The World as Will and Idea (Vol. 2 of 3)

When this is transposed into the first figure the minor must be converted, and thus runs: “Some metals are alkalis.” It therefore merely asserts that some metals lie in the sphere “alkalis,” thus [Figure 1], while our actual knowledge is that all alkalis lie in the sphere “metals,” thus [Figure 2]: It follows that if the first figure is to be regarded as the only normal one, in order to think naturally we would have to think less than we know, and to think indefinitely while we know definitely. This assumption has too much against it. Thus in general it must be denied that when we draw inferences in the second and third figures we tacitly convert a proposition. On the contrary, the third, and also the second, figure exhibits just as rational a process of thought as the first. Let us now consider another example of the other class of the third figure, in which the separableness of two predicates is the result; on account of which one premiss must here be negative:

As in the examples given above the compatibility of two properties is the problem of reflection, now their separableness is its problem, which here also must be decided by comparing them with one subject and showing [pg 302] that one of them is present in it without the other. Thus the end is directly attained, while by means of the first figure it could only be attained indirectly. For in order to reduce the syllogism to the first figure we must convert the minor, and therefore say: “Some rational beings are Buddhists,” which would be only a faulty expression of its meaning, which really is: “Some Buddhists are yet certainly rational.”

As the guiding principle of this figure I therefore give: for the affirmative moods: Ejusdem rei notœ, modo sit altera universalis, sibi invicem sunt notœ particulares; and for the negative moods: Nota rei competens, notœ eidem repugnanti, particulariter repugnat, modo sit altera universalis. Translated: If two predicates are affirmed of one subject, and at least one of them universally, they are also affirmed of each other particularly; and, on the contrary, they are denied of each other particularly whenever one of them contradicts the subject of which the other is affirmed; provided always that either the contradiction or the affirmation be universal.

In the fourth figure the subject of the major has to be compared with the predicate of the minor; but in the conclusion they must both exchange their value and position, so that what was the subject of the major appears as the predicate of the conclusion, and what was the predicate of the minor appears as the subject of the conclusion. By this it becomes apparent that this figure is merely the first, wilfully turned upside down, and by no means the expression of a real process of thought natural to the reason.

On the other hand, the first three figures are the ectypes of three real and essentially different operations of thought. They have this in common, that they consist in the comparison of two judgments; but such a comparison only becomes fruitful when these judgments have one conception in common. If we present the premisses to our imagination under the sensible form of two rods, we can [pg 303] think of this conception as a clasp that links them to each other; indeed in lecturing one might provide oneself with such rods. On the other hand, the three figures are distinguished by this, that those judgments are compared either with reference to the subjects of both, or to the predicates of both, or lastly, with reference to the subject of the one and the predicate of the other. Since now every conception has the property of being subject or predicate only because it is already part of a judgment, this confirms my view that in the syllogism only judgments are primarily compared, and conceptions only because they are parts of judgments. In the comparison of two judgments, however, the essential question is, in respect of what are they compared? not by what means are they compared? The former consists of the concepts which are different in the two judgments; the latter consists of the middle, that is, the conception which is identical in both.

It is therefore not the right point of view which Lambert, and indeed really Aristotle, and almost all the moderns have taken in starting from the middle in the analysis of syllogisms, and making it the principal matter and its position the essential characteristic of the syllogisms. On the contrary, its role is only secondary, and its position a consequence of the logical value of the conceptions which are really to be compared in the syllogism. These may be compared to two substances which are to be chemically tested, and the middle to the reagent by which they are tested. It therefore always takes the place which the conceptions to be compared leave vacant, and does not appear again in the conclusion. It is selected according to our knowledge of its relation to both the conceptions and its suitableness for the place it has to take up. Therefore in many cases we can change it at pleasure for another without affecting the syllogism. For example, in the syllogism:

I can exchange the middle “diamond” for “anthracite.” As an external mark by which we can recognise at once the figure of a syllogism the middle is certainly very useful. But as the fundamental characteristic of a thing which is to be explained, we must take what is essential to it; and what is essential here is, whether we place two propositions together in order to compare their predicates or their subjects, or the predicate of the one and the subject of the other.

Therefore, in order as premisses to yield a conclusion, two judgments must have a conception in common; further, they must not both be negative, nor both particular; and lastly, in the case in which the conceptions to be compared are the subjects of both, they must not both be affirmative.

The voltaic pile may be regarded as a sensible image of the syllogism. Its point of indifference, at the centre, represents the middle, which holds together the two premisses, and by virtue of which they have the power of yielding a conclusion. The two different conceptions, on the other hand, which are really what is to be compared, are represented by the two opposite poles of the pile. Only because these are brought together by means of their two conducting wires, which represent the copulas of the two judgments, is the spark emitted upon their contact—the new light of the conclusion.