If we associate with the thing B another thing C, we obtain a relation of the same nature as that obtained by the association of A and B. But at the same time a new relation arises which was not directly sought, namely, the association of A to C. If A recalls B, and B recalls C, A must inevitably recall C also. This psychologic law of nature is productive of numberless special results. For we can apply it directly to still another case, the association of a fourth thing D to the thing C, whereby new relations are necessarily established also between A and D as well as between B and D. By positing the _one_ relation C : D there arise two new relations not immediately given, namely, A : D and B : D. The reason the other relations arise is because C was not taken free from all relations, but had already attached to it the relations to A and B. These relations of C, therefore, brought A and B into the new relation with D. By this simplest and most general example we recognize the type of the deductive process (p. 41), namely, the discovery of relations which, it is true, have already been established by the accepted premises, but which do not directly appear in undertaking the corresponding operations. In the present case, to be sure, the deduction is so apparent that the recognition of the relations in question offers not the slightest difficulty. But we can easily imagine more complicated cases in which it is much more difficult to find the actually existing relations, and so in certain circumstances we may search for them a long time in vain. =21. The Group.= The aggregate of all individual things occurring in a definite concept, or the common characteristics of which make up this concept, is called a group. Such a group may consist of a limited or finite number of members, or may be unlimited, according to the nature of the concepts that characterize it. Thus, all the integers form an unlimited or infinite group, while the integers between ten and one hundred (or the two-digit numbers) form a limited or finite group. From the definition of the group concept follows the so-called classic _process of argumentation_ of the syllogism. Its form is: _Group A is distinguished by the characteristic of B_. _The thing C belongs to group A. Therefore C has the characteristic of B._ The prominent part ascribed by _Aristotle_ and his successors to this process is based upon the _certainty_ which its results possess. Nevertheless, it has been pointed out, especially by _Kant_, that judgments or conclusions of such a nature (which he called analytic) have no significance at all for the progress of science, since they express only what is already known. For in order to enable us to say that the thing C belongs to group A, we must already have recognized or proved the presence of the group characteristic B in C, and in that case the conclusion only repeats what is already contained in the second or minor premise.