In the course of these observations we have learned how co-ordination can be used for obtaining a number of fundamental and multifariously applied principles. From this alone the great importance of co-ordination is evident, and later we shall see that its significance is even more far-reaching. _The entire methodology of all the sciences is based upon the most manifold and many-sided application of the process of co-ordination_, and we shall have occasion to make use of it repeatedly. Its significance may be briefly characterized by stating that it is the most general means of bringing connection into the aggregate of our experiences. =29. Counting.= The group of integral numbers, because of its fundamental simplicity and regularity, is by far the best basis of co-ordination. For while arithmetic and the theory of numbers give us a most thorough acquaintance with the peculiarities of this group, we secure by the process of co-ordination the right to presuppose these peculiarities and the possibility of finding them again in every other group which we have co-ordinated with the numerical group. The carrying out of such co-ordination is called _counting_, and from the premises made it follows _that we can count all things in so far as we disregard their differences_. We count when we co-ordinate in turn one member of a group after another with the members of the number series that succeed one another until the group to be counted is exhausted. The last number required for the co-ordination is called the _sum_ of the members of the counted group. Since the number series continues indefinitely, every given group can be counted. Numerals have been co-ordinated with _names_ as well as with _signs_. The former are different in the different languages, the latter are international, that is, they have the same form in all languages. From this proceeds the remarkable fact that the written numbers are understood by all educated men, while the spoken numbers are intelligible only within the various languages. The purpose of counting is extremely manifold. Its most frequent and most important application lies in the fact that the amount affords a _measure for the effectiveness or the value_ of the corresponding group, both increasing and decreasing simultaneously. A further number serves as a basis for divisions and arrangements of all kinds to be carried out within the group, whereby liberal use is made of the principle that everything that can be effected in the given number group can also be effected in the co-ordinated counted group. =30. Signs and Names.= The co-ordination of names and signs with numbers calls for a few general remarks on co-ordination of this nature.