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Abstract
What makes a good category? Perceptually natural categories--object classes in which an infinity of distinct forms collapse compellingly into a unary description, such as triangle, or dot on a line--impose structure onto our perceived world. This thesis investigates the formal composition of simple category models, and the properties that distinguish such categories from arbitrary incoherent sets of unrelated objects. The goal is a formal characterization of human category inferences, including the rather subtle relationship between a perceiver's existing concepts and entailed inductive hypotheses. A critical issue is the formal relationship between mental models and actual world regularities (i.e., covariation in the world among logically orthogonal properties, or "natural modes"). The main formal structure is a lattice of category models, a relational structure that enumerates the various distinct uniform category models in a model class. The lattice serves as a kind of category hypothesis generator, providing the observer with a closed class of distinct models from which to select, each of which corresponds to a coherent "causal" model of the induced category. A computer program is developed to check the validity of the theory, and to generate the lattice category models for complex families.
A series of experiments are reported in which subjects were asked to induce simple categories from a very small set of unfamiliar sample objects (either one or three objects), and generate novel examples of the category. The results corroborate the lattice theory, and lobby against a view of categorization as any kind of a statistical summary of environmental frequency distributions. In several conditions, subjects' produced a frequency distribution that actually contained a larger number of modes (peaks) than there were objects in the sample set; in another condition, subjects' frequency distributions exhibited a mode in a region of the model space where they never observed any examples; and in another condition, subjects produced a frequency distribution that was distinctly modal in a region of the model space in which distribution they observed was carefully arranged to be perfectly flat. In all these cases, the frequency modes corresponded neatly with nodes on the theoretical category lattice computable from the sample set. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)
