You use a metaphor to describe some concept. The metaphor isn’t the thing you describe - it’s just a tool that you use. But someone takes the metaphor, and runs with it, making arguments that are built entirely on metaphor, but which bear no relation to the real underlying concept. And they believe that whatever conclusions they draw from the metaphor must, therefore, apply to the original concept.
— Metaphorical Crankery: a bad metaphor is like a steaming pile of …
While both, the metaphor and the analogy are tools of abstraction used to paraphrase the essential of a given concept by conveying similarity through comparison, the former being more isomorphic in its symbolism than the latter, neither are equivalent to the concept as they are not synonymous nor literal definitions but allegorical in their exposition of original meaning.
The introduction of suitable abstractions is our only mental aid to organize and master complexity.
— Edsger W. Dijkstra
To define the process of making an analogy in reference to reductionism is prone to fail as an analogy is a vessel of meaning and the perception of every, ultimately projected, meaning resides on a certain level. Both, reductionism and the analogy are mental aids used to master complexity by reducing the information content of a concept. Nevertheless, while the former is reducing a matter to its constituents the latter is reducing it to its quintessence.
That is, one might induce meaning from the constituents that give rise to it, or one might deduce its particular origin from the general that is the flash point of meaning, but one cannot transfer meaning from one particular to another particular by reducing the level of conception to one that is devoid of it. This makes the analogy reciprocal in its nature and handling of meaning. Naturally void of, it is imprinted with meaning to likewise convey the same through reinforcement.
The Art must have a purpose other than itself, or it collapses into infinite recursion.
— Twelve Virtues of Rationality
In all this the use of analogy is closely related to the very process of cognition. The analogy is the resonant system to store and transfer meaning. All meaning is in the mind, yet it cannot arise and persist without that on which it is projected. In fact, it is at the core of cognition as we can only understand reality by analogy. The most fundamental level of comprehension is forever out of reach for that it means to be, to become, not to contemplate but to experience. For that reason all cognition is by analogy. All meaning is communicated in reference to other words.
Further explanation of analogy can just be a demonstration of practicability and consistency. That is, an explanation can make a given analogy obvious by showing how it works and deepen its perceived consistency over more than a self-evident level. Yet any explanation is doomed to be a Language-game. We merely learn to accept by repetition. And as an analogy becomes a intuitively fixed model we incorporate it into our conceptual framework.
Here we are able to come closest to the true nature of analogy, what it IS. That is to state a recursive definition, the analogy defined in terms of itself. An analogy is a function that maps certain meaning comprised in an analogy to another analogy.
Therefore the analogy is not empirical as it is used not to gain but to transfer information. An analogy is the procedure and result of mapping the essential meaning of a concept to another as a means of communication and contemplation by transformation and exposure of the former.