''It is terrible to see how a single unclear idea, a single formula without meaning, lurking in a young man's head, will sometimes act like an obstruction of inert matter in an artery, hindering the nutrition of the brain, and condemning its victim to pine away in the fullness of his intellectual vigor and in the midst of intellectual plenty. Many a man has cherished for years as his hobby some vague shadow of an idea, too meaningless to be positively false; he has, nevertheless, passionately loved it, has made it his companion by day and by night, and has given to it his strength and his life, leaving all other occupations for its sake, and in short has lived with it and for it, until it has become, as it were, flesh of his flesh and bone of his bone; and then he has waked up some bright morning to find it gone, clean vanished away like the beautiful Melusina of the fable, and the essence of his life gone with it. I have myself known such a man; and who can tell how many histories of circlesquarers, metaphysicians, astrologers, and what not, may not be told in the old German story?'' [Peirce (, delete this paragraph - 1903.) 1]
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Formal concept analysis is a mathematical theory developed in the early 1980s by the Darmstadt research group around Rudolf Wille, Bernhard Ganter and Peter Burmeister. Formal concept analysis understands itself as an applied theory of order- and lattice theory. The development of formal concept analysis was intellectually influenced by the views of Hartmut von Hentig and his call for a restructuring of the sciences:
''... dann müssen die einzelnen Wissenschaften in erster Linie ihre Disziplinarität überprüfen, und das heißt, ihre unbewußten Zwecke aufdecken, ihre bewußten Zwecke deklarieren, ihre Mittel danach auswählen und ausrichten und ihre Berechtigung, ihre Ansprüche, ihre möglichen Folgen öffentlich und verständlich darlegen und dazu ihren Erkenntnisweg und ihre Ergebnisse über die Gemeinsprache (und die von mir sogenannte ’Anschauung’) zugänglich machen.'' (von Hentig 1974, p. 136) Rudolf Wille also argued in the sense of this demand in the abstract of his essay Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts: ''Lattice theory today reflects the general status of current mathematics: there is a rich production of theoretical concepts, results, and developments, many of which are reached by elaborate mental gymnastics; on the other hand, the connections of the theory to its surroundings are getting weaker and weaker, with the result that the theory and even many of its parts become more isolated. 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.'' The purely mathematical foundations of formal concept analysis were already laid in the 1930s by Garrett Birkhoff in the form of general lattice theory. The starting point of formal concept analysis is the mathematical formalization of the concept 'concept', which is inspired, among others, by the writings of Charles Sanders Peirce [see his evocatingly beautiful and at the same time irritatingly unsettling essay How to make our ideas clear].evocatingly beautifulevocatingly beautiful Nowadays, formal concept analysis finds practical application for example in data and text mining, knowledge management, software engineering or in bioinformatics. |