§ 1. Introductory: The Meaning of Logical
Special topic of this chapter
In the preceding chapters we have considered (i) what thinking is; (ii) the importance of its special training; (iii) the natural tendencies that lend themselves to its training; and (iv) some of the special obstacles in the way of its training under school conditions. We come now to the relation of logic to the purpose of mental training.
Three senses of term logical The practical is the important meaning of logical
In its broadest sense, any thinking that ends in a conclusion is logical—whether the conclusion reached be justified or fallacious; that is, the term logical covers both the logically good and the illogical or the logically bad. In its narrowest sense, the term logical refers only to what is demonstrated to follow necessarily from premises that are definite in meaning and that are either self-evidently true, or that have been previously proved to be true. Stringency of proof is here the equivalent of the logical. In this sense mathematics and formal logic (perhaps as a branch of mathematics) alone are strictly logical. Logical, however, is used in a third sense, which is at once more vital and more practical; to denote, namely, the systematic care, negative and positive, taken to safeguard reflection so that it may yield the best results under the given conditions. If only the word artificial were associated with the idea of art, or expert skill gained through voluntary apprenticeship (instead of suggesting the factitious and unreal), we might say that logical refers to artificial thought.
Care, thoroughness, and exactness the marks of the logical
In this sense, the word logical is synonymous with wide-awake, thorough, and careful reflection—thought in its best sense (ante, p. 5). Reflection is turning a topic over in various aspects and in various lights so that nothing significant about it shall be overlooked—almost as one might turn a stone over to see what its hidden side is like or what is covered by it. Thoughtfulness means, practically, the same thing as careful attention; to give our mind to a subject is to give heed to it, to take pains with it. In speaking of reflection, we naturally use the words weigh, ponder, deliberate—terms implying a certain delicate and scrupulous balancing of things against one another. Closely related names are scrutiny, examination, consideration, inspection—terms which imply close and careful vision. Again, to think is to relate things to one another definitely, to "put two and two together" as we say. Analogy with the accuracy and definiteness of mathematical combinations gives us such expressions as calculate, reckon, account for; and even reason itself—ratio. Caution, carefulness, thoroughness, definiteness, exactness, orderliness, methodic arrangement, are, then, the traits by which we mark off the logical from what is random and casual on one side, and from what is academic and formal on the other.
Whole object of intellectual education is formation of logical disposition
False opposition of the logical and psychological
No argument is needed to point out that the educator is concerned with the logical in its practical and vital sense. Argument is perhaps needed to show that the intellectual (as distinct from the moral) end of education is entirely and only the logical in this sense; namely, the formation of careful, alert, and thorough habits of thinking. The chief difficulty in the way of recognition of this principle is a false conception of the relation between the psychological tendencies of an individual and his logical achievements. If it be assumed—as it is so frequently—that these have, intrinsically, nothing to do with each other, then logical training is inevitably regarded as something foreign and extraneous, something to be ingrafted upon the individual from without, so that it is absurd to identify the object of education with the development of logical power.
Opposing the natural to the logical
The conception that the psychology of individuals has no intrinsic connections with logical methods and results is held, curiously enough, by two opposing schools of educational theory. To one school, the natural12 is primary and fundamental; and its tendency is to make little of distinctly intellectual nurture. Its mottoes are freedom, self-expression, individuality, spontaneity, play, interest, natural unfolding, and so on. In its emphasis upon individual attitude and activity, it sets slight store upon organized subject-matter, or the material of study, and conceives method to consist of various devices for stimulating and evoking, in their natural order of growth, the native potentialities of individuals.
Neglect of the innate logical resources
Identification of logical with subject-matter, exclusively
The other school estimates highly the value of the logical, but conceives the natural tendency of individuals to be averse, or at least indifferent, to logical achievement. It relies upon subject-matter—upon matter already defined and classified. Method, then, has to do with the devices by which these characteristics may be imported into a mind naturally reluctant and rebellious. Hence its mottoes are discipline, instruction, restraint, voluntary or conscious effort, the necessity of tasks, and so on. From this point of view studies, rather than attitudes and habits, embody the logical factor in education. The mind becomes logical only by learning to conform to an external subject-matter. To produce this conformity, the study should first be analyzed (by text-book or teacher) into its logical elements; then each of these elements should be defined; finally, all of the elements should be arranged in series or classes according to logical formulæ or general principles. Then the pupil learns the definitions one by one; and progressively adding one to another builds up the logical system, and thereby is himself gradually imbued, from without, with logical quality.
Illustration from geography,
This description will gain meaning through an illustration. Suppose the subject is geography. The first thing is to give its definition, marking it off from every other subject. Then the various abstract terms upon which depends the scientific development of the science are stated and defined one by one—pole, equator, ecliptic, zone,—from the simpler units to the more complex which are formed out of them; then the more concrete elements are taken in similar series: continent, island, coast, promontory, cape, isthmus, peninsula, ocean, lake, coast, gulf, bay, and so on. In acquiring this material, the mind is supposed not only to gain important information, but, by accommodating itself to ready-made logical definitions, generalizations, and classifications, gradually to acquire logical habits.
from drawing
This type of method has been applied to every subject taught in the schools—reading, writing, music, physics, grammar, arithmetic. Drawing for example, has been taught on the theory that since all pictorial representation is a matter of combining straight and curved lines, the simplest procedure is to have the pupil acquire the ability first to draw straight lines in various positions (horizontal, perpendicular, diagonals at various angles), then typical curves; and finally, to combine straight and curved lines in various permutations to construct actual pictures. This seemed to give the ideal "logical" method, beginning with analysis into elements, and then proceeding in regular order to more and more complex syntheses, each element being defined when used, and thereby clearly understood.
Formal method
Even when this method in its extreme form is not followed, few schools (especially of the middle or upper elementary grades) are free from an exaggerated attention to forms supposedly employed by the pupil if he gets his result logically. It
