Figure 56: Mary Hesse on analogies (1967)

 

 

New York, London: Macmillan, vol. 5,

Article: Models and analogy in science, 354-359

 

p. 354-355

 

Replicas and analogue machines.

 

There is a sense of "model" in science that is both nearest to its sense in ordinary language and furthest from the logician's sense.

Replicas, scale models, and analogues are familiär in various contexts and may be said to provide, after logical models, the second main source of ideas associated with the term "model" in the sciences. They may be used in science for expository purposes or even as calculating devices in cases where the building of a replica or analogue of a system as a working model is the simplest method of investigating the consequences of those natural laws that the system is believed to satisfy.

 

Various examples include wind-tunnel experiments, crystallographic models, electronic models of nerve nets, and hydraulic models of economic supply and demand. Not all these are examples of straightforward replicas, however; some of them do not resemble in substance the thing modeled but are merely similar in certain of the relations between its parts. It is perhaps better, therefore, to call them analogue machines.

Thus, economic supply and demand does not consist of pipes carrying colored fiuids, but the relations exhibited by such a model may enable conclusions to be drawn in an economic system when the appropriate interpretations are made. In such cases the similarity of relations between model and system modeled may be called isomorphism. This relation of isomorphism may be linked with the concept of logical model by remarking that if the laws of the system were explicitly set out in a formal system, then model and thing modeled would both be models of that system in something like the logical sense. The relation of isomorphism between the model and the thing modeled would therefore be the relation between two interpretations of the same formal system.

 

But this way of looking at analogue machines may be highly artificial in many practical cases, because such machines are often constructed precisely for cases where there is no known mathematical specification of a system or where this specification is so complex that the explicit drawing of deductive consequences is impossible or impracticable. Where this is the case, it is dangerous to attempt to apply to scientific models those arguments that are valid in connection with logical models of formal systems.

 

Before describing the senses of "mode!" that are more central to the structure of theoretical science and that contain some of the features of both logical and replica models, it is useful to give some account of the associated notion of analogy in terms of which different kinds of models can best be categorized.

 

Analogy in science.

 

The relation between model and thing modeled can be said generally to be a relation of analogy.

Two kinds of analogy relation can be distinguished in connection with models in the sciences.

 

First, in the rase of a logical model of a formal system, there is analogy of structure or isomorphism between model and system, deriving from the fact that the same formal axiomatic and deductive relations connect individuals and predicates of both the system and its model. This isomorphism consists of the correspondence between individuals and predicates of the system and the terms that are their interpretations in the model. Derivatively, we may say that there is an analogy of the same kind between two different models of the same formal system. A swinging pendulum and an oscillating electric circuit, for example, are analogous by virtue of the formal relations described in a wave equation satisfied by both. Let us call this type of analogy between systems formal analogy.

 

Second, however, we must consider the analogy exhibited by a replica with its parent system, which consists in something more than formal analogy. In a formal analogy there may be no similarity between the individuals and predicates of two models of the same formal system other than their relation of isomorphism. But in a replica model there are also what might be called material similarities between the parent system and its replica. The wings of an aircraft and its replica, for example, may have similar shape and hardness and may be made of the same material although they differ in at least one respect, size. Where two systems exhibit such similarities, which are not - or not simply - similarities by virtue of being logical models of the same formal system, we shall say that they have material analogy.

 

Two systems may have formal but not material analogy; two examples are the hydraulic model of economic systems and the various mechanical and electrical models of the wave equation. The systems may have both kinds of analogy, as do such replicas and near replicas as crystallographic models. lt does not seem possible to conceive of a material analogy without some formal analogy; if there is material analogy, there is presumably some consequent structural similarity that could - at least in principle - be formalized.

The distinction between formal and material analogy is difficult to make precise, but its significance will become clearer in considering the functions of theoretical models.

 

The relation of analogy, whether formal or material, generally implies differences as well as similarities. In analogous systems let us denote the set of similarities by the term "positive analogy" and the set of differences by "negative analogy."

 

The types of models to be described with the aid of these concepts of analogy are classified mainly in accordance with their function in relation to theories rather than with their intrinsic character. Thus, a model having various functions on the same or different occasions may very often come under different categories, and models of very different intrinsic kinds may come under the same category. Many other types of classification of models can be and have been produced (depending on whether they are mechanical or electrical, micromodels or macromodels, and so on). The categorization to be given now, however, seems to raise the most interesting philosophical questions in regard to the functions of models in science.

 

Mary Hesse

 

see also:

Mary Brenda Hesse: Operational Definition and Analogy in Physical Theories. British Journal for the Philosophy of Science 2.8, 1952, 281-294.

Mary Brenda Hesse: Models and Analogies in Science. London, New York: Sheed and Ward 1963;
2. ed. extended by two chapters, Notre Dame, Indiana: University of Notre Dame Press 1966, second printing 1970.

Mary Brenda Hesse: Analogy and Confirmation Theory. Philosphy of Science 31, 1964, 319-327.