On the Fourfold Root of the Principle of Sufficient...

From the summary given in the preceding chapter we gather, that two distinct applications of the principle of sufficient reason have been recognized, although very gradually, very tardily, and not without frequent relapses into error and confusion: the one being its application to judgments, which, to be true, must have a reason; the other, its application to changes in material objects, which must always have a cause. In both cases we find the principle of sufficient reason authorizing us to ask why? a quality which is essential to it. But are all the cases in which it authorizes us to ask why comprised in these two relations? If I ask: Why are the three sides of this triangle equal? the answer is: Because the three angles are so. Now, is the equality of the angles the cause of the equality of the sides? No; for here we have to do with no change, consequently with no effect which must have a cause.—Is it merely a logical reason? No; for the equality of the angle is not only a proof of the equality of the sides, it is not only the foundation of a judgment: mere conceptions alone would never suffice to explain why the sides must be equal, because the angles are so; for the conception of the equality of the sides is not contained in that of the equality of the angles. Here therefore we have no connection between conceptions and judgments, but between sides and angles.

The equality of the angles is not the direct, but the indirect reason, by which we know the equality of the sides; for it is the reason why a thing is such as it is (in this case, that the sides are equal): the angles being equal, the sides must therefore be equal. Here we have a necessary connection between angles and sides, not a direct, necessary connection between two judgments.—Or again, if I ask why infecta facta, but never facta infecta fieri possunt, consequently why the past is absolutely irrevocable, the future inevitable, even this does not admit of purely logical proof by means of mere abstract conceptions, nor does it belong either to causality, which only rules occurrences within Time, not Time itself. The present hour hurled the preceding one into the bottomless pit of the past, not through causality, but immediately, through its mere existence, which existence was nevertheless inevitable. It is impossible to make this comprehensible or even clearer by means of mere conceptions; we recognise it, on the contrary, quite directly and instinctively, just as we recognize the difference between right and left and all that depends upon it: for instance, that our left glove will not fit our right hand, &c. &c.

Now, as all those cases in which the principle of sufficient reason finds its application cannot therefore be reduced to logical reason and consequence and to cause and effect, the law of specification cannot have been sufficiently attended to in this classification. The law of homogeneity, however, obliges us to assume, that these cases cannot differ to infinity, but that they may be reduced to certain species. Now, before attempting this classification, it will be necessary to determine what is peculiar to the principle of sufficient reason in all cases, as its special characteristic; because the conception of the genus must always be determined before the conception of the species.