The Stanford Project on Language Universals began its activities in October 1967 and brought them to an end in August 1976. Its directors were Joseph H. Greenberg and Charles A. Ferguson. The Cologne Project on Language Universals and Typology [with particular reference to functional aspects], abbreviated UNITYP, had its early beginnings in 1972, but deployed its full activities from 1976 onwards and is still operating. This writer, who is the principal investigator, had the privilege of collaborating with the Stanford Project during spring of 1976. […] One of the leading Greenbergian ideas is that of implicational generalizations, has been integrated as a fundamental principle in the construction of continua and of universal dimensions as proposed by UNITYP. It is hoped that the following considerations on numeral systems will be apt to bear witness to this situation. They would be unthinkable without Greenberg’s pioneering work on "Generalizations about numeral systems" (Greenberg 1978: 249 ff., henceforth referred to as Greenberg, NS). Further work on this domain and on other comparable domains almost inevitably leads one to the view that generalizations of the Greenberg type have a functional significance and that a dimensional framework is apt to bring this to the fore. This is the view on linguistic behaviour as being purposeful, and on language as a problem- solving device. The problem consists in the linguistic representation of cognitive-conceptual ideas. The solution is represented by the corresponding linguistic structures in their diversity and the task of the linguist consists in reconstructing the program and subprograms underlying the process of problem-solving. It is claimed that the construct of continua and of universal dimensions makes these programs intelligible.