Imperfect Concepts.
It is said that outside of strictly scientific definitions very few persons agree in their concepts of the same thing. Each has his or her own concept of the particular thing which he or she expresses by the same term. A number of persons asked to define a common term like "love," "religion," "faith," "belief," etc., will give such a variety of answers as to cause wonderment. As Green says: "My idea or image is mine alone—the reward of careless observation if imperfect; of attentive, careful, and varied observation if correct. Between mine and yours a great gulf is fixed. No man can pass from mine to yours, or from yours to mine. Neither in any proper sense of the term can mine be conveyed to you. Words do not convey thoughts; they are not vehicles of thoughts in any true sense of that term. A word is simply a common symbol which each associates with his own idea or image."
The reason of the difference in the concepts of several persons is that very few of our concepts are nearly perfect; the majority of them are quite imperfect and incomplete. Jevons gives us an idea of this in his remarks on classification: "Things may seem to be very much like each other which are not so. Whales, porpoises, seals, and several other animals live in the sea exactly like a fish; they have a similar shape and are usually classed among fish. People are said to go whale fishing. Yet these animals are not really fish at all, but are much more like dogs and horses and other quadrupeds than they are like fish. They cannot live entirely under water and breathe the air contained in the water like fish, but they have to come to the surface at intervals to take breath. Similarly, we must not class bats with birds because they fly about, although they have what would be called wings; these wings are not like those of birds, and, in truth, bats are much more like rats and mice than they are like birds. Botanists used at one time to classify plants according to their size, as trees, shrubs, or herbs, but we now know that a great tree is often more similar in character to a tiny herb than it is to other great trees. A daisy has little resemblance to a great Scotch thistle; yet the botanist regards them as very similar. The lofty growing bamboo is a kind of grass, and the sugar cane also belongs to the same class with wheat and oats."
It is a matter of importance that clear concepts should be formed regarding at least the familiar things of life. The list of clear concepts should be added to from time to time by study, investigation, and examination. The dictionary should be consulted frequently, and a term studied until one has a clear meaning of the concept the term seeks to express. A good encyclopedia (not necessarily an expensive one, in these days of cheap editions) will also prove very useful in this respect. As Halleck says: "It must be borne in mind that most of our concepts are subject to change during our entire life; that at first they are made only in a tentative way; that experience may show us, at any time, that they have been erroneously formed, that we have abstracted too little or too much, made the class too wide or too narrow, or that here a quality must be added or there one taken away."
It is a good practice to make a memorandum of anything of which you may hear, but of which you know nothing, and then later to make a brief but thorough investigation of that thing, by means of the dictionary and encyclopedia, and of whatever good works may be obtained on the subject, not leaving it until you feel that you have obtained at least a clear idea of what the thing really means. A half hour each evening devoted to exercise of this kind will result in a wonderful increase of general information. We have heard of a man who made a practice of reading a short article in the encyclopedia every evening, giving preference to subjects generally classed as familiar. In a year he made a noticeable advance in general knowledge as well as habits of thought. In five years he was looked upon by his associates as a man of a remarkably large field of general information and of more than ordinary intelligence, which verdict was a just one. As a rule we waste far more time on worthless fiction than we are willing to devote to a little self-improvement of this kind. We shrink at the idea of a general course of instructive reading, little realizing that we can take our study in small installments and at a very little cost in time or labor.
Our concepts form the material which our intellect uses in its reasoning processes. No matter how good a reasoner one may be, unless he has a good supply of general information about the things of which he is reasoning, he will not make much real headway. We must begin at the bottom and build a firm foundation upon which the intellectual structure may be erected. This foundation is composed of facts. These facts are represented by our clear and correct concepts.
CHAPTER XXIII.
Judgments.
WE have seen the several steps of the mental process whereby simple sensations are transformed into percepts and then into concepts or general ideas. The formation of the concept is considered as the first great step in thinking. The second great step in thinking is that of the formation of the "judgment." The definition of "judgment," as the term is used in logic; is "the comparing together in the mind of two ideas of things, and determining whether they agree or disagree with each other, or that one of them does or does not belong to the other. Judgment is, therefore, (a) affirmative or (b) negative, as (a) 'Snow is white,' or (b) 'All white men are not Europeans.'"
What in logic is called a "proposition" is the expression in words of a logical judgment. Hyslop defined the term "proposition" as follows: "Any affirmation or denial of an agreement between two conceptions." For instance, we compare the concepts "sparrow" and "bird" and find that there is an agreement, and that the former belongs to the latter; this mental process is a judgment. We then announce the judgment in the proposition: "The sparrow is a bird." In the same way we compare the concepts "bat" and "bird," find that there is a disagreement, and form the judgment that neither belongs to the other, which we express in the proposition: "The bat is not a bird." Or we may form the judgment that "sweetness" is a quality of "sugar," which we express in the proposition: "Sugar is sweet." Likewise, we may form the judgment which results in the proposition: "Vinegar is not sweet."
While the process of judgment is generally considered as constituting the second great step of thinking, coming after the formation of the concept, and consisting of the comparing of concepts, it must be remembered that the act of judging is far more elementary than this, for it is found still farther back in the history of thought processes. By that peculiar law of paradox which we find everywhere operative in mind processes, the same process of forming judgments which is used in comparing concepts also has been used in forming the same concepts in the stage of comparison. In fact, the result of all comparison, high or low, must be a judgment.
Halleck says: "Judgment is necessary in forming concepts. When we decide that a quality is or is not common to a class, we are really judging. This is another evidence of the complexity and unified action of the mind." Brooks says: "The power of judgment is of great value in its products. It is involved in or accompanies every act of the intellect, and thus lies at the foundation of all intellectual activity. It operates directly in every act of the understanding, and even aids the other faculties of the mind in completing their activities and products. * * * Strictly speaking, every intelligent act of the mind is accompanied with a judgment. To know is to discriminate and, therefore, to judge. Every sensation or cognition involves a knowledge and so a judgment that it exists. The mind cannot think at all without judging; to think is to judge. Even in forming the notions which judgment compares, the mind judges. Every notion or concept implies a previous act of judgment to form it; in forming a concept we compare the common attributes before we unite them, and comparison is judgment. It is thus true that 'Every concept is a contracted judgment; every judgment an expanded concept.'"
It is needless to say that as judgments lie at the base of our thinking, and also appear in every part of its higher structure, the importance of correct judgment in thought cannot be overestimated. But it is often very difficult to form correct judgment even regarding the most familiar things around us. Halleck says: "In actual life things present themselves to us with their qualities disguised or obscured by other conflicting qualities. Men had for ages seen burning substances and had formed a concept of them. A certain hard, black, stony substance had often been noticed, and a concept had been formed of it. This concept was imperfect; but it is very seldom that we meet with perfect, sharply-defined concepts in actual life. So it happened that for ages the concept of burning substance was never linked by judgment to the concept of stone coal. The combustible quality in the coal was overshadowed by its stony attributes. 'Of course stone will not burn,' people said. One cannot tell how long the development of mankind was retarded for that very reason. England would not to-day be manufacturing products for the rest of the world had not some one judged coal to be a combustible substance. * * * Judgment is ever silently working and comparing things that to past ages seemed dissimilar; and it is constantly abstracting and leaving out of the field of view those qualities which have simply served to obscure the point at issue."
Gordy says: "The credulity of children is proverbial; but if we get our facts at first hand, if we study 'the living, learning, playing child,' we shall see that he is quite as remarkable for incredulity as for credulity. The explanation is simple: He tends to believe the first suggestion that comes into his mind, no matter from what source; and since his belief is not the result of any rational process, he cannot be made to disbelieve it in any rational way. Hence it is that he is very credulous about any matter about which he has no ideas; but let the idea once get possession of his mind, and he is quite as remarkable for incredulity as before for credulity. * * * If we study the larger child,—the man with a child's mind, an uneducated man,—we shall have the same truth forced upon us. If the beliefs of men were due to processes of reasoning, where they have not reasoned they would not believe. But do we find it so? Is it not true that the men who have the most positive opinions on the largest variety of subjects—so far as they have ever heard of them—are precisely those who have the least right to them? Socrates, we remember, was counted the wisest man in Athens because he alone resisted his natural tendency to believe in the absence of evidence; he alone would not delude himself with the conceit of knowledge without the reality; and it would scarcely be too much to say that the intellectual strength of men is in direct proportion to the number of things they are absolutely certain of. * * * I do not, of course, mean to intimate that we should have no opinions about matters that we have not personally investigated. We take, and ought to take, the opinion of some men about law, and others about medicine, and others about particular sciences, and so on. But we should clearly realize the difference between holding an opinion on trust and holding it as the result of our own investigations."
Brooks says: "It should be one of the leading objects of the culture of young people to lead them to acquire the habit of forming judgments. They should not only be led to see things but to have opinions about things. They should be trained to see things in their relations and to put these relations into definite propositions. Their ideas of objects should be worked up into thoughts concerning the objects. Those methods of teaching are best which tend to excite a thoughtful habit of mind that notices the similitudes and diversities of objects and endeavors to read the thoughts which they embody and of which they are the symbols."
The study of logic, geometry, and the natural sciences is recommended for exercise of the faculty of judgment and the development thereof. The study and practice of even the lower branches of mathematics are also helpful in this direction. The game of checkers or chess is recommended by many authorities. Some have advocated the practice of solving enigmas, problems, rebuses, etc., as giving exercise to this faculty of the mind. The cultivation of the "Why?" attitude of mind, and the answering of one's own mental questions, is also helpful, if not carried to excess. "Doubting Thomas" is not always a term of reproach in these days of scientific habits of thought, and "the man from Missouri" has many warm admirers.
CHAPTER XXIV.
Primary Laws of Thought.
IN connection with this subject we herewith call the attention of the student to the well-known Primary Laws of Thought which have been recognized as valid from the time of the ancient Greek logicians. These laws are self-evident, and are uncontradictable. They are axiomatic. Jevons says of them: "Students are seldom able to see at first their full meaning and importance. All arguments may be explained when these self-evident laws are granted; and it is not too much to say that the whole of logic will be plain to those who will constantly use these laws as their key." Here are the Three Primary Laws of Thought:—
I. Law of Identity. "Whatever is, is."
II. Law of Contradiction. "Nothing can both be and not be."
III. Law of Excluded Middle. "Everything must either be or not be; there is no middle course."
I. The first of these laws, called "The Law of Identity," informs us that a thing is always itself, no matter under what guise or form it is perceived or may present itself. An animal is always a bird if it possesses the general characteristics of a "bird," no matter whether it exhibits the minor characteristics of an eagle, a wren, a stork, or a humming bird. In the same way a whale is a mammal because it possesses the general characteristics of a mammal notwithstanding that it swims in the water like a fish. Also, sweetness is always sweetness, whether manifested in sugar, honey, flowers, or products of coal tar. If a thing is that thing, then it is, and it cannot be logically claimed that it is not.
II. The second of these laws, called "The Law of Contradiction," informs us that the same quality or class cannot be both affirmed and denied of a thing at the same time and place. A sparrow cannot be said to be both "bird" and "not bird" at the same time. Neither can sugar be said to be "sweet" and "not sweet" at the same time. A piece of iron may be "hot" at one end and "not hot" at another, but it cannot be both "hot" and "not hot" at the same place at the same time.
III. The third of these laws, called "The Law of Excluded Middle," informs us that a given quality or class must be affirmed or denied to everything at any given time and place. Everything either must be of a certain class or not, must possess a certain quality or not, at a given time or place. There is no other alternative or middle course. It is axiomatic that any statement must either be or not be true of a certain other thing at any certain time and place; there is no escape from this. Anything either must be "black" or "not black," a bird or not a bird, alive or not alive, at any certain time or place. There is nothing else that it can be; it cannot both be and not be at the same time and place, as we have seen; therefore, it must either be or not be that which is asserted of it. The judgment must decide which alternative; but it has only two possible choices.
But the student must not confuse opposite qualities or things with "not-ness." A thing may be "black" or "not black," but it need not be white to be "not black," for blue is likewise "not black" just as it is "not white." The neglect of this fact frequently causes error. We must always affirm either the existence or non-existence of a quality in a thing; but this is far different from affirming or denying the existence of the opposite quality. Thus a thing may be "not hard" and yet it does not follow that it is "soft"; it may be neither hard nor soft.