Factor analytic studies suggest that there are six replicable second order cognitive factors. These six factors lend themselves to being interpreted as aspects of Royce's (1964) three "ways of knowing." This view provides a unified explanation of the second and third order factors. We hypothesize that each second order factor represents either the number of cognitive schemata of a particular type that a person possesses or the quality of these schemata, and the types of schemata are linked to "ways of knowing." The division of second order factors into qualitative and quantitative aspects, with the qualitative aspects being more subject to deterioration with age, and the quantitative aspects more trainable and subject to personality influence, provides an avenue for linking cognitive abilities to the other personality traits. The theory also resolves several theoretical problems concerning cognitive abilities, including distinguishing aptitudes from achievements, measuring creativity, and determining the relationship between rote memory and intelligence.