It seems analogies of many kinds are one of the main foundations of understanding and explaining, and that one basic principle that is involved is the following heuristic assumption (that is supported by most experience):

• What is similar in some known respects is also similar in some further respects.

This has always been an important heuristic principle of explanation, and there is a modern mathematical explanation of analogy in terms of morphisms (isomorphisms or homomorphisms) that has the merits of both clarifying analogy itself, namely in terms of sameness of form, and of suggesting why analogies are important in cognition.

1. Analogy and induction: One important class of arguments that depend to some considerable extent on analogies of some kind are inductive generalizations of the kind 'unobserved cases of so-and-so will be like observed cases of so-and-so', 'the future of such-and-such will be like the past of such-and-such', etcetera.

These are not deductively valid but it may be argued they are better - more probably true - in proportion to the strength of the analogy (or analogies) that is (or are) involved. (See: Keynes, Stebbing)

One problem here is that it is difficult or impossible to give a good general theory that establishes the strength of analogies.

2. Analogy and thinking: It is clear that analogies of many kinds are involved in human thinking, since much of that is based on representing something A, that often is only partially known and/or partially accessible, as if it were something B (a model, mock-up, imitation, diagram, verbalization, equation or tale of A), that is far better known or far better accessible than is A itself, and then trying to infer properties and relations of A from properties and relations that can be established about B.

This also holds in cases where the analogy is one of kinds: The shapes of airplanes are determined in part by experimentation in wind tunnels on small models (and the fact that this works seems to show analogies in the flows of air around small objects and much larger objects of the same form), and one's reactions to and assessments of other persons depend to a considerable extent on the kind of person they are deemed to be, and the inferences about such kinds of person that are then applied to that specific person.