And they are facts merely because there is no life in them. In music there are also facts, so there is a part of music which we can say we know. The modern European knows a certain number of musical sounds which are the facts of music. They can be described in various ways, but as European musical facts they are twelve semi-tones repeated in series between two arbitrarily selected points which are the highest and the lowest notes comfortably audible to the human ear. Each of these semi-tones is an arbitrarily selected note or vibration number chosen out of all the masses of vibrations which we call noises by virtue of an inner unity, a mathematical symmetry which gives it form and makes it a musical sound. But even this mathematical symmetry is a fiction, a thing made by the human mind; and these sounds, like the letters of the alphabet, have no life or meaning in themselves. But at this point a reservation must be made. For most, possibly for all, the letters of the alphabet have a varied character, a character which derives (_a_) from their different shapes, (_b_) from their different sounds. The effect of their shape belongs to the world of graphic art, the effect of their sound belongs to the world of music. We may think of these impressions as the residuary fossils left by giantlike primitive emotions which have stalked through those other worlds. A certain artistic use can be made of them, and indeed we find that every new wave of artistic expression is preluded by a breakdown of the abstract combinations of symbols in which the symbols had become most completely devitalized, and a return to a sense of a meaning, a colour, a life in the symbol itself. This results in simplification, which ultimately gives place to a new complication. What is called progress in art consists mainly of this process. Whether there is another kind of progress underlying this process must be considered in another chapter. Now that we have become clear as to what facts are we can perceive what knowledge is. But I must prevent the danger of a mere logomachy between reader and writer by stating at once that I am giving here definitions of “knowledge” and “life” to which we must both adhere. If any reader likes to give the name of “true knowledge” to what I call life and says that what I call knowledge is not true knowledge at all, he is welcome to do so. But I am going to use my own terms, and I shall continue to use the term “life” instead of so idiotic a term as “true knowledge.”