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AKiSTOTELIANISM 249 ARITHMETIC two sorts of knowledge: mediate, and immediate. From immediate knowledge, which we gain through the experience of particulars, we derive mediate knowledge, by means of argumentation, whose theory it is the office of logic to properly ex- pound. Logic is, therefore, the instru- ment of all science; but only quoad formam, for it is experience which sup- plies the matter to be worked upon. The formal part of reasoning he accordingly expounds better than any man either be- fore or since his time. He, indeed, created logic, and this system stands erect through the changes of centuries. He most profoundly bases his logic upon the laws of contradiction, and he even rec- ognizes that of sufficient reason as a reg- ulative principle in the evolution of truth. After logic, he took up all the sciences, rational, empirical, and mixed, except one alone, viz., history. He seems to have divided philosophy into logic, physics, and ethics, or into speculative and practical knowledge, (1) Speculative philosophy contemplates the real order of things, -rrespective of hu- man control; practical philosophy dis- cusses affairs voluntary and accidental. Real substances are either invariable, or variable; while sublunary matters are variable, and perishable; the deity alone is imperishable, ".nc unchangeable. Do men pursue the real in an abstract way? Then, metaphysics and mathematics emerge. Do they pursue knowledge as to its objects? Then physics, cosmology, psychology, theology emerge. (2) Prac- tical philosophy again comprehends ethics, politics, and economy. A word or two on each of these heads', and first , of speculative philosophy. 1. Physics, or natural philosophy. Na- ture is the sum of all existences, which are disclosed to us by our perceptive faculties. The knowledge of nature is properly the knowledge of the laws of bodies in motion. Nature, cause, ac- cident, end, change, infinitude, space, time, and motion, are included in this science. In his "Cosmology," Aristotle discusses astronomy, using that term in its widest signification. It appears to Us modems obscure and inconsistent, and is by no means satisfactory. Physiology is indebted to Aristotle for its first essay. The soul is, according to him, the active principle of organized life. It is distinct from the body, yet, considered as its form or entelechy, it is inseparable from it. Its faculties are production, nutrition, sensation, thought, and will or impulse. 2. The ruling idea of his practical phi- losophy was that of a sovereign good, and final end or aim of action. This final end he denominated happiness, which is the result of the perfect energies of the soul, and is the highest of which our nature is capable. It arises from the perfect exercise of reason, and is or- dinarily called virtue. This he describes as the mean between two extremes, which is the character of nearly the whole of his philosophy. He distinguishes the moral virtues into seven cardinal ones, of which justice, in a sense, embraces all the rest. Under the head of right, he distinguishes that belonging to a family from that belonging to a city. A perfect unity of plan prevails throughout his morals, politics and economics. Both of the latter have for their object to show how this perfect virtue, already described, may be attained in the civil and domestic relationships, through a good constitution of the state and the household. The principle of the science of politics is expediency, and its per- fection consists of suitableness of means to the end proposed. By this principle Aristotle proves the legality of slavery; and all education he refers to the ulti- mate end of political society. ARISTOXENUS (ar-is-tox'e-nus), an ancient Greek musician and philosopher of Tarentum, born about B. C. 324. He studied music under his father Mnesias, and philosophy under Aristotle, whose successor he aspired to be. He en- deavored to apply his musical knowledge to philosophy, and especially to the science of mind. We have a work on the "Elements of Harmony" by him. ARITHMETIC. Viewed as a science, arithmetic is a branch of mathematics; lookea on as an art, its object is to carry out for practical nurposes certain rules regarding numbers, without troubling it- self to investigate the foundation on which those rules are based. It is variously divided, as into integral and fractional arithmetic, the former treating of integers and the latter of fractions. Integral arithmetic is some- times called vulgar or common arithme- tic; and from fractional arithmetic is sometimes separated decimal arithmetic, treating, as the name implies, of decimals. There are also logarithmic arithmetic for computation by logarithms, and instru- mental arithmetic for calculation by means of instruments or machines. An- other division is into theoretical arith- metic, treating of the science of numbers, and practical arithmetic, which points out the best method of practically work- ing questions or sums. Political arith- metic is arithmetic applied to political economy, as is done in the statistical re-