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How does reasoning by analogy use a known situation to understand a new one?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — Applied logic Aristotle, marble portrait bust, Roman copy (2nd century bce) of a Greek original (c. 325 bce); in the Museo Nazionale Romano, Rome.

Reasoning by analogy is a form of inductive inference that involves applying knowledge from a familiar domain to a new or unknown situation. By identifying a similarity in proportional or functional relationships between two sets of items, one can infer that a relationship not yet understood is comparable to one already familiar.12

Aristotle formalized this process with the structures "As A is to B, so C is to D" and "As A is in B, so C is in D". In practice, this requires recognizing that the relationship between one pair of items—whether they are objects, diagrams, or concepts—is the same as the relationship between a different pair. For example, one might use a functional analogy to understand that a key relates to a padlock in the same way a can opener relates to a tin can.123

While analogies are powerful tools for elucidating unfamiliar points or suggesting scientific hypotheses, they carry risks. An argument by analogy is only as strong as the relevance of the resemblances noted; if the two situations are too dissimilar or the comparison is merely superficial, the reasoning may be misleading or invalid.12