An algebraic perspective on abstract and concrete domains

Abstract

Abstract Looking at isomorphic constructs from an algebraic perspective, this article suggests that every concrete construct is understood by reference to an underlying abstract schema in the mind of comprehender. The complex form of every abstract schema is created by the gradual development of its elementary form. Throughout the process of cognitive development, new features are added to the elementary form of abstract schema, which leads to gradual formation of a fully-developed abstract schema. Every developed abstract schema is the underlying source for understanding an infinite number of concrete isomorphic constructs. It is suggested that the process of the mapping of base domain (base construct) unto target domain (target construct) is conducted and mediated by an abstract domain. This abstract domain, which is free from concrete features of base and target, is isomorphic to both base and target domains. To describe the mediatory role of this abstract domain, it might be argued that the chain process of understanding a less familiar domain in terms of a relatively more familiar domain (salience imbalance model) cannot continue infinitely. This chain must stop at some point. This point is the abstract domain, which is isomorphic to base and target domains.