Generalizing

Generalizing is the process of extending a concept, rule, or pattern from particular instances to a broader context. It is central to scientific inquiry, mathematics, philosophy, and everyday reasoning, enabling people to apply known ideas to new situations. Generalization can involve forming universal statements, defining more inclusive categories, or recognizing common structures across different domains.

In logic and mathematics, generalization is formal: from a statement about an arbitrary object, one infers a universal claim, or from a specific case to a broader class. It also appears as extending a theorem to larger domains or abstracting a concept to a more general definition, such as generalizing prime numbers to algebraic integers.

In science and statistics, generalization denotes the extent to which conclusions drawn from data or experiments apply to settings beyond the observed sample. Researchers assess generalization through replication, cross-validation, and theoretical justification; poor generalization can result in overgeneralization, where inferences fail outside the original context.

Cognition uses generalization to categorize new experiences by comparing them with known concepts, a process that supports learning but can lead to biases when the observed cases are unrepresentative.

Generalization is distinct from abstraction; abstraction creates higher-level concepts by omitting details, while generalization enlarges the scope of the idea itself. A common pitfall is hasty generalization, drawing broad conclusions from too few examples.

See also discussions of generalization in machine learning, induction, universal quantification, and the philosophy of science.