Analogy

Analogism or analogical inference (Greek ἀναλογισμός analogismós) is an inference based on analogy between two objects according to the pattern:

A has similarity to B. B has property C. So A has property C too.

Objects can be beings, things or phenomena, the similarity can consist in other properties, symptoms, structures, relations and functions.

This method of inference is also called inference per analogiam (Latin ratiocinatio per analogiam). The conclusion by analogy is often granted probative value (which, however, is at best only conditionally given) and is then called proof by analogy.

Two basic types of analogy inference arise from the distinction between structural and functional analogy.

History

Antiquity to scholasticism

Analogism was already to be found as a paradeigma in Aristotle (in: first analytics). Theophrastus called this procedure of inference a conclusion from hypothetical premises. The Epicureans consider this procedure (o kata ten omoioteta tropos) as a means from appearances to the unknown. In Boethius this inference is called exemplum. In the theological doctrines of scholasticism the procedure acquires a special value for theological needs, especially with regard to positive statements about the divine conception according to the so-called analogy of being.

Analogies according to scholasticism

While David Hume counts analogy conclusions among the probability conclusions, Wilhelm Wundt classifies them among the subsumption conclusions (in: Logik I).

Approaches to the use of analogies in the general methodology of the natural sciences are first found in Francis Bacon and, in a more developed form, in John Stuart Mill.

Theory

Analogism is not, strictly speaking, a proof - it consists in inferring the uncertain parts of a not fully known system from knowledge of a similar but fully known one. It is therefore primarily an instrument for hypothesizing ­and has "only heuristic value".

The conclusion by analogy can only be a proof if the two systems, i.e. the mapping and the mapped system, are isomorphic to each other, at least in the corresponding subdomain for which the proof is given, and as long as the appropriate transformation rules are observed.

Conclusions by analogy proved to be extraordinarily fruitful and yielded important partial insights, until the realization of the quantization of energy and orbits in the case of atomic structures made the essential difference between the conditions of a solar system and the atomic structure apparent. This example shows at the same time the problem of analogism: it is a conclusion of probability. In the borderline case the analogy changes into isomorphism, the analogy, which at first is gained partially, i. e. starts from the agreement in some essential properties, structures etc., can be totalized by assigning corresponding elements. On the other hand, conclusions by analogy prove to be false if, apart from all similarity or agreement, an essential difference between the phenomena set in the analogy is demonstrable.