Into the formation of concepts, therefore, two factors are operative, an objective empirical factor, and a subjective or purposive factor. The fitness of a concept is seen in relation to its purpose, which we shall now consider.
The purpose of a concept is its use for prediction. The old logic set up the syllogism as the type of thought-activity, and its simplest example is the well-known
All men are mortal,
Caius is a man,
Therefore Caius is mortal.
In general, the scheme runs
To the concept M belongs the element B,
C belongs under the concept M,
Therefore the element B is found in C.
One can say that this method of reasoning is in regular use even to this day. It must be added, however, that this use is of a quite different nature from that of the ancients. Whereas formerly the setting up of the first proposition or the major premise was considered the most important thing, and the establishment of the second proposition or minor premise was thought to be a rather trifling matter, now the relation is reversed. The major premise contains the description of a concept, the minor makes the assertion that a certain thing belongs under this concept. What right exists for such an assertion? The most palpable reply would be, since all the elements of the concept M (including B) are found in C, C belongs under the concept M. Such a conclusion would indeed be binding, but at the same time quite worthless, for it only repeats the minor premise. Actually the method of reasoning is essentially different, for the minor premise is not obtained by showing that all the elements of the concept M are found in C, but only some of them. The conclusion is not necessary, but only probable, and the whole process of reasoning runs: Certain elements are frequently found together, therefore they are united in the concept M. Certain of these elements are recognized in the thing C, therefore probably the other elements of the concept M will be found in C.
The old logic, also, was familiar with this kind of conclusion. It was branded, however, as the worst of all, by the name of incomplete induction, since the absolute certainty demanded of the syllogism did not belong to its results. One must admit, however, that the whole of modern science makes use of no other form of reasoning than incomplete induction, for it alone admits of a prediction, that is, an indication of relations which have not been immediately observed.
How does science get along with the defective certainty of this process of reasoning? The answer is, that the probability of the conclusion can run through all degrees from mere conjecture to the maximum probability, which is practically indistinguishable from certainty. The probability is the greater the more frequently an incomplete induction of this kind has proven correct in later experience. Accordingly we have at our command a number of expressions which in their simplest and most general form have the appearance: If an element A is met within a thing, then the element B is also found in it (in spatial or temporal relationship).
If the relation is temporal, this general statement is known by some such name as the law of causality. If it is spatial, one talks of the idea (in the Platonic sense), or the type of the thing, of substance, etc.
From the considerations here presented we get an easy answer to many questions which are frequently discussed in very different senses. First, the question concerning the general validity of the law of causality. All attempts to prove such a validity have failed, and there has remained only the indication that without this law we should feel an unbearable uncertainty in reference to the world. From this, however, we see very plainly that here it is merely a question of expediency. From the continuous flux of our experiences we hunt out those groups which can always be found again, in order to be able to conclude that if the element A is given, the element B will be present. We do not find this relationship as "given," but we put it into our experiences, in that we consider the parts which correspond to the relationship as belonging together.