We now have side by side four justifiable world-outlooks, each with significance for its particular domain. Between Materialism and Idealism there is a certain transition. The crudest kind of materialism—one can observe it specially well in our day, although it is already on the wane—will consist in this, that people carry to an extreme the saying of Kant—Kant did not do this himself!--that in the individual sciences there is only so much real science as there is mathematics. This means that from being a materialist one can become a ready-reckoner of the universe, taking nothing as valid except a world composed of material atoms. They collide and gyrate, and then one calculates how they inter-gyrate. By this means one obtains very fine results, which show that this way of looking at things is fully justified. Thus you can get the vibration-rates for blue, red, etc.; you take the whole world as a kind of mechanical apparatus, and can reckon it up accurately. But one can become rather confused in this field. One can say to oneself: “Yes, but however complicated the machine may be, one can never get out of it anything like the perception of blue, red, etc. Thus if the brain is only a complicated machine, it can never give rise to what we know as soul-experiences.‿ But then one can say, as Du Bois-Raymond once said: If we want to explain the world in strictly mathematical terms, we shall not be able to explain the simplest perception, but if we go outside a mathematical explanation, we shall be unscientific. The most uncompromising materialist would say, “No, I do not even calculate, for that would presuppose a superstition—it would imply that I assume that things are ordered by measure and number.‿ And anyone who raises himself above this crude materialism will become a mathematical thinker, and will recognize as valid only whatever can be treated mathematically. From this results a conception of the universe that really admits nothing beyond mathematical formulae. This may be called Mathematism.