A theory, according to most accounts, is a set of hypotheses or verifiable statements that seek to explain a set of observed data. In the present case, the data for which a theory is to be constructed are voluminous, albeit not as complete or satisfactory as one might like. The data consist, essentially, of information on the correlations of variables that come primarily from psychological tests, but occasionally also from observations of behavior from sources other than tests, such as school marks, ratings of competence and various personal attributes, and the like. They consist also of the results of factor analyses of such data according to a scheme that displays the loadings of variables or factors on latent traits at several levels of a hierarchy of abilities from fairly specific (at the first stratum) to highly general (at a third stratum). An adequate theory of cognitive abilities should provide statements concerning the nature and placement of abilities at each level of this hierarchy. Desirably, it should also provide statements or hypotheses about the sources of individual differences in these abilities, at whatever level in the hierarchy.