to suggest that they are more properly called "theories in propositional form" yet (in my opinion), given that they are both merely "structural" statements about the observational regularities of measured data sets these "theorettes" are not even properly called propositional theories per se but are mere abstract empirical generalizations plain and simple (see Ballantyne, 1995).

It is just here that Kaplan's contrast between the "theory of evolution" and the "geneticist's" empirical-mathematical heritability estimates is highly instructive. As Charles Lawler once pointed out, a heritability estimate "has nothing to do with the real interaction of genes and environment- just as 'widthability' has nothing to do with the real relations of the actual length and width or with the variations of the areas or perimeters" (see Lawler, 1978, p. 148). A heritability estimate is merely a descriptive mathematical statement about the observational regularities of a data set and not an ontological statement about the origin of those regularities. Evolutionary theory itself (which in its updated form suggests not only a natural and social but also cultural selection mechanism for change between human generations) provides the latter explanatory (rather than merely "descriptive") encapsulation.

The empirical-mathematical structure, tenuous ontological status, and ultimate fate of our Triarctic or Big-Five data factors is essentially the same as the heritability estimate. When placed into the context of a longitudinal life-span study, such abstracted observational regularities about empirical test score performance might eventually become part of a more concrete description of human intellectual or personality development but as they stand on their own they are very far indeed from anything resembling an explanatory theory. -P.B.

Bibliography:

Ballantyne, P.F. (1995). From Initial Abstractions to a Concrete Concept of Personality. In I. Lubek, et al. (Eds.). Recent Trends in Theoretical Psychology (Vol. 4, 151-157). New York: Springer.

Kaplan, A. (1964). "Chapter VII: Models" (pp. 258-291). In The Conduct of Inquiry: Methodology for Behavioral Science. San Francisco, CA: Chandler.

Lawler, J.M. (1978). "Heritability" (pp. 133-158). In I.Q. Heritability, and Racism. New York: International Publishers.