Aristotelianism
or PERIΡΑ- TETICISM, the doctrine of philosophy of Aristotle. Aristotle attempted to steer a medium course between the ultraidealism of his master Plato, and the low sensationalism of the physical school of Elea. His genius was as wide as nature. He keenly combated the ideal theory of Plato, or that which expounded the deity as holding in himself the archetypal ideas after which the world was fashioned, and which it was the business of reason and science to discover. But while denying these ideas of his master, he nevertheless agreed with him in the view that knowledge contains an element radically distinct from sensation. He also differed from the Eleatics and the Epicureans, inasmuch as he denied that sensation could account for the whole of knowledge; but maintained, with them, that without this sensation, knowledge would be impossible. possible. The celebrated maxim that "there is is nothing in the intellect which was not previously in the sense," if not Aristotle's, at least well expresses a side of his doctrine; but, when he insists upon the distinction between the necessary and the contingent, the absolute and the relative, he rises altogether above the sphere of sensation, and takes emphatically his place with reason. Philosophy, according to Aristotle, is properly science arising from the love of knowledge. There are ARISTOTELIANISM 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 expound. Logic is, therefore, the instrument of all science; but only quoad formam, for it is experience which supplies the matter to be worked upon. The formal part of reasoning he accordingly expounds better than any man either before 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 recognizes that of sufficient reason as a regulative 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) real order of things, irrespective of human control; practical philosophy disman control; practical philosophy dis- Real substances are either invariable, or variable, and perishable; the deity alone men pursue the real in an abstract way?
Then, metaphysics and mathematics its objects? Then physics, cosmology, psychology, theology emerge. (2) Practical 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. Nature is the sum of all existences, which 1. Physics, or natural philosophy. Nafaculties. The knowledge of nature is properly the knowledge of the laws of bodies in motion. Nature, cause, acproperly the knowledge of the laws of time, and motion, are included in this science. In his "Cosmology," Aristotle us moderns 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. principle of organized life. It is distinct sensation, thought, and will or impulse. 2. The ruling idea of his practical philosophy was that of a sovereign good, and final end or aim of action. This final ARITHMETIC 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 oris the character of nearly the whole of 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, all the rest. Under the head of right, 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 perto the end proposed. By this principle to the end proposed. By this principle Aristotle proves the legality of slavery; and all education he refers to the ultimate end of political society.
ARISTOXENUS (ar-is-tox'ē-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 endeavored 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; looked on as an art, its object is to carry out for practical purposes certain rules self to investigate the foundation on which those rules are based. and fractional arithmetic, the former treating of integers and the latter of times called vulgar or common arithmetic; and from fractional arithmetic is sometimes separated decimal arithmetic, treating, as the name implies, of decimals. logarithms, and instrutreating, as the name implies, of decimals. computation by log mental arithmetic for calculation by means of instruments or machines. Anmeans of instruments or machines. Anmetic, treating of the science of numbers, and practical arithmetic, which points Political arithout the best method of practically working questions or sums. metic is arithmetic applied to political economy, as is done in the statistical re- ARITHMETICAL COMPLEMENT 250 turns so continually presented to Parliament or Congress. Finally, universal arithmetic is a name sometimes applied to algebra. The chief subjects generally treated under the science or art of arith- ARIZONA the fourth; the equality of two differences or arithmetical ratios. In such cases the sum of the extremes is that of the means.
ARI THORGILSSON (ä-rë tōr'gilsson), the father of Icelandic literature metic are: (1) numeration and notation; (2) addition; (3) subtraction; (4) mul- (1067-1148). He was the first Icelander tiplication; (5) division; (6) reduction; to use his mother tongue as a literary (7) compound addition; (8) compound subtraction; (9) compound multiplication; (10) compound division; (11) simple proportion (rule of three); (12) compound proportion; (13) vulgar fractions; (14) decimal fractions; (15) duodecimals; (16) involution; (17) evolution; (18) ratios, proportions, and progressions; (19) fellowship or partnership; (20) simple interest; (21) compound interest, and (22) position. Of these, the most important are the simple processes of addition, subtraction, multiplication and division, the judicious use of which, singly or in combination, will solve the most complex arithmetical questions.
ARITHMETICAL COMPLEMENT, that which a number wants to make it reach the next highest decimal denomination. Thus the arithmetical complement of 4 is 6, for 4+6 are = 10, and that of 642 is 358, because 642 + 358 are = 1,000. The arithmetical complement of a logarithm is what it wants to make it reach 10.
ARITHMETICAL MEAN. (1) The number, whether it be an integer or a fraction, which is exactly intermediate between two others. Thus, 5 is the arithmetical mean between 2 and 8; for 2+3 are = 5, and 5+3 are =8. To find such a mean add the numbers together and divide their sum by 2; thus, 2+8=10, and 10÷2=5. (2) Any one of several numbers in an arithmetical ratio interposed between two other numbers. Thus, if 6, 9 and 12 be interposed between 3 and 15, any one of then may be called an arithmetical mean between these two numbers.