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As of now, we do not know exactly what the structure of the set of classifications over a set is, and a complete theory of classifications is still to arise. Only a few parts of it exist in scientific literature. As we have seen, the more convincing of them are concerned, for the moment, with finite partitions, hierarchies and chains. But the global situation is quite different. The boisterous ocean of partitions, the unruly storm of classes, usually escape the searchers and widely elude, at the present time, the most powerful mathematical tools we have at our disposal. If we try, however, to shed new light on the problem, we must be able to tell the difference between the approach of a general theory of classifications, carried out in Chap.  6, and the one we performed in this chapter, that we have called, using a prefix familiar to mathematicians, "metaclassification".

DOI: 10.1007/978-3-0348-0609-1_7

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