INTRODUCTION. LESSON I. DEFINITION AND SPHERE OF THE SCIENCE. LOGIC may be most briefly defined as the Science of Reasoning. It is more commonly defined, however, as the Science of the Laws of Thought, and some logicians think it desirable to specify still more accurately that it is the Science of the Formal, or of the Necessary Laws of Thought. Before these definitions can be of any real use to us we must come to a clear understanding as to the meaning of the expressions; and it will probably appear that there is no great difference between them. By a Law of Thought we mean a certain uniformity or agreement which exists and must exist in the modes in which all persons think and reason, so long as they do not make what we call mistakes, or fall into self-contradiction and fallacy. The laws of thought are natural laws with which we have no power to interfere, and which are of course not to be in any way confused with the artificial laws of a country, which are invented by men and can be altered by them. Every science is occupied in detecting and describing the natural laws which are inflexibly observed by the objects treated in the Science. The science of astronomy investigates the uniform or similar way in which the heavenly bodies, and in fact all material substances, tend to fall towards each other as a stone falls towards the earth, or to move round each other under the influence of this tendency. The universal law of gravitation is thus the natural law or uniformity treated in physical astronomy. In chemistry the law of equivalent proportions describes the well ascertained fact that each chemical substance enters into combination with every other chemical substance only in certain definite proportions; as when exactly eight parts by weight of oxygen unite with one part of hydrogen to form water, or sixteen parts of oxygen and six parts of carbon unite to form carbonic acid in the ordinary burning of a flame or fire. Whenever we can detect uniformities or similarities we so far create science and arrive at natural laws. But there may be, and are, many things so fickle, complicated, and uncertain, that we can never be sure we have detected laws that they will uniformly obey; in such cases no science, in the proper sense of the word, is possible. There is no such thing, for instance, as a real science of human character, because the human mind is too variable and complicated a subject of investigation. There are no two persons so much alike that you may be sure of one acting in all circumstances as the other would; it thus becomes impossible to arrange persons in classes so that all who are in the same class shall act uniformly in the same manner in any given circumstances. But there is a science of human reason or thought apart from the many other acts of mind which belong to human character, because there are modes in which all persons do uniformly think and reason, and must think and reason. Thus if two things are identical with a third common thing they are identical with each other. This is a law of thought of a very simple and obvious character, and we may observe concerning it,— I. That all people think in accordance with it, and agree that they do so as soon as they understand its meaning. 2. That they think in accordance with it whatever may be the subject about which they are thinking. Thus if the things considered are— London, The Metropolis, The most populous city in Great Britain, since "the Metropolis is identical with London," and "London is identical with the most populous city in Great Britain," it follows necessarily in all minds that "the metropolis is identical with the most populous city in Great Britain." Again, if we compare the three following things Iron, The most useful metal, The cheapest metal,— and it be allowed that "The most useful metal is Iron," and "Iron is the cheapest metal," it follows necessarily in all minds that "the most useful metal is the cheapest." We here have two examples of the general truth that things identical with the same thing are identical with each other; and this we may say is a general or necessary form of thought and reasoning. Compare, again, the following three things,— The earth, Planets, Bodies revolving in elliptic orbits. We cannot say, as before, that "the earth is identical with the planets;" it is identical only with one of the |