Understanding Aristotle's Categoriae as a classification of things which are linguistically names, 1) I have tried to show what the classification of predicates would look like if we should construct it on Categoriae, 2) then the status of predicates with regard to Categoriae as the classification of things was briefly mentioned. 3) The notions of 'purely ontological copula' and 'purely ontological predication' were then introduced, trying to show what the most basic form of predication in the above mentioned system of predicates was, and thereafter 4) the problem of accidental predication was treated, where all the possible types of predication except one were rendered to one type of predication. 5) Finally the problem of self-predication, which was not reducible to the basic type, was treated as to its informative ability, where it was at the same time shown that the system of Lesniewski's Ontology at least partly coincided with the system of predication constructed along the above mentioned line.