Three Levels of Cognition: Particulars, Universals, and Representals

It is shown that apart from the two well known levels of cognition involving the epistemological concepts particulars and universals, there is an intermediate level of cognition necessitating a new epistemological concept which we call represental. This has become necessary as a result of emergence of statistics (an empirical science), the theory of probability (a branch of pure mathematics), and quantum mechanics (as a branch of physics) at the beginning of the nineteenth century. We attribute to a particular man (like Mr. Jones) well defined properties (like a definite number of children) whereas we attribute to a man, the universal, only some general properties (like having an erect body). Thus particulars and universals involve two levels of cognition. In statistics we deal with the properties of a large number of particulars denoted by a universal, without referring to such details as which particular has which properties. Thus statistics involves a new level of cognition. In statistics, we attribute all the statistical properties to a single entity and refer to it as the represental (entity); the concept of represental man is only a generalization of the concept of average man proposed by Quetelet in 1869. These three epistemological concepts are distinguished by the relation they bear with respect to the possible “states” of the particulars. For instance, Mr. Jones, a particular man, can be in the state of having either 0, or 1, or 2, … children only; a man, the universal, cannot be said to have either 0, or 1, or 2, … children, though the state of having children is relevant to him (but not to a chair, the universal); the represental man has 0 child with probability P(0), 1 child with probability P(1), 2 children with probability P(2), …Thus the possible states are mutually exclusive in particulars, are only relevant to the universal, and coexist in the represental with respective probabilities. By recognizing that in statistics, the theory of probability, and quantum mechanics we deal with a new level of cognition involving the epistemological concept of represental, the interpretational problems of statistical phenomena are resolved.