Motivation and Philosophical Background
In his article Restructuring Lattice Theory (1982) initiating formal concept analysis as a mathematical discipline, Rudolf Wille starts from a discontent with the current lattice theory and pure mathematics in general: The production of theoretical results - often achieved by "elaborate mental gymnastics" - were impressive, but the connections between neighbouring domains, even parts of a theory were getting weaker.
Restructuring lattice theory is an attempt to reinvigorate connections with our general culture by interpreting the theory as concretely as possible, and in this way to promote better communication between lattice theorists and potential users of lattice theory.
This aim traces back to Hartmut von Hentig, who in 1972 plaided for restructuring sciences in view of better teaching and in order to make sciences mutually available and more generally (i.e. also without specialized knowledge) criticable. Hence, by its origins formal concept analysis aims at interdisciplinarity and democratic control of research.
It corrects the starting point of lattice theory during the development of formal logic in 19th century. Then - and later in model theory - a concept as unary predicate had been reduced to its extent. Now again, the philosophy of concepts should become less abstract by considering the intent. Hence, formal concept analysis is oriented towards the categories extension and intension of linguistics and classical conceptual logic.
FCA aims at the clarity of concepts according to Charles S. Peirce's pragmatic maxim by unfolding observable, elementary properties of the subsumed objects. In his late philosophy, P
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