Under mathematics, which is the subject of four small volumes, Wolff also treats of architecture and military science. One of the propositions in Architecture is this: “Windows must be wide enough for two persons.” The making of a door is also propounded as a task, and the solution thereof given. The next best example comes from the art of warfare. The “Fourth proposition. The approach to the fortress must always be harder for the enemy the nearer he comes to it.” Instead of saying, because the danger is greater, which would be trivial, there follows the “Proof. The nearer the enemy comes to the fortress, the greater the danger. But the greater the danger the greater the resistance that must be offered in order to defy the attacks, and, so far as may be, avert the danger. Hence the nearer the enemy is to the fort the harder must the approach be made for him. Q.E.D.”[278] Since the increase of the danger is given as the reason, the whole is false, and the contrary may be said with equal truth. For if at the beginning all possible resistance is offered to the enemy, he cannot get nearer the fortress at all, and thus the danger cannot become greater. The greater resistance has a real cause, and not this foolish one—namely, that because the garrison is now at closer quarters, and consequently operates in a narrow field, it can offer a greater resistance. In this most trivial way Wolff proceeds with every sort of content. This barbarism of pedantry, or this pedantry of barbarism, represented as it is in its whole breadth and extent, necessarily brought itself into disrepute; and without there being a definite consciousness of the reason why the geometric method is not the only and ultimate method of knowledge, instinct and an immediate consciousness of the foolishness of its applications caused this method to be set aside. 3. THE POPULAR PHILOSOPHY OF GERMANY.