Form being given, we can reason about the form of existence in general. We can have ready in our minds systems of pure forms to apply to all the various cases of our experience. And this will help us in unravelling the problems of reality, and in extending our knowledge in those fields with which we are little acquainted. Far be it from us to consider the definitions, the operations, and the results of the formal sciences as purely verbal; if they were, mathematics would lose all the great importance which it undeniably possesses, and become mere verbiage. I confess that I do not understand Mr. Dixon when he says: “It is only because our reasoning faculties are limited that symbolic arguments are necessary at all.” In my opinion all mental activity is symbolic. Every idea is a symbol that signifies something. It is not because our reasoning faculties are limited that symbolic arguments are necessary at all, but symbolism is the nature of our mind, and symbols are the elements with which our reasoning faculties have to deal. In this sense, every argument is symbolic. If it symbolises sense-experience, it represents our knowledge of what may be called the materiality of things. If it symbolises operations with pure forms, it represents the purely formal relations of mathematics logic, algebra, etc. The doctrine of the conservation of matter and energy in reality means nothing more or less than that there is no increase or decrease in the world at large. Nothing originates out of, and nothing disappears into, nothing. It means that twice 1 + 1 is 1 + 1 + 1 + 1, neither more nor less; or, in other words, it means that all events are transformations. New things originate, but their newness consists in their forms. In this sense the law of the conservation of matter and energy would have to be called, from Mr. Dixon’s standpoint, other differences neglected, a truism. It is not a truism, in the sense of being arbitrary, but in the sense of being a purely formal truth, as are all mathematical theorems.