ABSTRACT
The relation between a set and an ordering principle constitutes the infrastructure of any order. This relation allows for two logical possibilities: an ordering principle is either external to its set or internal to it. Being “external” means that the principle is independent of the particular sets and it therefore can be understood and contemplated apart from any particular case. The “external” principle is thus like an idea or a pattern that is capable of being imprinted in different materials and of reaching a variety of degrees in the accuracy of its imprinting. Being “internal” means that the principle cannot be detached from the particular set in which it is found and cannot be separately contemplated as an abstract, independent formula. The “internal” principle consists of the relations among the elements of a particular set; these relations do not maintain the same character in a different set that consists on other elements. In other words, the elements of the set constitute their own principle by generating an individual net of interrelationships among them. The nature of these relationships as well as the diversity between “external” and “internal” principles will be elaborated and analyzed in the following chapters. There is, however, no third alternative.
