Natural Philosophy

by Wilhelm Ostwald

20. Association.

The experience of the connection or relation between various things is also derived from the nature of our experiences in the most general sense. When we recall a thing A, another thing B comes to our mind, the memory of which is called forth by A, and vice versa. The cause of this invariably lies in some experiences in which A and B occur together. In fact, A and B must have occurred together a number of times. Otherwise they would have disappeared from memory. In other words, it is the fact of the complex concept which appears in such connections between various things. Two things, A and B, which are connected with each other in such a way, are said to be associated. Association in the most general sense means nothing more than that when we think of B we also have A in our consciousness, and vice versa. However, we can at will make the association more definite, so that quite definite thoughts or actions will be connected with the association of B. These thoughts and actions are then the same for all the individual cases occurring under the concept A and B.

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.

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.