Twin concepts

"Twin concepts" are concepts that are not blended (see conceptual blending), but are defined in relation to each other. Examples are body and soul, space and time, form and content, negative and positive, etc.
There are some other uses of the term, for example here in :
The twin concepts of purchasing power parities (PPP) of currencies and the international average prices of commodities []
The twin concepts of freedom of self-determination and freedom from tyranny []
The twin concepts of studium and punctum: studium denoting the cultural, linguistic, and political interpretation of a photograph, punctum denoting the wounding, personally touching detail which establishes a direct relationship with the object or person within it.
The twin concepts of perestroika and glasnost, meaning economic/political restructuring and openness, respectively []
The reason why they are important is that they may lead the reader to the understanding of recursion in informal logic and natural languages or human language.
body and soul
space and time
form and content
negative and positive
Comments
Now most practitioners in Formal Logic believe in concept analysis, where a concept is defined as a pair of concepts of objects and properties. They do not see them as twin concepts, neither they believe that relation is another entity that should also be a part of the total picture. They consider them however as the semantic primitives of a core or upper ontology (language that has some words to its vocabulary. This is how they would like to picture the above concepts visually, in 2D or 3D, a method deemed to serve understanding better than words only.
"Natural property clusters correspond one-for-one with natural object clusters, and a concept is a pair containing both a natural property cluster and its corresponding natural object cluster. The family of these concepts obeys the mathematical axioms defining a lattice, and is called a concept lattice (in French this is called a Treillis de Galois because the relation between the sets of concepts and attributes is a Galois connection).
Note the strong parallel between "natural" property clusters and definitions in terms of individually necessary and jointly sufficient conditions, on one hand, and between "natural" object clusters and the extensions of such definitions, on the other. Provided the input objects and input concepts provide a complete description of the world (never true in practice, but perhaps a reasonable approximation), then the set of attributes in each concept can be interpreted as a set of singly necessary and jointly sufficient conditions for defining the set of objects in the concept. Conversely, if a set of attributes is not identified as a concept in this framework, then those attributes are not singly necessary and jointly sufficient for defining any non-empty subset of objects in the world." quote from concept analysis
Now to say that "a concept is a pair containing both a natural property cluster and its corresponding natural object cluster" means that the concept of natural object clusters and the concept of natural property clusters are in fact twin concepts. No concept can contain natural objects, or properties, save their concepts. Objects and properties are concepts as they are the result of abstraction and conceptualization.

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