If in the two judgments to be compared the relation between the predicate of the one and the subject of the other is the object of the comparison, the first figure appears. This figure alone has the advantage that the conceptions which in the conclusion are subject and predicate both appear already in the same character in the premisses; while in the two other figures one of them must always [pg 298] change its roll in the conclusion. But thus in the first figure the result is always less novel and surprising than in the other two. Now this advantage in the first figure is obtained by the fact that the predicate of the major is compared with the subject of the minor, but not conversely, which is therefore here essential, and involves that the middle should assume both the positions, i.e., it is the subject in the major and the predicate in the minor. And from this again arises its subordinate significance, for it appears as a mere weight which we lay at pleasure now in one scale and now in the other. The course of thought in this figure is, that the predicate of the major is attributed to the subject of the minor, because the subject of the major is the predicate of the minor, or, in the negative case, the converse holds for the same reason. Thus here a property is attributed to the things thought through a conception, because it depends upon another property which we already know they possess; or conversely. Therefore here the guiding principle is: Nota notæ est nota rei ipsius, et repugnans notæ repugnat rei ipsi.
If, on the other hand, we compare two judgments with the intention of bringing out the relation which the subjects of both may have to each other, we must take as the common measure their predicate. This will accordingly be here the middle, and must therefore be the same in both judgments. Hence arises the second figure. In it the relation of two subjects to each other is determined by that which they have as their common predicate. But this relation can only have significance if the same predicate is attributed to the one subject and denied of the other, for thus it becomes an essential ground of distinction between the two. For if it were attributed to both the subjects this could decide nothing as to their relation to each other, for almost every predicate belongs to innumerable subjects. Still less would it decide this relation if the predicate were denied of both the subjects. From this follows the fundamental characteristic of the second [pg 299] figure, that the premisses must be of opposite quality; the one must affirm and the other deny. Therefore here the principal rule is: Sit altera negans; the corollary of which is: E meris affirmativis nihil sequitur; a rule which is sometimes transgressed in a loose argument obscured by many parenthetical propositions. The course of thought which this figure exhibits distinctly appears from what has been said. It is the investigation of two kinds of things with the view of distinguishing them, thus of establishing that they are not of the same species; which is here decided by showing that a certain property is essential to the one kind, which the other lacks. That this course of thought assumes the second figure of its own accord, and expresses itself clearly only in it, will be shown by an example:
All fishes have cold blood;
No whale has cold blood:
Thus no whale is a fish.
In the first figure, on the other hand, this thought exhibits itself in a weak, forced, and ultimately patched-up form:
Nothing that has cold blood is a whale;
All fishes have cold blood:
Thus no fish is a whale,
And consequently no whale is a fish.