Ontario. Department of Education

Nature of Thinking.—In the study of general method, as well as in that of the foregoing mental processes, it has been taken for granted that our minds are capable of identifying different objects on the basis of some common feature or features. This tendency of the mind to identify objects and group individual things into classes, depends upon its capacity to detect similarity and difference, or to make comparisons. When the mind, in identifying objects, events, qualities, etc., discovers certain relations between its various states, the process is especially known as that of thinking. In its technical sense, therefore, thought implies a more or less explicit apprehension of relation.

Thinking Involved in all Conscious States.—It is evident, however, that every mental process must involve thinking, or a grasping of relations. When, by my merely touching an object, my mind perceives it is an apple, this act of perception, as already seen, takes place because elements of former experience come back as associated factors. This implies, evidently, that the mind is here relating elements of its past experience with the present touch sensation. Perception of external objects, therefore, implies a grasping of relations. In the same way, if, in having an experience to-day, one recognizes it as identical with a former experience, he is equally grasping a relation. Every act of memory, therefore, implies thinking. Thus in all forms of knowledge the mind is apprehending relations; for no experience could have meaning for the mind except as it is discriminated from other experiences. In treating thinking as a distinct mental process, however, it is assumed that the objects of sense perception, memory, etc., are known as such, and that the mind here deals more directly with the relations in which ideas stand one to another. As a mental process, thinking appears in three somewhat distinct forms, known as conception, judgment, and reasoning.

CONCEPTION

The Abstract Notion.—It was seen that at least in adult life, the perception of any object, as this particular orange, horse, cow, etc., really includes a number of distinct images of quality synthesised into the unity of a particular idea or experience. Because of this union of a number of different sensible qualities in the notion of a single individual, the mind may limit its attention upon a particular quality, or characteristic, possessed by an object, and make this a distinct problem of attention. Thus the mind is able to form such notions as length, roundness, sweetness, heaviness, four-footedness, etc. When such an attribute is thought of as something distinct from the object, the mental image is especially known as an abstract idea, or notion, and the process as one of abstraction.

The Class Notion.—One or more of such abstracted qualities may, moreover, be recognized as common to an indefinite number of objects. For instance, in addition to its ability to abstract from the perception of a dog, the abstract notions four-footedness, hairy, barking, etc., the mind further gives them a general character by thinking of them as qualities common to an indefinite number of other possible individuals, namely, the class four-footed, hairy, barking objects. Because the idea representing the quality or qualities is here accepted by the mind as a means of identifying a number of objects, the idea is spoken of as a class notion, and the process as one of classification, or generalization. Thus it appears that, through its ability to detect sameness and difference, or discover relations, the mind is able to form two somewhat different notions. By mentally abstracting any quality and regarding it as something distinct from the object, it obtains an abstract notion, as sweetness, bravery, hardness, etc.; by synthesising and symbolizing the images of certain qualities recognized in objects, it obtains a general, or class, notion by which it may represent an indefinite number of individual things as, triangle, horse, desert, etc. Thus abstract notions are supposed to represent qualities; class notions, things. Because of its reference to a number of objects, the class notion is spoken of especially as a general notion, and the process of forming the notion as one of generalization. These two types of notions are technically known as concepts, and the process of their formation as one of conception.

Formal Analysis of Process.—At this point may be recalled what was stated in Chapter XV concerning the development of a class notion. Mention was there made of the theory that in the formation of such concepts, or class notions, as cow, dog, desk, chair, adjective, etc., the mind must proceed through certain set stages as follows:

1. Comparison: The examination of a certain number of particular individuals in order to discover points of similarity and difference.

2. Abstraction: The distinguishing of certain characteristics common to the objects.

3. Generalization: The mental unification, or synthesis, of these common characteristics noted in different individuals into a class notion represented by a name, or general term.

But Conception is Involved in Perception.—From what has been seen, however, it is evident that the development of our concepts does not proceed in any such formal way. If the mind perceives an individual object with any degree of clearness, it must recognize the object as possessing certain qualities. If, therefore, the child can perceive such an object as a dog, it implies that he recognizes it, say, as a hairy, four-footed creature. To recognize these qualities, however, signifies that the mind is able to think of them as something apart from the object, and the child thus has in a sense a general notion even while perceiving the particular dog. Whenever he passes to the perception of another dog, he undoubtedly interprets this with the general ideas already obtained from this earlier percept of a dog. To say, therefore, that to gain a concept he compares the qualities found in several individual things is not strictly true, for if his first percept becomes a type by which he interprets other dogs, his first experience is already a concept. What happens is that as this concept is used to interpret other individuals, the person becomes more conscious of the fact that his early experience is applicable to an indefinite number of objects. So also, when an adult first perceives an individual thing, say the fruit of the guava, he must apprehend certain qualities in relation to the individual thing. Thereupon his idea of this particular object becomes in itself a copy for identifying other objects, or a symbol by which similar future impressions may be given meaning. In this sense the individual idea, or percept, will serve to identify other particular experiences. Such being the case, this early concept of the guava has evidently required no abstraction of qualities beyond apprehending them while perceiving the one example of the fruit. This, however, is but to say that the perception of the guava really implied conception.

Comparison of Individuals Necessary for Correct Concepts.—It is, of course, true that the correctness of the idea as a class symbol can be verified only as we apply it in interpreting a number of such individual things. As the person meets a further number of individuals, he may even discover the presence of qualities not previously recognized. A child, for instance, may have a notion of the class triangle long before he discovers that all triangles have the property of containing two right angles. When this happens, he will later modify his first concept by synthesising into it the newly discovered quality. Moreover, if certain features supposed to be common are later found to be accidental, if, for instance, a child's concept of the class fish includes the quality always living in water, his meeting with a flying fish will not result in an utterly new concept, but rather in a modification of the present one. Thus the young child, who on seeing the Chinese diplomat, wished to know where he had his laundry, was not without a class concept, although that concept was imperfect in at least one respect.

Concept and Term.—A point often discussed in connection with conception is whether a general notion can be formed without language. By some it is argued that no concept could exist in the mind without the name, or general term. It was seen, however, that our first perception of any object becomes a sort of standard by which other similar experiences are intercepted, and is, therefore, general in character. From this it is evident that a rudimentary type of conception exists prior to language. In the case of the young child, as he gains a mental image of his father, the experience evidently serves as a centre for interpreting other similar individuals. We may notice that as soon as he gains control of language, other men are called by the term papa. This does not imply an actual confusion in identity, but his use of the term shows that the child interprets the new object through a crude concept denoted by the word papa. It is more than probable, moreover, that this crude concept developed as he became able to recognize his father, and had been used in interpreting other men before he obtained the term, papa. On the other hand, it is certain that the term, or class name, is necessary to give the notion a definite place in consciousness.

FACTORS INVOLVED IN CONCEPT

It will appear from the foregoing that a concept presents the following factors for consideration:

1. The essential quality or qualities found in the individual things, and supposed to be abstracted sooner or later from the individuals.

2. The concept itself, the mental image or idea representative of the abstracted quality; or the unification of a number of abstracted qualities, when the general notion implies a synthesis of different qualities.

3. The general term, or name.

4. The objects themselves, which the mind can organize into a class, because they are identified as possessing common characteristics. When, however, a single abstracted quality is taken as a symbol of a class of objects, for example, when the quality bitterness becomes the symbol for the class of bitter things, there can be no real distinction between the abstracted quality and the class concept. In other words, to fix attention upon the quality bitterness as a quality distinct from the object in which it is found, is at the same time to give it a general character, recognizing it as something which may be found in a number of objects—the class bitter things. Here the abstract term is in a sense a general notion representative of a whole class of objects which agree in the possession of the quality.

Intension of Concepts.—Certain of our general notions are, however, much more complex than others. When a single attribute such as four-footedness is generalized to represent the class four-footed objects, the notion itself is relatively simple. In other words, a single property is representative of the objects, and in apprehending the members of the class all other properties they chance to possess may be left out of account. In many cases, however, the class notion will evidently be much more complex. The notion dog, for instance, in addition to implying the characteristic four-footedness, may include such qualities as hairy, barking, watchful, fearless, etc. This greater or less degree of complexity of a general notion is spoken of as its intensity. The notion dog, for instance, is more intensive than the notion four-footed animals; the notion lawyer, than the notion man.

Extension of Concepts.—It is to be noted further that as a notion increases in intension it becomes limited to a smaller class of objects. From this standpoint, notions are said to differ in extension. The class lawyer, for instance, is not so extensive as the class man; nor the class dog, as the class four-footed objects. It will appear from the above that an abstract notion viewed as a sign of a class of objects is distinguished by its extension, while a class notion, so far as it implies a synthesis of several abstracted qualities, is marked rather by its intension.

AIMS OF CONCEPTUAL LESSONS

So far as school lessons aim to establish and develop correct class notions in the minds of the pupils, three somewhat distinct types of work may be noted:

1. TO DEFINE CLASSES

In some lessons no attempt is made to develop an utterly new class notion, or concept; the pupils in fact may already know the class of objects in a general way and be acquainted with many of their characteristics. The object of the lesson is, therefore, to render the concept more scientific by having it include the qualities which essentially mark it as a class and especially separate it from other co-ordinate classes. In studying the grasshopper; for instance, in entomology, the purpose is not to give the child a notion of the insect in the ordinary sense of the term. This the pupil may already have. The purpose is rather to enable him to decide just what general characteristics distinguish this from other insects. The lesson may, therefore, leave out of consideration features which are common to all grasshoppers, simply because they do not enter into a scientific differentiation of the class.

2. TO ENLARGE A CONCEPT

In many lessons the aim seems to be chiefly to enlarge certain concepts by adding to their intensiveness. The pupil, for instance, has a scientific concept of a triangle, that is, one which enables him to distinguish a triangle from any other geometrical figure. He may, however, be led to see further that the three angles of every triangle equal two right angles. This is really having him discover a further attribute in relation to triangles, although this knowledge is not essential to the concept as a symbol of the members of the class. In the same way, in grammar the pupil is taught certain attributes common to verbs, as mood and tense, although these are not essential attributes from the standpoint of distinguishing the verb as a special class of words.

3. TO BUILD UP NEW CONCEPTS

A. Presentation of Unknown Individuals.—In many lessons the chief object seems to be, however, to build up a new concept in the mind of the child. This would be the case when the pupil is presented with a totally unknown object, say a platypus, and called upon to examine its characteristics. In such lessons two important facts should be noticed. First, the child finds seemingly little difficulty in accepting a single individual as a type of a class, and is able to carry away from the lesson a fairly scientific class notion through a study of the one individual. In this regard the pupil but illustrates what has been said of the ability of the child to use his early percepts as standards to interpret other individuals. The pupil is able the more easily to form this accurate notion, because he no doubt has already a store of abstract notions with which to interpret the presentation, and also because his interest and attention is directed into the proper channels by the teacher.

B. Division of Known Classes.—A second common mode of developing new concepts in school work is in breaking up larger classes into co-ordinate sub-classes. This, of course, involves the developing of new concepts to cover these sub-classes. In such cases, however, the new notions are merely modified forms of the higher class notion. When, for example, the pupil gains general notions representative of the classes, proper noun and common noun, the new terms merely add something to the intension of the more extensive term noun. This will be evident by considering the difference between the notions noun and proper noun. Both agree in possessing the attribute used to name. The latter is more intensive, however, because it signifies used to name a particular object. Although in such cases the lesson seems in a sense to develop new general notions, they represent merely an adding to the intension of a notion already possessed by the child.

Use of the Term.—A further problem regarding the process of conception concerns the question of the significance of a name. When a person uses such a term as dog, whale, hepatica, guava, etc., to name a certain object, what is the exact sense, or meaning, in which the name is to be applied? A class name, when applied scientifically to an object, is evidently supposed to denote the presence in it of certain essential characteristics which belong to the class. It is clear, however, that the ordinary man rarely uses these names with any scientific precision. A man can point to an object and say that it is a horse, and yet be ignorant of many of the essential features of a horse. In such cases, therefore, the use of the name merely shows that the person considers the object to belong to a certain class, but is no guarantee that he is thinking of the essential qualities of the class. It might be said, therefore, that a class term is used for two somewhat different purposes, either to denote the object merely, or to signify scientifically the attributes possessed by the object. It is in the second respect that danger of error in reasoning arises. So far as a name represents the attributes of a class, it will signify for us just those attributes which we associate with that class. So long, therefore, as the word fish means to us an animal living in the water, we will include in the class the whale, which really does not belong to the class, and perhaps exclude from the class the flying fish, although it is scientifically a member of the class.

THE DEFINITION

It has been noted that, when man discovers common characteristics in a number of objects, he tends on this basis to unite such objects into a class. It is to be noted in addition, however, that in the same manner he is also able, by examining the characteristics of a large class of objects, to divide these into smaller sub-classes. Although, for example, we may place all three-sided figures into one class and call them triangles, we are further able to divide these into three sub-classes owing to certain differences that may be noted among them. Thus an important fact regarding classification is that while a class may possess some common quality or qualities, yet its members may be further divided into sub-classes and each of these smaller classes distinguished from the others by points of difference. Owing to this fact, there are two important elements entering into a scientific knowledge of any class, first, to know of what larger class it forms a part, and secondly, to know what characteristics distinguish it from the other classes which go with it to make up this larger class. To know the class equilateral triangle, for instance, we must know, first, that it belongs to the larger class triangle, and secondly, that it differs from other classes of triangles by having its three sides equal. For this reason a person is able to know a class scientifically without knowing all of its common characteristics. For instance, the large class of objects known as words is subdivided into smaller classes known as parts of speech. Taking one of these classes, the verb, we find that all verbs agree in possessing at least three common characteristics, they have power to assert, to denote manner, and to express time. To distinguish the verb, however, it is necessary to note only that it is a word used to assert, since this is the only characteristic which distinguishes it from the other classes of words. When, therefore, we describe any class of objects by first naming the larger class to which it belongs, and then stating the characteristics which distinguish it from the other co-ordinate classes, we are said to give a definition of the class, or to define it. The statement, "A trimeter is a verse of three measures," is a definition because it gives, first, the larger class (verse) to which the trimeters belong, and secondly, the difference (of three measures) which distinguishes the trimeter from all other verses. The statement, "A binomial is an algebraic expression consisting of two terms," is a definition, because it gives, first, the larger class (algebraic expression) to which binomials belong, and secondly, the difference (consisting of two terms) which distinguishes binomials from other algebraic expressions.

JUDGMENT

Nature of Judgment.—A second form, or mode, of thinking is known as judgment. Our different concepts were seen to vary in their intension, or meaning, according to the number of attributes suggested by each. My notion triangle may denote the attributes three-sided and three-angled; my notion isosceles triangle will in that case include at least these two qualities plus equality of two of the sides. This indicates that various relations exist between our ideas and may be apprehended by the mind. When a relation between two concepts is distinctly apprehended in thought, or, in other words, when there is a mental assertion of a union between two ideas, or objects of thought, the process is known as judgment. Judgment may be defined, therefore, as the apprehension, or mental affirmation, of a relation between two ideas. If the idea, or concept, heaviness enters as a mental element into my idea stone, then the mind is able to affirm a relation between these concepts in the form, "Stone is heavy." In like manner when the mind asserts, "Glass is transparent" or "Horses are animals," there is a distinct apprehension of a relation between the concepts involved.

Judgment Distinguished from Statement.—It should be noted that judgment is the mental apprehension of a relation between ideas. When this relation is expressed in actual words, it is spoken of as a proposition, or a predication. A proposition is, therefore, the statement of a judgment. The proposition is composed of two terms and the copula, one term constituting the subject of the proposition and the other the predicate. Although a judgment may often be expressed in some other form, it can usually be converted into the above form. The proposition, "Horses eat oats," may be expressed in the form, "Horses are oat-eaters"; the proposition, "The sun melts the snow," into the form, "The sun is a-thing-which-melts-snow."

Relation of Judgment to Conception.—It would appear from the above examples that a judgment expresses in an explicit form the relations involved within the concept, and is, therefore, merely a direct way of indicating the state of development of any idea. If my concept of a dog, for example, is a synthesis of the qualities four-footed, hairy, fierce, and barking, then an analysis of the concept will furnish the following judgments:

Because in these cases a concept seems necessary for an act of judgment, it is said that judgment is a more advanced form of thinking than conception. On the other hand, however, judgment is implied in the formation of a concept. When the child apprehends the dog as a four-footed object, his mind has grasped four-footedness as a quality pertaining to the strange object, and has, in a sense, brought the two ideas into relation. But while judgment is implied in the formation of the concept, the concept does not bring explicitly to the mind the judgments it implies. The concept snow, for instance, implies the property of whiteness, but whiteness must be apprehended as a distinct idea and related mentally with the idea snow before we can be said to have formed, or thought, the judgment, "Snow is white." Judgment is a form of thinking separate from conception, therefore, because it does thus bring into definite relief relations only implied in our general notions, or concepts. One value of judgment is, in fact, that it enables us to analyse our concepts, and thus note more explicitly the relations included in them.

Universal and Particular Judgments.—Judgments are found to differ also as to the universality of their affirmation. In such a judgment as "Man is mortal," since mortality is viewed as a quality always joined to manhood, the affirmation is accepted as a universal judgment. In such a judgment as "Men strive to subdue the air," the two objects of thought are not considered as always and necessarily joined together. The judgment is therefore particular in character. All of our laws of nature, as "Air has weight," "Pressure on liquids is transmitted in every direction," or "Heat is conducted by metals," are accepted as universal judgments.

Errors in Judgment due to: A. Faulty Concepts.—It may be seen from the foregoing that our judgments, when explicitly grasped by the mind and predicated in language, reflect the accuracy or inaccuracy of our concepts. Whatever relations are, as it were, wrapped up in a concept may merge at any time in the form of explicit judgments. If the fact that the only Chinamen seen by a child are engaged in laundry work causes this attribute to enter into his concept Chinaman, this will lead him to affirm that the restaurant keeper, Wan Lee, is a laundry-man. The republican who finds two or three cases of corruption among democrats, may conceive corruption as a quality common to democrats and affirm that honest John Smith is corrupt. Faulty concepts, therefore, are very likely to lead to faulty judgments. A first duty in education is evidently to see that children are forming correct class concepts. For this it must be seen that they always distinguish the essential features of the class of objects they are studying. They must learn, also, not to conclude on account of superficial likeness that really unlike objects belong to the same class. The child, for instance, in parsing the sentence, "The swing broke down," must be taught to look for essential characteristics, and not call the word swing a gerund because it ends in "ing"; which, though a common characteristic of gerunds, does not differentiate it from other classes of words. So, also, when the young nature student notes that the head of the spider is somewhat separated from the abdomen, he must not falsely conclude that the spider belongs to the class insects. In like manner, the pupil must not imagine, on account of superficial differences, that objects really the same belong to different classes, as for example, that a certain object is not a fish, but a bird, because it is flying through the air; or that a whale is a fish and not an animal, because it lives in water. The pupil must also learn to distinguish carefully between the particular and universal judgment. To affirm that "Men strive to subdue the air," does not imply that "John Smith strives to subdue the air." The importance of this distinction will be considered more fully in our next section.

B. Feeling.—Faulty concepts are not, however, the only causes for wrong judgments. It has been noted already that feeling enters largely as a factor in our conscious life. Man, therefore, in forming his judgments, is always in danger of being swayed by his feelings. Our likes and dislikes, in other words, interfere with our thinking, and prevent us from analysing our knowledge as we should. Instead, therefore, of striving to develop true concepts concerning men and events and basing our judgments upon these, we are inclined in many cases to allow our judgments to be swayed by mere feeling.

C. Laziness.—Indifference is likewise a common source of faulty judgments. To attend to the concept and discover its intension as a means for correct judgment evidently demands mental effort. Many people, however, prefer either to jump at conclusions or let others do their judging for them.

Sound Judgments Based on Scientific Concepts.—To be able to form correct judgments regarding the members of any class, however, the child should know, not only its common characteristics, but also the essential features which distinguish its members from those of co-ordinate classes. To know adequately the equilateral triangle, for instance, the pupil must know both the features which distinguish it from other triangles and also those in which it agrees with all triangles. To know fully the mentha family of plants, he must know both the characteristic qualities of the family and also those of the larger genus labiatae. From this it will be seen that a large share of school work must be devoted to building up scientific class notions in the minds of the pupils. Without this, many of their judgments must necessarily be faulty. To form such scientific concepts, however, it is necessary to relate one concept with another in more indirect ways than is done through the formation of judgments. This brings us to a consideration of reasoning, the third and last form of thinking.

REASONING

Nature of Reasoning.—Reasoning is defined as a mental process in which the mind arrives at a new judgment by comparing other judgments. The mind, for instance, is in possession of the two judgments, "Stones are heavy" and "Flint is a stone." By bringing these two judgments under the eye of attention and comparing them, the mind is able to arrive at the new judgment, "Flint is heavy." Here the new judgment, expressing a relation between the notions, flint and heavy, is supposed to be arrived at, neither by direct experience, nor by an immediate analysis of the concept flint, but more indirectly by comparing the other judgments. The judgment, or conclusion, is said, therefore, to be arrived at mediately, or by a process of reasoning. Reasoning is of two forms, deductive, or syllogistic, reasoning, and inductive reasoning.

DEDUCTION

Nature of Deduction.—In deduction the mind is said to start with a general truth, or judgment, and by a process of reasoning to arrive at a more particular truth, or judgment, thus:

Expressed in this form, the reasoning process, as already mentioned, is known as a syllogism. The whole syllogism is made up of three parts, major premise, minor premise, and conclusion. The three concepts involved in the syllogism are known as the major, the minor, and the middle term. In the above syllogism, heavy, the predicate of the major premise, is the major term; flint, the subject of the minor premise, is the minor term; and stone, to which the other two are related in the premises, is known as the middle term. Because of this previous comparison of the major and the minor terms with the middle term, deduction is sometimes said to be a process by which the mind discovers a relation between two concepts by comparing them each with a third concept.

Purpose of Deduction.—It is to be noted, however, as pointed out in Chapter XV, that deductive reasoning takes place normally only when the mind is faced with a difficulty which demands solution. Take the case of the boy and his lost coin referred to in Chapter II. As he faces the problem, different methods of solution may present themselves. It may enter his mind, for instance, to tear up the grate, but this is rejected on account of possible damage to the brickwork. Finally he thinks of the tar and resorts to this method of recovery. In both of the above cases the boy based his conclusions upon known principles. As he considered the question of tearing up the grate, the thought came to his mind, "Lifting-a-grate is a-thing-which-may-cause-damage." As he considered the use of the tar, he had in mind the judgment, "Adhesion is a property of tar," and at once inferred that tar would solve his problem. In such practical cases, however, the mind seems to go directly from the problem in hand to a conclusion by means of a general principle. When a woman wishes to remove a stain, she at once says, "Gasoline will remove it." Here the mind, in arriving at its conclusion, seems to apply the principle, "Gasoline removes spots," directly to the particular problem. Thus the reasoning might seem to run as follows:

Here the middle term of the syllogism seems to disappear. It is to be noted, however, that our thought changes from the universal idea "stains," mentioned in the statement of the principle, to the particular idea "this stain" mentioned in the problem and in the conclusion. But this implies a middle term, which could be expressed thus:

The syllogism is valuable, therefore, because it displays fully and clearly each element in the reasoning process, and thus assures the validity of the conclusion.

Deduction in School Recitation.—It will be recalled from what was noted in our study of general method, that deduction usually plays an important part during an ordinary developing lesson. In the step of preparation, when the pupil is given a particular example in order to recall old knowledge, the example suggests a problem which is intended to call up certain principles which are designed to be used during the presentation. In a lesson on the "Conjunctive Pronoun," for instance, if we have the pupil recall his knowledge of the conjunction by examining the particular word "if" in such a sentence as, "I shall go if they come," he interprets the word as a conjunction simply because he possesses a general rule applicable to it, or is able to go through a process of deduction. In the presentation also, when the pupil is called on to examine the word who in such a sentence as, "The man who met us is very old," and decides that it is both a conjunction and a pronoun, he is again making deductions, since it is by his general knowledge of conjunctions and pronouns that he is able to interpret the two functions of the particular word who. Finally, as already noted, the application of an ordinary recitation frequently involves deductive processes.

INDUCTION

Nature of Induction.—Induction is described as a process of reasoning in which the mind arrives at a conclusion by an examination of particular cases, or judgments. A further distinguishing feature of the inductive process is that, while the known judgments are particular in character, the conclusion is accepted as a general law, or truth. As in deduction, the reasoning process arises on account of some difficulty, or problem, presented to the mind, as for example:

To satisfy itself upon the problem, the mind appeals to actual experience either by ordinary observation or through experimentation. These observations or experiments, which necessarily deal with particular instances, are supposed to provide a number of particular judgments, by examining which a satisfactory conclusion is ultimately reached.

Example of Induction.—As an example of induction, may be taken the solution of such a problem as, "Does air exert pressure?" To meet this hypothesis we must evidently do more than merely abstract the manifest properties of an object, as is done in ordinary conception, or appeal directly to some known general principle, as is done in deduction. The work of induction demands rather to examine the two at present known but disconnected things, air and pressure, and by scientific observation seek to discover a relation between them. For this purpose the investigator may place a card over a glass filled with water, and on inverting it find that the card is held to the glass. Taking a glass tube and putting one end in water, he may place his finger over the other end and, on raising the tube, find that water remains in the tube. Soaking a heavy piece of leather in water and pressing it upon the smooth surface of a stone or other object, he finds the stone can be lifted by means of the leather. Reflecting upon each of these circumstances the mind comes to the following conclusions:

How Distinguished from, A. Deduction, and B. Conception.—Such a process as the above constitutes a process of reasoning, first, because the conclusion gives a new affirmation, or judgment, "Air exerts pressure," and secondly, because the judgment is supposed to be arrived at by comparing other judgments. As a process of reasoning, however, it differs from deduction in that the final judgment is a general judgment, or truth, which seems to be based upon a number of particular judgments obtained from actual experience, while in deduction the conclusion was particular and the major premise general. It is for this reason that induction is defined as a process of going from the particular to the general. Moreover, since induction leads to the formation of a universal judgment, or general truth, it differs from the generalizing process known as conception, which leads to the formation of a concept, or general idea. It is evident, however, that the process will enrich the concept involved in the new judgment. When the mind is able to affirm that air exerts pressure, the property, exerting-pressure, is at once synthesised into the notion air. This point will again be referred to in comparing induction and conception as generalizing processes.

In speaking of induction as a process of going from the particular to the general, this does not signify that the process deals with individual notions. The particulars in an inductive process are particular cases giving rise to particular judgments, and judgments involve concepts, or general ideas. When, in the inductive process, it is asserted that air holds the card to the glass, the mind is seeking to establish a relation between the notions air and pressure, and is, therefore, thinking in concepts. For this reason, it is usually said that induction takes for granted ordinary relations as involved in our everyday concepts, and concerns itself only with the more hidden relations of things. The significance of induction as a process of going from the particular to the general, therefore, consists in the fact that the conclusion is held to be a wider judgment than is contained in any of the premises.

Particular Truth Implies the General.—Describing the premises of an inductive process as particular truths, and the conclusion as a universal truth, however, involves the same fiction as was noted in separating the percept and the concept into two distinct types of notions. In the first place, my particular judgment, that air presses the card against the glass, is itself a deduction resting upon other general principles. Secondly, if the judgment that air presses the card against the glass contains no element of universal truth, then a thousand such judgments could give no universal truth. Moreover, if the mind approaches a process of induction with a problem, or hypothesis, before it, the general truth is already apprehended hypothetically in thought even before the particular instances are examined. When we set out, for instance, to investigate whether the line joining the bisecting points of the sides of a triangle is parallel with the base, we have accepted hypothetically the general principle that such lines are parallel with the base. The fact is, therefore, that when the mind examines the particular case and finds it to agree with the hypothesis, so far as it accepts this case as a truth, it also accepts it as a universal truth. Although, therefore, induction may involve going from one particular experiment or observation to another, it is in a sense a process of going from the general to the general.

That accepting the truth of a particular judgment may imply a universal judgment is very evident in the case of geometrical demonstrations. When it is shown, for instance, that in the case of the particular isosceles triangle ABC, the angles at the base are equal, the mind does not require to examine other particular triangles for verification, but at once asserts that in every isosceles triangle the angles at the base are equal.

Induction and Conception Interrelated.—Although as a process, induction is to be distinguished from conception, it either leads to an enriching of some concept, or may in fact be the only means by which certain scientific concepts are formed. While the images obtained by ordinary sense perception will enable a child to gain a notion of water, to add to the notion the property, boiling-at-a-certain-temperature, or able-to-be-converted-into-two-parts-hydrogen-and-one-part-oxygen, will demand a process of induction. The development of such scientific notions as oxide, equation, predicate adjective, etc., is also dependent upon a regular inductive process. For this reason many lessons may be viewed both as conceptual and as inductive lessons. To teach the adverb implies a conceptual process, because the child must synthesise certain attributes into his notion adverb. It is also an inductive lesson, because these attributes being formulated as definite judgments are, therefore, obtained inductively. The double character of such a lesson is fully indicated by the two results obtained. The lesson ends with the acquisition of a new term, adverb, which represents the result of the conceptual process. It also ends with the definition: "An adverb is a word which modifies a verb, adjective, or other adverb," which indicates the general truth or truths resulting from the inductive process.

Deduction and Induction Interrelated.—In our actual teaching processes there is a very close inter-relation between the two processes of reasoning. We have already noted on page 322 that, in such inductive lessons as teaching the definition of a noun or the rule for the addition of fractions, both the preparatory step and the application involve deduction. It is to be noted further, however, that even in the development of an inductive lesson there is a continual interplay between induction and deduction. This will be readily seen in the case of a pupil seeking to discover the rule for determining the number of repeaters in the addition of recurring decimals. When he notes that adding three numbers with one, one, and two repeaters respectively, gives him two repeaters in his answer, he is more than likely to infer that the rule is to have in the answer the highest number found among the addenda. So far as he makes this inference, he undoubtedly will apply it in interpreting the next problem, and if the next numbers have one, one, and three repeaters respectively, he will likely be quite convinced that his former inference is correct. When, however, he meets a question with one, two, and three repeaters respectively, he finds his former inference is incorrect, and may, thereupon, draw a new inference, which he will now proceed to apply to further examples. The general fact to be noted here, however, is that, so far as the mind during the examination of the particular examples reaches any conclusion in an inductive lesson, it evidently applies this conclusion to some degree in the study of the further examples, or thinks deductively, even during the inductive process.

Development of Reasoning Power.—Since reasoning is essentially a purposive form of thinking, it is evident that any reasoning process will depend largely upon the presence of some problem which shall stimulate the mind to seek out relations necessary to its solution. Power to reason, therefore, is conditioned by the ability to attend voluntarily to the problem and discover the necessary relations. It is further evident that the accuracy of any reasoning process must be dependent upon the accuracy of the judgments upon which the conclusions are based. But these judgments in turn depend for their accuracy upon the accuracy of the concepts involved. Correct reasoning, therefore, must depend largely upon the accuracy of our concepts, or, in other words, upon the old knowledge at our command. On the other hand, however, it has been seen that both deductive and inductive reasoning follow to some degree a systematic form. For this reason it may be assumed that the practice of these forms should have some effect in giving control of the processes. The child, for instance, who habituates himself to such thought processes as AB equals BC, and AC equals BC, therefore AB equals AC, no doubt becomes able thereby to grasp such relations more easily. Granting so much, however, it is still evident that close attention to, and accurate knowledge of, the various terms involved in the reasoning process is the sure foundation of correct reasoning.