There is one point which I have emphasised and which it appears to me Professor Mach neglects, namely that our noumenal world of ideas has an objective meaning. The ideal constructs represent realities. They do not consist of scaffolds alone and there is no scaffold which has not been erected to help in building up representations of facts. Let us call the representation of facts positive science or simply truth and the scaffolding the mythology of science, and we shall see that the road to truth leads everywhere through mythology. Certain facts of the surrounding world impress themselves upon a sentient being and these impressions come to represent facts. These facts are not seen at once in their causal connection, they appear unconnected among themselves, and in the attempt to formulate them, to represent them, to construct them in mental images, we fill out the gaps of our knowledge with such inventions as are supplied by analogy. Mythology is, in religion as well as in science, the indispensable ladder to truth. We cannot build without scaffolds. So we cannot construct truth without mythology. We have to introduce allegorical expressions in order to fill out gaps with analogies. Mythology becomes fatal to the building up of truth, as soon as we consider it as truth itself. The scaffold is erected simply as an assistance for building and if the building is finished the scaffold should be torn down. The progress of science which is so much helped by mythology has periods of purification in which the mythology is discarded. This is sometimes a difficult task, because the very terms of science are mostly both at the same time truth and mythology, building-stones and scaffold. Take, for instance, the term atom. The chemist observes that the elements always combine in certain proportions and formulates the law of the equivalence of their atomic weights. In order to think this process, to reconstruct it in mental images, he imagines that matter consists of infinitely small particles of constant weight. This is a fiction useful for its purpose but it may be just as erroneous as the method employed in the infinitesimal calculus of thinking of a continuous curve as consisting of a broken line of infinitely small parts, or of thinking of a certain force as being composed of a parallelogram of forces. The parallelogram of forces is a scaffold helpful for representing in mental symbols the coexistence of different abstractions of the same kind (e. g. motions of a different velocity and direction). But this scaffold is not a mere scaffold, it is not erected without any purpose, its final aim is the description of facts.