The “argument from analogy” is an argument which compares two ratios, that is to say four terms, in a crossed reasoning, of the type ”if a is to b what c is to d”. It is therefore a matter of making an idea understood by transposing it into another domain, by means of analogy and according to a certain structure. The metaphor is a poetic analogy even if it can convey a rhetorical desire to persuade the interlocutor. Aristotle can be quoted with an example of an analog argument:
“As the eyes of the bat are dazzled by the light of day, so our intelligence is dazzled by the most naturally obvious things.” (Aristotle, Metaphysics)
Analogy has a powerfully heuristic (which reveals a truth) and educational role; however, the use of images allows manipulative diversions (this is the case in science for example: metaphor sometimes simplifies theory too much).
Reasoning by analogy is reasoning by association of ideas, combination and synthesis.
The analogy should not be confused with mental maps, which are based on hierarchical conceptions, inherited from Aristotle, in particular through his work on categories. The etymology tells us the reason: the prefix kata in Greek means from top to bottom, hence the hierarchies, an entry point at the top and then an analytical division into increasingly finer genres, which results in a catalog. The prefix ana in Greek means the exact opposite movement, ie from bottom to top. Analogue is therefore, etymologically, exactly the opposite of catalog and therefore of mental maps. The analogy consists in extending the application of the logic proper to a particular fact to another particular fact. It therefore does not proceed from an analysis, but achieves an increase in the field of application of a particular logical principle.
The strict definition of analogy is A is to B what C is to D. Therefore, by asserting such an analogy, I assert that whatever is true in the relation between A and B, is also true in the relationship between C and D; and also that everything that is false in the relation between A and B is also false in the relation between C and D.
The analogy is often used in science and in philosophy, because it makes it possible to transfer the results which are known in a first domain towards a second domain, this in an efficient way. In order to apply the same logic in parallel, it suffices to substitute faithfully both A by C and B by D to obtain undoubtedly correct results in the relationship between C and D. From this point of view, the analogy is a perfectly rational operation. It is a simple calculation in parallel. If the substitution gives erroneous results, the analogy is false.
Note that in the analogy A is to B what C is to D, neither A, nor B, nor C, nor D need to be defined explicitly, only their respective relation counts.
Incidentally, this makes it possible to invent ad hoc notions, for example an entity D such that C is to D what A is to B, therefore to extend the concepts in a coherent manner with the knowledge already acquired. For example the moment of inertia was invented in such a way that it is to the rotational movement what the inertial mass is to the translational movement or even the angular momentum was invented in such a way that it is to the rotational movement what the momentum is to translational motion.
Note also the fact that an analogy does not expressly express the relationship between concepts, but simply indicates the existence of an identical relationship. The nature of the relation appears only in the idea of the one who looks at it, not in the literal expression. It is therefore to understanding that the analogy appeals.
Several works in monkeys suggest that they can associate relations of identity or difference with each other, and therefore have the premises of reasoning by analogy.
Includes text translated and adapted from Wikipedia