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straction, no other gives in the same degree the habit of accuracy, because none require it so imperatively; or, rather (for it is false to say that any serious subject requires less accuracy than another), none detect so surely the want of it. Accuracy is the first and essentially necessary quality to aim at. Acuteness of reasoning, however valuable, however desirable, may yet be dispensed with by the generality even of educated persons; but accuracy is indispensably requisite for every moral as well as intellectual purpose of reasoning, the essential condition of sound judgment on whatever subjects the latter is exercised.

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Nor is any severe course of mathematics necessary to aid us in this respect; if so it would be a vain recommendation, to the majority of women especially; the mental training this study affords, may fortunately be attained at a far less cost of labour. The mere rudiments of mathematics are sufficient to answer the purpose in some degree, that is, to imbue the mind with the principles of just reasoning, to teach the nature of a proof, the value of exact definitions, the method by which strict investigation is carried on step by step, and rigorous conclusions drawn out. These are advantages which we may, perhaps, labour long in other branches of knowledge without acquiring; but which the study of one book of Euclid, with a view to attaining them, can hardly leave us without.

It is on this account that Locke says he would have everybody learn something of mathematics, "not so much to make them mathematicians, as to make them reasonable creatures.” * So, likewise, an eminent philosopher of our own day ders some knowledge of abstract science" highly desirable in general education, if not indispensably necessary, to impress on us the distinction between vague and strict reasoning, to show us what demonstration really is." † The same author also strongly exemplifies in another point of view, the advantage of mathematics as a training for the reason, namely, as saving the mind from all groping and hesitation, from all confusion or possible misapprehension of terms. Speaking of the abstract sciences generally, he says, "Their objects are so definite, and our notions of them so distinct, that we can reason about them with an assurance that the words and signs used in our reasonings are full and true representatives of the things signified; and, consequently, that when we use language and signs in argument, we neither by their use introduce extraneous notions, nor exclude any part of the case before us from consideration. For example-the words: space, square, circle, a hundred, &c., convey to the mind notions so complete in

* Essay on the Conduct of the Human Understanding, Sec. vi. † Sir J. Herschel's Discourse on the Study of Natural Philosophy, p. 22.

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themselves, and so distinct from everything else, that we are sure when we use them, we know and have in view the whole of our meaning. It is widely different with words expressing natural objects and mixed relations. Take, for instance, iron. Different persons attach very different ideas to this word. One who has never heard of magnetism has a very different notion of iron from one in the contrary predicament. The vulgar who regard this metal as incombustible, and the chemist who sees it burn with the utmost fury, and who has other reasons for regarding it as one of the most combustible bodies in nature; the poet who uses it as an emblem of rigidity, and the smith and engineer, in whose hands it is plastic and moulded like wax into every form; the jailor who prizes it as an obstruction, and the electrician who sees in it only a channel of open communication, by which that most impassable of obstacles the air, may be traversed by his imprisoned fluid, have all different, and all imperfect notions of the same word. The meaning of such a term is like a rainboweverybody sees a different one, and all maintain it to be the same. So it is with nearly all our terms of sense. Some are indefinite, as hard or soft, light or heavy (terms which were at one time the sources of innumerable mistakes and controversies); some excessively complex, as man, life, instinct. But what is worst of all, some, nay, most, have two or three meanings, sufficiently distinct from each other to make a proposition true in one sense and false in another, or even false altogether, yet not distinct enough to keep us from confounding them in the process by which we arrived at it, or to enable us immediately to recognise the fallacy which led to it by a train of reasoning, each step of which, we think, we have examined and approved.






It is, in fact, in this double or incomplete sense of words that we must look for the origin of a very large portion of the errors into which we fall. Now the study of the abstract sciences, such as arithmetic, geometry, algebra, &c., while they afford scope for the exercise of reasoning about objects that are, or at least may be conceived to be, external to us, yet, being freer from those sources of error and mistake, accustom us to the strict use of language as an instrument of reason, and by familiarising us in our progress towards truth, to walk uprightly and straight-forward on firm ground, give us that proper and dignified carriage of mind, which would never be acquired by having always to pick our steps among obstructions and loose fragments, or to steady them in the reeling tempest of conflicting meanings."*

In this passage the value of a rigid school of reasoning, and

* Discourse on the Study of Natural Philosophy, p. 19.



the danger of error where that rigid exactness cannot be enforced, are admirably set forth. While, however, we derive this benefit from mathematics, we must not forget that common language is the only vehicle of expression for every subject on which thought can be exercised beyond the limits of abstract science; for every question relating to the highest interests of religion and morals, no less than for those which regard the common affairs of life; and that if the name of a substance such as iron admits of the ambiguity above-mentioned, far greater is the chance of error when speaking of human actions, or feelings, or interests, in which the use of terms is still more undefined, and the literal and metaphorical sense still more liable to be confounded, either ignorantly or wilfully, by the writer or speaker. Such is the language used by the historian, the legislator, the moral philosopher, the language of our daily business and conversation, and finally of the Bible, on the verbal interpretation of which such vast systems have been built. Admitting, then, that mathematics offer the best school in which to begin training the power of reasoning, to acquire the free use of our instrument unimpeded by fear of error, or of wasted labour; yet as the subjects on which it is most essential that we should reason justly do not admit of the rigidity of mathematical symbols, but must be studied through the medium of ordinary language, poor, ambiguous, and insufficient as it may be, it is essential that we should learn to conquer its difficulties, and to beware of the errors into which it may lead us.

It is not sufficient for this purpose to learn use of language as an instrument, such as it is the province of grammar and logic to teach it; we require to know something of the laws of thought itself, from which language springs, and on which every mental operation is based. The confusion that results from ignorance of these, is, in strict science, unfelt to a certain extent, by the beginner. The very exactness that he is learning to prize, the one straight path that he is forced to follow, act in some measure as leading-strings to the mind, and it is not till he turns to other subjects that the want of clearness in his own thoughts becomes apparent to him. Hence the value of some study of mental philosophy, as a school for the reason, to throw light on the operations of thought, and on the sources whence confusion may arise.

Every thoughtful mind is naturally inclined to turn its contemplation inwards; and to examine its own workings, and their consequences. This fact would seem naturally to suggest, that in order to create habit of thought, where it is wanting, it is expedient to lead the mind to this kind of inward contemplation;


to make it scrutinise its own powers, and examine what use it is making of them. Such investigation (which may be more or less profound, according to individual inclination and capacity) is, we believe, to a certain extent, indispensable for all who desire to have the free use and command of the powers with which they are endowed. It is vain to expect anything but confusion in the mind which has never examined itself; nor in such a case, is the action of the intellectual faculties alone rendered uncertain; but the power and nature of the will, the boundaries of reason and conscience remaining unknown, the moral consequences are no less pernicious than those which result to the intellect. The attempt to cultivate reason while this inward darkness prevails, may be compared to working with a machine of which all the springs and internal constructions are unknown to us; and with which, therefore, we can only perform a certain routine operation, without knowing how far its power might be extended, or its working facilitated or hindered. Nor let it be said that we are leading the young into the mazes of unfathomable questions; for one great purpose of some acquaintance with these subjects is, that we should learn to distinguish what we know from what we cannot know,—a most essential point, confusion concerning which has created such incalculable error and suffering. We do not recommend the study of mental science for the sake of subtle and difficult inquiries, which from their very nature can perhaps never lead to absolute results, and on which crude and superficial notions are most earnestly to be deprecated; but as a means of teaching the young to regulate and improve the action of their own faculties, to study them as they are matters of consciousness and acknowledged experience; to investigate the operation of thought; to see what it is that makes that operation at times clear and simple, at others confused and feeble; to learn the obstacles that stand in the way of the free use of reason, the limits set to its exercise by the constitution of our nature, and those which are placed in its way arbitrarily and unlawfully, by the prejudice or ignorance of man. These are points which cannot be left in the dark without weakening mental power; and the careful study of some parts of such a work as Locke's,-whatever its errors,-will do more in this respect to clear the way for the cultivation of reason than months of other study; while the whole inner economy of the instrument by which we are enabled to study remains unknown to us.

We need not dwell here on the importance to us of some acquaintance with mental philosophy, in every other point of view, in which any branch of knowledge can be regarded; whether as bearing on moral and intellectual improvement in general, or as



pointing to sublime and consoling truths, or as leading to the most. important practical results in all that concerns the government, training, or influencing our fellow-creatures. We shall have occasion, in a future chapter, to consider it in the latter respect; our present object is to show the effect of such a study on the cultivation of the reason only. In this respect, then, besides the advantages already spoken of, mental science is valuable as affording the means of forming habits of careful investigation, (while under the necessity of guarding against the errors and ambiguities of language,) of acute observation, and nice discrimination of difference and distinctions; of weighing conflicting and often faint or obscure evidence; and, lastly, of abstraction and generalisation, as we reason from our own minds to those of others, laying aside peculiarities to seize upon the broader features of human nature. The importance of such advantages needs no comment.

When some acquaintance with first principles has thus cleared our mental vision, we find, on proceeding to moral questions, that the field of thought opened by them affords both a continual and practical exercise of reason. Everything here bears immediately on the highest concerns that can affect us; and if the mind is, by any means, to be roused from indolence, and its powers stimulated to exertion, it will surely be among such inquiries. The examination of the nature and basis of truth, and of the grounds on which we assent to certain propositions as true, or remain in doubt, leads directly, as we have before explained,*—to the analysis of our own opinions and of the principles on which they are founded, and thence to the investigation of the consequences they lead to, and of those which are actually exhibited in our character and conduct; thus necessitating the daily practical exercise of reason among subjects of contemplation no less difficult than interesting. Independently of all other considerations, the mind to which such an exercise has become habitual, that has learnt to unfold the intricacies of its own ideas, to clear away the mists of prejudice from its own mental vision, and to examine the sources of its principles and actions, has thereby trained the reason to a high capability of exertion in any other field.


The difference of the mode in which the judgment is frequently exercised, in mental science and in mathematics, gives the former some advantages as a practical school. The latter, in its beginnings (and we do not speak of the higher branches of sciencet), offers almost too rigid a course, grounds

Chap. v., sec. 2 and 3.

We are most anxious to guard against misconception on this point. It is of the mere alphabet of mathematics that we speak when alluding to its

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