perfect globe, the imaginary properties of which are demonstrated in Geometry, though the thing itself has no real existence in nature. Geometry shows nothing of the existence of things, but only what they are, suppo sing them to exist really such as they are conceived by the mind. And, indeed, were all created things existing annihilated, geometry would not lose a single point of its demonstrations; the circle would still remain a round figure, of which all the points of the circumference would be equally distant from the centre."

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Ø 287. Of the influence of demonstrative reasoning on the mental

character. A considerable skill in demonstrative reasoning is on a number of accounts desirable, although it cannot be denied that very frequent practice and great readiness in it are not alwaysfavourable; so that it seems proper briefly to mention some of the effects, both propitious and unpropitious, on the mental character.

(1.) A frequency of practice in demonstrative reasoning greatly aids in giving one a ready command of his attention. And this is said for two reasons. First, because the subjects of such reasoning are not objects of the senses, but immaterial; are conceptions rather than existences; the abstractions of things rather than things themselves; and, consequently, are not distinctly comprehensible without considerable effort. And, second, because, in this species of reasoning, the propositions follow each other in such regular order and so closely, and so great is the importance of perceiving the agreement or disagreement of each succeeding one with that which goes before, that a careless, unfixed, and dissipated state of the mind seems to be utterly inconsistent with carrying on such a process with any sort of success to the conclusion. As, therefore, the strictest attention is here so highly necessary, the more a person subjects himself to this discipline, the more ready and efficient will be the particular application of the mind to which we give that

And we often find distinguished individuals in political life and in the practice of the law who are desirous of holding their mental powers in the most prompt and systematic obedience, imposing on themselves exercises in geometry and algebra for this purpose.


(II.) This mode of reasoning accustoms one to care and discrimination in the examination of subjects.--In all discussions where the object is to find out the truth, it is necessary to take asunder all the parts having relation to the general subject, and bestow upon them a share of our consideration. And, in general, we find no people more disposed to do this than mathematicians; they are not fond of reasoning, as Mr. Locke expresses it. in the lump, but are for going into particulars, for allowing everything its due weight and nothing more, and for resolutely throwing out of the estimate all propositions which are not directly and fully to the point.-It must further be said, as a general remark closely connected with what has just been observed, that those departments of science which require demonstrative reasoning are promotive of a characteristic of great value-a love of the truth.

(III.) Demonstrative reasoning, although this beneficial result is not exclusively appropriate to this mode of reasoning, gives to the mind an increased grasp or comprehension. This result, it is true, will not be experienced in the case of those who have merely exercised themselves in the study of a few select demonstrations; it implies a familiarity of the mind with long and complicated trains of deductions. A thorough mathematician, who has made it a business to exercise himself in this method of reasoning, can hardly have been otherwise than sensible of that intellectual comprehension, or length and breadth of survey, which we have in view; since one demonstration is often connected with another, much in the same way as the subordinate parts of separate demonstrations are connected with each other; and he therefore finds it necessary, if he would go on with satisfaction and pleasure, to gather up and retain, in the grasp of his mind, all the general and subordinate propositions of a long treatise.

288. Further considerations on the influence of demonstrative rea

soning. But, on the other hand, there are some results of a

power of belief.

very great attention to sciences, which require the exclusive application of demonstrative reasoning, of a less favourable kind.--(I.) An exclusive culture of demonstrative reasoning unfavourably affects the operations of the susceptibility of belief on all subjects out of the circle of the mathematical; or perhaps we may say, in direct terms, that out of that circle it positively diminishes the

The exclusive mathematician has been accustomed to yield his assent to demonstratio only; and it is but natural that he should find some difficulty in being satisfied with any lower degree of evidence. This disposition to doubt will be in some measure experienced, even in the transition from pure to mixed mathematics; at least there will be an absence of that full and de lighted satisfaction which had hitherto been enjoyed Still more will it be felt when he is called upon to judge of events, and duties, and actions of common life, which do not admit of the application of deinonstration. In a word, it has been supposed to unfit the mind in a considerable degree for accurate discriminations as to moral evidence on all subjects whatever, where that species of evidence is alone admissible; and also for fair and correct judgment in matters of taste.

(11.) Again, it has been thought, among other things, that this form of reasoning, when carried to a great length, Kas a tendency to render the mind mechanical. That is, while it increases its ability of acting in a given way, it diminishes the power of invention, and prevents its striking out into a new path, different from that which it has been in the habit of going over. And hence it is that men of the strictest virtue and the most powerful intellect have sometimes discovered an unexpected weakness and made extraordinary mistakes when placed in certain new situations.-We may illustrate our meaning hy one or two instances. The celebrated Turgot, who combined the purest moral sentiments with the rarest intellectual endowments,


be termed a mathematical politician. History has recorded the result. When the King of France called him to direct the political concerns of the French empire, he decidedly failed, where half the talents and integrity had firmly held the

was what

helm amid political tempests. When called from the abstractions of science to deal with the realities of life, with the interests, and prejudices, and passions of mankind, mathenatician and philosopher as he was, he found, too late, that we cannot estimate the intellect as we can estimate the arc of a circle, and that the calculus which can measure the motions of the stars may not succeed in ascertaining the momentum and the obliquities of human nature.—But La Place, a far higher name on the list of eminent mathematicians, is an instance still more to our purpose. After the accession of Napoleon to the first Consulship in France, La Place was appointed Minister of the Interior; an office which he held six weeks, and was then dismissed. “A geometrician of the first rank,” says Napoleon," he did not reach mediocrity as a states

From the first, the Consuls became sensible that they had made a mistake in his appointment. He never viewed any subject in its true light; he was always occupied with subtilties; his notions were all problematic, and he carried the spirit of the infinitely small into the administration.”

Such, on the whole, being the result of an exclusive attention to sciences which admit of demonstration alone, it is obvious, when pursuing studies of that kind, that we should avail ourselves of the benefit resulting from other modes of mental discipline. Those who aim at a perfect education will not " canton out to themselves a little Goshen in the intellectual world,” which is to receive all their labours, and leave the rest of the vast field of the mind to neglect, but will bestow a suitable share of culture on every part of it.


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Ø 289. Of the subjects and importance of moral reasoning. MORAL REASONING, which is the second great division or kind of reasoning, concerns opinions, actions, and

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even!s; erobracing, in general, those subjects which do not come within the province of demonstrative reasoning. The subjects to which it relates are often briefly expressed by saying that they are matters of fact ; nor would this definition, concise as it is, be likely to give an erroneous idea of them.

Skill in this kind of reasoning is of great use in the formation of opinions concerning the duties and the general conduct of life. Some may be apt to think, that those who have been most practised in demonstrative reasoning can find no difficulty in adapting their intellectual habits to matters of mere probability. This opinion is not altogether well-founded, as we have seen in the preceding chapter. Although that species of reasoning has a favourable result in giving persons a command over the attention, and, in some other respects, whenever exclusively employed, it has the effect in some degree to disqualify them for a correct judgment on those various subjects which properly belong to moral reasoning.-The last, therefore, which has its distinctive name from the primary signification of the Latin MORES, viz., manners, customs, &c., requires a separate consideration.

s 290. Of the nature of moral certainty. Moral reasoning causes in us different degrees of assent, and in this respect differs from demonstrative. In demonstration there is not only an immediate perception of the relation of the propositions compared together, but, in consequence of their abstract and determinate nature, there is also a knowledge or absolute certainty of their agreement or disagreement. In moral reasoning the case is somewhat different.-In both kinds we begin with certain propositions, which are either known or re garded as such. In both there is a series of propositions successively compared. But in moral reasoning, in consequence of the propositions not being abstract and fixed, and, therefore, often uncertain, the agreement or disagreement among them is in general not said to be known, but presumed ; and this presumption may be more or less, admitting a great variety of degrees. While, therefore, one mode of reasoning is attended with

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