Comte failed to postulate a fourth mode of thinking, namely, socialized thinking, or a system of thought which would emphasize not simply the use of natural forces, but the use of natural forces for social ends, for the purpose of building constructive, just, and harmonious societies, and of developing personalities who will evaluate life in terms of the welfare of other personalities. Comte, however, should be credited with opening the way for the rise of socialized thinking. A third phase of Comte’s system was his classification of the sciences, with sociology as the latest and greatest of the group. The Greek thinkers, it will be recalled, undertook to classify all knowledge under three headings: physics, ethics, and politics. Bacon made the divisions correlative to the so-called mental faculties of memory, imagination, and reason, namely: history, poetry, and science. Comte chose as his principle of classifying knowledge, the order of increasing dependence. He arranged the sciences so that each category may be grounded on the principal laws of the preceding category, and serve as a basis for the next ensuing category.[XIII-5] The order, hence, is one of increasing complexity and decreasing generality. The most simple phenomena must be the most general--general in the sense of being everywhere present.[XIII-6] Comte began with mathematics, the tool of the mind. Accurate thinking is always done in terms of mathematics. With mathematics as its chief tool, the mind of man can go anywhere in its thinking. Mathematics is the most powerful instrument which the mind may use in the investigation of natural laws.[XIII-7] Mathematics is not a constituent member of the group of sciences. It is the basis of them all. It holds the first place in the hierarchy of the sciences, and is the best point of departure in all education, whether general or special.[XIII-8] It is the oldest and most perfect of all the sciences.[XIII-9] Mathematics is the science which measures precisely the relations between objects and ideas. It is _the_ science.[XIII-10] The Greeks had no other. Its definition is the definition of all science. Its function is that of ascertaining relationships, a process which is basic to scientific thinking in all fields. Education that is based on any other method is faulty, inexact, and unreliable. It is only through mathematics that we can understand science. The highest form of mathematics is calculus. There is no scientific inquiry in which calculus is not used. Even the physician in prescribing for the cure of a disease, must provide for the mixing together of different quantities of different medicines, so that, when taken at determined intervals of time, they will possess the right qualities for bringing the human body back to its normal state. Calculus is the branch of science which has the highest intellectual dignity. In it the proportion of reasoning to observation is greater than elsewhere.