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Category membership concerns whether an object or event is assigned to a specified category. It is distinct from its judged typicality, how confident a person is about the judgment and how quickly the judgment is made. A category can have a precise membership rule while its examples differ in familiarity.

For example, 3 and 97 are both odd integers: each has the form $2k+1$ for an integer $k$. A participant might nevertheless consider one a more typical example or identify it faster. Those responses concern the categorization process, rather than making one integer mathematically more odd than the other.

Sharon Lee Armstrong and collaborators compared typicality judgments and category verification for everyday categories and well-defined categories including odd and even numbers. Their experiments show why graded responses alone cannot establish that the underlying membership conditions are graded. Distinguishing membership, typicality and reaction time avoids drawing a stronger representational conclusion than the task supports.^[ref]

Category verification is a task in which a person decides whether an example belongs to a stated category. A participant might judge “a robin is a bird” as true and “a robin is a fish” as false. Researchers measure accuracy and reaction time while controlling features such as wording, familiarity and the expected response.

The task is useful because equally correct category members need not be verified equally quickly. However, response speed concerns the categorization process, not a mathematical degree of membership. Sharon Lee Armstrong and colleagues compared typicality judgments with classification for well-defined categories such as odd integers, showing why graded judgments alone need not imply fuzzy category boundaries.^[ref]

Human categories show robust category typicality gradients, but those gradients do not uniquely demonstrate that knowledge is stored as a single concept prototype. A concept prototype is a central or especially representative category representation. In prototype theory, new cases are judged through their similarity to that summary. This challenges a simple classical theory of concepts in which every familiar category is represented solely by equally necessary defining features. The crucial distinction is between evidence that members are psychologically unequal and evidence for the particular representation producing that inequality.

Eleanor Rosch's studies showed that category members are not interchangeable in judgments and processing. People agree that some examples are better representatives than others, and a category name can differentially prepare the processing of good and poor members. Her semantic priming experiments went beyond explicit category typicality ratings: a category-name cue preceded judgments on example pairs, and even physically identical pairs were processed differently depending on their representativeness. Convergence across ratings and performance is important because it reduces the chance that category typicality is only an artifact of being asked to rate goodness.^[ref]

The family resemblance account explains what can make an example representative. In Eleanor Rosch and colleagues' work, participants listed attributes of members of natural categories. More prototypical examples tended to share many attributes with other members of their category while sharing fewer with contrasting categories. Thus an item's usefulness as a representative depends on distributions of features both within and across categories, rather than on one feature occurring in every member. Such structure can support efficient generalization from incomplete evidence. But a descriptive relation between feature overlap and category typicality is not itself an algorithm for learning or storing a concept prototype.^[ref]

Artificial-category experiments make the abstraction claim more testable. In Michael I. Posner and colleagues' 1968 study, participants learned to classify distortions of dot patterns without seeing the underlying prototypes. They subsequently classified the unseen prototypes especially well relative to control patterns from the learned categories, and training variability influenced generalization to new distortions. The result is striking because direct familiarity with the test concept prototype cannot explain its advantage. A summary preserving the regularities among training examples supplies a natural explanation.^[ref]

It is not, however, a unique explanation. In exemplar theory, a new object is compared with stored examples. A central unseen item can resemble many stored examples at once and therefore receive greater summed support than a less central old item. Robert M. Nosofsky's identification–categorization experiments used multidimensional perceptual stimuli and linked classification to stored instances and selective attention to diagnostic dimensions. This provides an explicit alternative to treating every concept prototype advantage as proof of an abstract average. Theories must be distinguished by predictions across learning, transfer and individual trials, not merely by whether they can generate a category typicality effect.^[ref]

A second challenge concerns the difference between identification and membership. Sharon Lee Armstrong and colleagues applied category typicality-rating and verification-time methods to categories including mathematically well-defined ones. Even these categories produced graded judgments and processing differences: an example can seem more representative while being no more genuinely a member. All odd integers, for example, meet the same parity criterion, irrespective of their familiarity or apparent category typicality. Category typicality can therefore reflect an identification heuristic, accessible examples or feature salience rather than the full constitutive content of a concept.^[ref]

This observation limits, rather than abolishes, concept prototype explanations. It remains possible that many everyday categories have probabilistic feature structure while some concepts require rules or deeper knowledge. It also creates a challenge of conceptual combination: a theory should explain how familiar concepts combine into a new one, including cases where the combination's typical instances are not predicted by simply averaging the separate prototypes. If category typicality is all that a representation contains, logical and compositional inference may become difficult to explain.

Context and goals provide a further constraint. Lawrence W. Barsalou compared common taxonomic categories with goal-derived categories. Central tendency, ideals associated with a goal and frequency of encountering an item could make different contributions to category typicality; central tendency was not a sufficient general account of the goal-derived cases. A food may be a good member of a goal-defined category because it is especially suited to the goal, rather than because it is statistically average. This makes a permanently fixed, context-free central representation implausible as a complete account.^[ref]

The theoretical implication is a distinction among levels of explanation. Category typicality gradients and family-resemblance structure are phenomena to explain; concept prototype, exemplar, rule-based and knowledge-sensitive models propose mechanisms that can overlap in their predictions. Strong tests manipulate the distribution of training cases, diagnostic features, goals and novelty, then evaluate predicted generalization and errors while controlling familiarity and task demands. A hybrid or flexible system is plausible, but should earn its flexibility by predicting when different information will guide behavior.

The evidence decisively rejects the idea that familiar category members are psychologically equivalent; it does not establish a universal concept prototype-only architecture. Prototypes can organize efficient recognition and generalization, while instance memory, explicit criteria and goal-dependent knowledge constrain how that organization is used. Confusing graded category typicality with graded truth of membership would overstate what the experiments show.

A cognitive psychologist who investigated how graded category typicality can coexist with sharply defined membership criteria.^[ref]

Typicality is how representative an example seems of a category. A robin may be judged a more typical bird than a penguin, although both are birds. Such judgments can reflect familiarity, similarity to other members or the purposes for which a category is used; they are not the same measurement as a yes-or-no judgment of category membership.

Even a sharply defined mathematical category can produce graded psychological judgments. People can regard some odd integers as better examples than others, despite every odd integer satisfying the same membership rule. Sharon Lee Armstrong and colleagues used such cases to show that graded typicality does not, by itself, establish that a concept lacks a definition.^[ref]