CASES THAT ARE NOT INCLUDED AMONG THE PREVIOUSLY ESTABLISHED MEANINGS OF THE PRINCIPLE

From the summary given in the previous chapter, it follows as a general result that two applications of the principle of sufficient reason have been distinguished, although at first gradually and surprisingly late, and not without frequent encounters anew with confusions and mistakes. The one application is to judgements that, in order to be true, always must have a reason, and the other is to alterations of real objects that always must have a cause. We see that in both cases the principle of sufficient reason justifies the question why, and this property is essential to it. But are all cases in which we are justified in asking why included under these two relations? Suppose I ask, why are the three sides of this triangle equal? Then the answer is: because the angles are equal. Now is the equality of the angles the cause of the equality of the sides? No, since here the question is not of alteration and, thus, not of an effect that must have a cause. – Is it mere cognitive ground? No, since the equality of the angles is not mere proof of the equality of the sides, not mere ground of a judgement; indeed, from mere concepts it is never to be understood that because the angles are equal, the sides too must be equal, since the concept of the equality of the angles does not contain that of the equality of the sides. Thus here there is no connection between concepts or judgements, but between sides and angles. The equality of the angles is not immediately the ground for the cognition of the equality of the sides, but only mediately, in that it is the ground of something's being so – here of the sides’ being equal; thus, the angles being equal, the sides must be equal. Here there is a necessary connection between the angles and the sides, not immediately a necessary connection of two judgements.