Concept Theory

Although concepts have been studied thousand years, people still do not have a generally accepted agreement on what concepts are. Researchers often credit Plato (424 – 348 BC) and Aristotle (384 – 322 BC) being the earliest scholars to study concept formally. However, their ideas of concepts provide an important reference on the study of concepts but not a generally accepted consensus. Scholars propose many theories of concepts and discuss many views of concepts, and that does not result in consensus but in enlarging the border of our understanding of concepts. Hjørland (2009) systematically survey the theories of concepts and

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classify these theories into four families. His classification is based on epistemological viewpoint, and he uses theories of knowledge to classify theories of concepts.

We describe these four families here because it can give us a reference framework when we want to understand our proposed concept definition. These four families of theories of concepts are empiricism, rationalism, historicism, and pragmatism.

Empiricism argues that knowledge is draw from observations. These observations are given by settings and are not contextual or theory-dependent. When applying empiricism to semantic, empiricism argues that meanings are defined based on observable features. When applying empiricism to concepts, empiricism argues that human’s sensations derive the concept. In computer science, empiricism argues that neural networks can be seen as modeling concept in empiricism.

Rationalism argues that knowledge is based on predefined structures or rules, which can be logics, principles, or ontology. Plato’s theory of Forms is in this family. When applying rationalism to concepts, rationalism argues that concepts are prior to human’s sensations.

Hjørland (2009) regard Formal Concept Analysis (FCA) (Priss, 2004, 2006) as a prominent mathematical formation of rationalist concept theory. The FCA uses features to define concept, and these features are regarded as simple and well-defined for the human.

Historicism argues that knowledge has its social context and is time-variant. It argues that observations are theory-dependent and always be influenced by cultures, environments, or contexts. When applying historicism to concepts, historicism argues that concepts are always evolving. The concepts will change when the cognitive mechanisms are functioning.

To understand a concept, historicism concerns about discovering the effective assumptions behind the concept and tracing the changes of these assumptions.

Pragmatism argues that knowledge is based on “the analysis of goals, purposes, values, and consequences“. That is to say, knowledge is always based on some specific aspects of

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reality. Pragmatism also argues that observations are theory-dependent, but it argues that knowledge cannot be neutral because it is derived for some purposes. When applying pragmatism to concepts, pragmatism argues that concepts are faceted. A concept describes reality in some aspects and ignores other aspects of the reality for their purposes.

Hjørland (2009) gives three examples to illustrate the difference of concept theories, but we summarize three factors to make a more concise distinctions of these concept theories. The factors are structure-depend, time-variant, and faceted. We show the summary in Table 1.

Family Factor Structure-depend Time-variant Faceted

Empiricism No No No

Rationalism Yes No No

Historicism Yes Yes No

Pragmatism Yes Yes Yes

Table 1. The differences of families of theories of concepts

In Table 1, we replace theory-dependent with structure-depend because the theory sometimes refers to ontology or reflects a specific world structure. In those cases, structure is more precise for describing the idea. In historicism and pragmatism, the structure is from the context or the purpose, which are different from rationalism. The time-variant factor in historicism and pragmatism contains the cases that the perceived concepts may affect the process of following concept perception. In terminology of machine learning, system feeds outputs to its inputs, which may result in recurrent neural network architecture. We do not put any implication between time-variant factor and self-feed architecture here.

With the theories of concepts in mind, we can use it to explain our concept definition.

Before defining concept, we put some words on the distinctions between concept definition

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and theories of concepts.

When we use the term definition, it means we refer one term to something. For example, a concept definition is to refer concept to something. Abstractly speaking, a definition connects object to other objects and use criteria to rate the goodness of this connection. In the philosophy of science, this means we use something to explain concept in order to reach a good understanding of concept. The criteria of judging the goodness of explanation is not easy to formulate. According to Friedman (1974), the judgment is the problem of scientific explanation:

In Friedman’s article, he describes three views of scientific explanations. One of viewpoints of explanation is that “scientific explanations give us understanding of the world by relating (or reducing) unfamiliar phenomena to familiar ones.” We adopt this viewpoint when we construct our concept definition¹.

In our concept definition, we relate concept to a computational architecture, which is unambiguous and well-defined mathematical computation model. In this way, we avoid the use of human interpreted terms in defining concept. Next section, we will ground our concept definition to existing computation models.