Memory also stores conceptual knowledge about things in general as well as representations of specific objects and events. Bruner noted that this conceptual knowledge plays an important role in perception: In fact, every act of perception is an act of categorization. A great deal of research in cognitive psychology has sought to understand the way in which conceptual knowledge is organized in the mind.

According to the classical view handed down by Aristotle, concepts are represented by a list of features that are singly necessary and jointly sufficient to define the category in question. For example, in geometry, all triangles are closed two-dimensional figures with three sides and three angles, and a sharp boundary divides all triangles from all quadrilaterals. However, in the 1970s it became clear that however satisfying such a definition might be philosophically, it did not reflect how concepts are represented in human minds. When perceivers judge equilateral and right triangles to be "better" triangles than isosceles triangles, they are referring to something other than a list of defining features. According to the classical view, all members of a category are equally good representatives of that category. For this and other reasons, the classical view of concepts as proper sets has been replaced with a revisionist probabilistic view of concepts as fuzzy sets. According to the fuzzy set view, features are only imperfectly correlated with category membership, and concepts themselves are represented by prototypes (real or imagined) that possess many features that are characteristic of category members. The probabilistic view permits some instances (e.g., robin) of a category (bird) to be better than others (e.g., emu), even though all possess the same set of defining features. Moreover, it permits the boundaries between categories to be somewhat blurred (is a tomato a fruit or a vegetable?).

Both the classical and the probabilistic view regard concepts as summary descriptions of category members. However, an alternative exemplar view holds that concepts are represented as collections of instances rather than as summary descriptions. Thus, when we seek to determine whether an object is a bird, we compare it to other birds we know rather than to some abstract notion of what a bird is. Just as there is empirical evidence allowing us to firmly reject the classical view of conceptual structure as inadequate, so too there are studies showing that objects are slotted into categories if they resemble particular instances of the category in question, even if they do not resemble the category prototype. Perhaps novices in a domain categorize with respect to abstract prototypes, whereas experts categorize with respect to specific exemplars.

Regardless of whether concepts are represented by prototypes or exemplars, categorization is a special case of similarity judgment: The perceiver assigns an object to a category by matching its features to those of his or her category representation, prototype or exemplar. There is no absolute threshold for similarity, however: Categorization, like signal detection, is always a matter of judgment.

Although categorization seems to be special case of similarity judgment, and the most recent development in theories of concepts has been stimulated by evidence of certain anomalies of similarity. For example, subjects judge gray clouds to be similar to black clouds and different from white clouds, but they judge gray hair to be similar to white hair but different from black hair. The brightness of the color patches is identical, so the judgment must be based on something other than perceptual similarity, such as the perceiver's theory about how hair changes with age or how clouds change with the weather. According to the theory-based view of categorization, concepts are not represented by lists of features or instances, and categorization does not proceed by feature matching. Instead, concepts are represented by theories that make certain features and instances relevant and that explain how features and instances are related to each other, and categorization proceeds by applying the theory to the case at hand. It remains to be seen, however, whether the theory-based view of concepts and categorization will supplant, or merely supplement, the similarity-based view.

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