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upon them en masse, and pronounce judgment upon them impromptu ? Taken in this latter way, (and this is the prevailing method of those who urge this objection to the diagrams,) almost any of the systems of illustration employed in modern science, would appear equally reprehensible. To one previously unacquainted with them, how similarly complicated and incomprehensible must appear the symbolic expressions in algebra, the diagrams in geometry, the maps in physical geography, or the wonderful system of nomenclature so prevalent in modern chemistry ? And yet, nothing is plainer to the true scientist, than that any or all these, taken from their proper starting point, and pursued according to a progressive method, will eventually unfold themselves to the learner, as eminently simple, clear, and satisfactory. The truth is, complexity and obscurity in science are altogether relative to the position and temper of the observer, and not at all due to the intrinsic nature of the thing observed. So far, then, from touching the real merit of the diagrams, the objection rather recoils upon both the common sense and candor of the objector himself.
THE REAL COMPLEXITY IS DUE TO THE NATURE OF
LANGUAGE ITSELF. There is, however, another consideration bearing upon this point. The objector charges that the diagrams are complicated and difficult of comprehension. But what are they intended to represent ? Not merely, the restricted etymological forms and syntactical relations of single words to each other, in which he has been accustomed to sum up the whole of grammar. They represent rather the logical distinctions and relations of ideas and propositions to each other in the thoughts, either simple, com
pound, or complex, which the mind is ever evoking from its inner life and activity, and which it is constantly evolving in words, phrases, sentences, and complete periods. Now, by just so much as these products of our mental activity, in both their ideal substance and oral forms, must, to meet the infinitely varying wants and phases of life and thought, differ in their nature, number, combinations, and extension,-by just so much must the diagrams, as graphic illustrations of these facts in the science of language, be themselves, in their complete scheme, diversified and complicated. One of two conclusions, then, becomes inevitable. If the objection be valid, it holds just as good against language itself, as against the diagrams; if it be invalid, it passes harmlessly over the diagrams, and falls with crushing force upon the objector himself as altogether wanting in a just knowledge of the language.
3d Objection. They are imperfect. Another objection, and one usually urged as unanswerable,) is, that the diagrams are imperfect—they do not truly represent all the facts of the existing relations.
THE SAME MAY BE CHARGED AGAINST EVERY METHOD OF
But, do any of the methods of graphic illustration in science do any better? Geographic symbols are accepted as both legitimate and necessary ; but how exact is their representation of the various facts of the objects themselves? Your symbol for a river or a mountain,-how near does it come to perfection ? Who, that never has seen those objects, would recognize them in their sym
bols? Nay, who, having seen them, is able to obtain from the symbol, any just idea of their distinctive features, without a close and vigorous exercise of the constructive imagination ?
Or take, if you will, the diagrams in solid geometry. Suppose that you wish to represent a cube. Draw it in perspective, and how exactly will the figure, in the relative direction and length of its receding lines, or the comparative magnitude of their included angles, correspond to the actual facts of the solid itself ? Draw it according to the isometrical projection, and, while you secure a technical conformity in the lines and angles, to the form of the body represented, the figure fails to give you the receding or remote elements, in their proportions or relations, as the mind apprehends them. Your exact geometrical diagram must, then, be, of necessity, either false to the objective form, or false to the subjective image.
THE ALLEGED DEFECT GROWS OUT OF THE VERY NATURE OF
LANGUAGE, AND THE EXACT ACCORDANCE OF THE DIAGRAMS
But the case is even stronger than this. Let the objector look nearer home. He complains that the diagrams do not, and cannot, represent all the relations and offices of the various elements in the sentence, with equal accuracy. But how is it in the case of the language itself ? Speech, with all its wonderful subtlety and fullness, does not, and does not even pretend to, present all of our ideas in their real relations, with any greater accuracy. For example, you employ several adjectives as alike relating to and modifying the same noun ; you use the same adjective as relating alike to two or more
nouns, and modifying them in common; you give two or more subjects a similar and common reference to the same predicate ; you present several objects as similarly dependent on one verb, or different subsequents as holding a common relation to the same preposition ; or you give one pronoun a diverse, and even widely separate dependence on two altogether dissimilar parts of speech ; and yet, by no artifice whatever, either in oral or written expression, can you give the elements having this common relation or dependence, a grammatical position or connection exactly similar. In the necessary order of the words, only one of the terms thus applied in common, can hold the exact place indicative of its relation or dependence : the relation or dependence of the others must, by a . purely logical exercise, be carried on, either through or over the intervening terms, to the desired point. If, then, the diagrams fail, it is just where, and precisely as, the language which they represent fails ;-in other words, the two coincide exactly in the point raised by the objector. One of two conclusions is, then, inevitable, either the language itself is first, and equally, in fault, or the diagrams as a means of representation, are intrinsically more consistent and accurate because of the very feature which the objector condemns. It will be seen, then, that this objection, like the former one, recoils upon the objector himself : it shows him to be as ignorant of the language, as he is of the diagrams.
4th Objection. They are unnecessary. As a final objection, it is sometimes urged, that the diagrams, if not a positive hindrance, are, at least, unnecessary. The ground taken by the objector is, that, granting all that may be claimed as to the capacity of the dia
grams to perform the work allotted them, it is not only possible for all the facts involved to be clearly apprehended in abstract, or without sensible illustration, but it is better discipline for the mind to be compelled to seek out and master them, through this abstract contemplation alone.
THE SAME HOLDS WITH EQUAL FORCE AGAINST GRAPHIC ILLUS
TRATION IN OTHER BRANCHES OF SCIENCE.
To this objection, the answer is at once, that the same thing may be said of graphic illustration in other branches of science. The objection, if valid, holds, for example, equally good against the use of diagrams in geometry. In considering any proposition, it is, doubtless, possible for the process of demonstration to be carried on without the aid of a sensible figure, or diagram, and the discipline of such an exercise will be, beyond question, far more severe than that of the ordinary method. Nay, more, the use of the diagram in the study of geometry may be said to be even more inexcusable; since it is possible for the mind to construct the requisite figure in pure thought, and to proceed with the demonstration in accordance with its conceived elements and facts alone.
THE PROPOSED DISCIPLINE IS NOT ACCORDANT WITH NATURE, OR
ACCESSIBLE THROUGH MORE PROFITABLE CHANNELS.
And yet, while this idea has been broached as practically of great importance, scholars have neither been foolish nor rash enough to press its adoption. And this, for the simple reason that so long as the spiritual activity is not only leagued with, but is somewhat subject to the