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Analogical reasoning solves new problems by mapping the structure of a known source domain onto an unfamiliar target domain. Successful analogies preserve relational structure, not surface features. Understanding which analogies transfer reveals how people abstract problem structure and apply it to novel situations.
From your prerequisite study of analogical reasoning, you understand that analogies involve mapping one domain onto another—the atom resembles the solar system, electric current behaves like water flow. What structure-mapping theory (developed by Dedre Gentner) adds is a precise, testable account of *what* gets mapped and *why* some analogies are more useful than others. The central claim is that good analogies preserve relational structure rather than surface similarity, and this distinction predicts which analogies people find compelling, which transfer to problem-solving, and which mislead.
Consider the analogy between the atom and the solar system. The surface features are completely mismatched—an atom is tiny, quantum mechanical, and governed by electromagnetic forces; a solar system is enormous, classical, and governed by gravity. What matches is the relational structure: the nucleus *is more massive than* the electrons, just as the sun *is more massive than* the planets; electrons *orbit* the nucleus, planets *orbit* the sun; the nucleus *exerts attractive force on* electrons, the sun *exerts attractive force on* planets. Structure mapping identifies which objects in the source (solar system) correspond to which objects in the target (atom) by finding the mapping that preserves the most *systematically connected* relational structure. This is the systematicity principle: good analogies don't just match isolated pairs of similar relations, they map coherent *systems* of mutually constraining relations—if A exerts force on B and B orbits A, both of those relations should be preserved in the mapping simultaneously.
The theory explains a well-documented empirical puzzle: people are often *worse* at using analogies with high surface similarity when the relational structure differs, and *better* at using analogies with low surface similarity when the relational structure matches. Students given two story problems with identical surface features (both involve water, both involve pipes) but different mathematical structures don't spontaneously recognize the analogy; students given two problems with different surface features but identical relational structure (one about water flow, one about electrical circuits) successfully transfer solution methods once they see the structural match. This shows that analogical transfer is driven by structural recognition, not surface noticing. Expertise in a domain means accumulating abstract schemas—relational patterns stripped of their surface details—that can be recognized and applied across superficially dissimilar instances.
Candidate inferences are the mechanism by which analogy generates new knowledge beyond what was explicitly observed. Once the structural mapping is established between source and target, you can look at relations true in the source domain that don't yet have counterparts in the target domain, and project those relations as hypotheses. The solar system analogy suggested that if electrons orbit in stable paths, perhaps only certain discrete orbits are possible—a structural candidate inference that contributed to early quantum models. This projection from mapped structure is what makes analogy more than mere comparison; it is a knowledge-generation engine that uses known structure to generate predictions about unknown domains. The limits of any analogy are exactly the points where the mapped structure breaks down—and identifying those limits is as important as exploiting the analogy, because those are the points where the analogy will mislead you.