Analogy (Greek ảναλογία – proportionality, proportion) – the relation of similarity between objects; reasoning by analogy – the conclusion about the properties of one object by its similarity with other objects. General schemes of reasoning by analogy:
- the object α has the properties A1, A2, …. An, An + 1;
- object β has the properties A1, A2, …., An;
- it is likely that β has the property An + 1;
- the objects α, α1, α2, …, αn have the property A;
- it is likely that αn + 1 has the property A.
The idea of ”transferring” properties from one object to another goes back to antiquity. The Pythagoreans used the term “analogy”. Aristotle mentions proof utilizing an example (παραδειγμα) as a rhetorical device connecting induction with a syllogism; the properties of one object are transferred to the other by the formation of a general probabilistic judgment covering both objects; the conclusion is not certain, but only probable.
Leibniz gave a different meaning to the analogy, seeing in it not the formal mode of probabilistic deduction, but the universal method of scientific and philosophical cognition, resulting from the principle of “identity of indistinguishable”: objects can be considered relatively identical if the difference between them is “vanishingly small”, i.e., becomes less than any preassigned value. Such objects can replace each other in all contexts “with preservation of truth”. Therefore, the establishment of an analogy is a general condition of all scientific and philosophical proof; universal truths obtained in such proofs refer to ideal constructs acting as analogs of real objects. The analogy method is multistep; Theoretical systems use analogies with previously constructed ideal constructs.
The ontological foundation of the analogy method in Leibniz’s philosophy is the principle of “optimality”: the world is governed by a minimally simple system of laws and at the same time contains a maximum of object diversity. Therefore, rational explanation of similar phenomena for the same reasons. But the researcher’s task is to establish the maximum similarity, up to the “identity of indistinguishable”. Thus, the analogy, according to Leibniz, plays a dual methodological role: as a powerful heuristic source of ideal constructs and as an incentive for their heuristic perfection. The historical development of representations about analogy involves a complex interaction of logical (Aristotelian) and logical-methodological (Leibniz) ideas. In the evaluation of the analogy, the epistemological and methodological principles of various philosophical doctrines were refracted.
Thus Hegel called the analogy the “instinct of reason”, grasping the basis of empirical definitions in the inner nature of objects, and Mill, assessing the analogy as a kind of induction and the way to achieve reliable results, saw its value mainly in the heuristic reception of hypotheses that stimulated empirical research. The general scheme of reasoning by analogy is a whole spectrum of different forms of inference, which can be arranged in order of increasing degree of reliability of the conclusion (simple, widespread, strict or complete, isomorphic objects, etc.). Among the conditions that increase the likelihood of inference by analogy are:
a) the maximum number and heterogeneity of the properties or objects being compared (latitude of analogy);
b) the materiality of the properties being compared (the depth of analogy);
c) the production of the transferred property from the general properties being compared;
d) the absence of properties in the object of derivational judgment, which obviously exclude the transferred property, etc.
However, observance of such conditions does not guarantee the full reliability of inferences by analogy.
In some modern works, the inference is considered by analogy as a derivation from the model to the original. The object (or class of objects) that is the direct object of the study is called a model, and the object to which the information obtained on the model is transferred is the original or prototype. In those cases when using models constructed using the theory of similarity, the conclusions by analogy have complete certainty.
The history of science gives many examples of the use of analogy. Thus, an analogy between the motion of an abandoned body and the motion of celestial bodies played an important role in the development of classical mechanics; the analogy between geometric and algebraic objects is realized by Descartes in analytic geometry; Darwin used the analogy of selective work in cattle breeding in his theory of natural selection; the analogy between light, electric and magnetic phenomena turned out to be fruitful for Maxwell’s theory of the electromagnetic field. An extensive class of analogies is used in modern scientific disciplines: in architecture and the theory of urban planning, bionics and cybernetics, pharmacology and medicine, logic and linguistics, and others.
Numerous examples of false analogies are also known. Such are the analogies between the movement of the fluid and the spread of heat in the doctrine of the “warmth” of the 17th and 18th centuries, the biological analogies of the “social Darwinists” in explaining social processes, etc. The evaluation of reasoning by analogy must be concrete-historical. So, many of them (later turned out to be incorrect or limited) had a heuristic value in a certain period: for example, the analogy with the clock mechanism in the physical picture of the world in the 17th century promoted the liberation of scientific thought from providentialism; The analogy with the hydraulic system helped U. Garvey’s contemporaries understand his discovery of blood circulation, etc. A heuristic source of analogy in science may be an idea taken from extranational spheres – everyday experience, art, etc.
But in developed science, as a rule, analogies, derived from the experience of the scientific disciplines themselves, prevail. Often the main “supplier” of analogies is the “leading” field of science. Thus, the physics of modern times gave rise to many analogies in humanitarian and biological knowledge, and in our time biological analogies are widely used in the technical sciences. The enormous role of mathematical modeling causes the spread of mathematical analogies in all areas of modern science. In a number of works on the logic and methodology of science (J.Snid, V.Stegmuller) it is noted that a number of “paradigmatic” examples of its application (examples of solving problems) are included in the structure of developed scientific theory; the appearance of problems for which there is no analogy is considered an anomaly and entails either the extension of a given set or the replacement of the theory itself. Thus, the concept of analogy is included in the methodological scheme of the evolution of scientific theories.
In the context of scientific creativity, the subject of special analysis is the ability to produce and perceive analogies. In this aspect, the concept of analogy acquires psychological and didactic characteristics. The study of this ability is important for the development of technical devices for “artificial intelligence”. Analogy appears as a complex problem of the theory of knowledge, logic and methodology, the history of science and the psychology of creativity, pedagogy and cybernetics.