An algebraic perspective on implicit and explicit knowledge

The isomorphic relationship between an infinite number of concrete algebraic groups and the existence of a single abstract group that underlies all these concrete groups is one of the most fundamental subjects in Abstract Algebra. Looking at the process of explicit learning from a mathematical perspective, this article suggests that explicit knowledge of a certain concrete structure can be viewed as consciousness of an abstract algebraic structure that underlies that structure. On the other hand, implicit knowledge can be regarded as knowing something without being conscious of the abstract structure that underlies that knowledge. Explicit knowledge enables the learner to know what features are shared by these concrete groups or structures. These shared features are the defining elements of underlying abstract structure. The abstract structure is constructed in the mind by the suppression of irrelevant data. Therefore, it is suggested that while implicit learning is a receiving-oriented mode of learning, explicit learning is a suppression-oriented one. The sub-process of suppression enables the cognitive system to focus on abstract structure and its defining features, making the process of explicit learning deeper.