This is evident in the classic example: All men are mortal. Caius is a man. Therefore Caius is mortal. For if Caius's mortality were not known (here we are not concerned how this knowledge was obtained), we should have no right to call him a man. At the same time the character of the really scientific conclusion based upon the incomplete induction becomes clear. It proceeds according to the following form. The attributes of the group A are the characteristics of a, b, c, d. We find in the thing C the characteristics a, b, c. Therefore we presume that the characteristic d will also be found in C. The ground for this presumption is that we have learned by experience that the characteristics mentioned have always been found together. It is for this reason, and for this reason only, that we may assume from the presence of a, b, c the presence of d. In the case of an arbitrary combination, in which it is possible to combine other characteristics, the conclusion is unfounded. But if, on the other hand, the formation of the concept A with the characteristics of a, b, c, d has been caused by repeated and habitual experience, then the conclusion is well founded; that is, it is probable. As a matter of fact, however, that classic example which is supposed to prove the absolute certainty of the regular syllogism turns out to be a hidden inductive conclusion of the incomplete kind. The premise, Caius is a man, is based on the attributes a, b, c (for example, erect bearing, figure, language), while the attribute d (mortality) cannot be brought under observation so long as Caius remains alive. In the sense of the classic logic, therefore, we are not justified in the minor premise, Caius is a man, while Caius is alive. The utter futility of the syllogism is apparent, since, according to it, it is only of dead men that we can assert that they are mortal. From these observations it becomes further apparent that logic, whether it is the superfluous classic logic or modern effective inductive logic, is nothing but a part of the group theory, or science of manifoldness, which appears as the first, because it is the most general member of the mathematical sciences (this word taken in its widest significance). But according to the hierarchic system in harmony with which the scheme of all the sciences had been consciously projected, we cannot expect anything else than that those sciences which are needful for the pursuit of all other sciences (and logic has always been regarded as such an indispensable science, or, at least, art) should be found collected and classified in the first science.