conclusions. Mis-statement, in one form or another, may indeed be considered as a most fruitful source of controversy; and, amid the contests of rival disputants, the chief difficulty which meets the candid inquirer after truth, is to have the subject presented to his mind without distortion. Hence the importance, in every inquiry, of suspending our judgment, and of patiently devoting ourselves to clear the subject from all imperfect views and partial statements. Without the most anxious attention to this rule, a statement may appear satisfactory, and a deduction legitimate, which are in fact leading us widely astray from the truth.

After every possible care in any process of reasoning, we may still find, in many cases, a degree of doubt, and even certain varieties of opinion in regard to the import and bearing of the argument. This arises partly from actual differences in the power of judging, or what we call, in common language, vigour of mind; and partly from differences in attention, or in the habit of applying the judgment closely to the elements of an inquiry. Hence the varieties of opinion that may be held by different individuals on the same subject, and with the same facts before them; and the degree of uncertainty which attends various processes of reasoning.There is one species of reasoning which is free from all this kind of uncertainty, namely, the mathematical; and the superiority of it depends upon the following circumstances:

1. Nothing is taken for granted, or depends upon mere authority; and, consequently, there is no room for fallacy or doubt in regard to the premises on which the reasoning is founded. No examination of facts is required in any degree analogous to that which is necessary in physical science. The mathematician, indeed, proceeds upon assumptions of such a kind that it is in his own power to clear

them from all ambiguity, and from every thing not connected with the subject.

2. In the farther progress of a mathematical argument, if we have any doubt of a proposition which is assumed as the result of a former process, we have only to turn to the demonstration of it, and be immediately satisfied. Thus, if any step of a process be founded upon the principle that all the angles of a triangle are equal to two right-angles, or that the square of the hypotenuse is equal to the sum of the squares of the two sides, should we have any doubt of the truth of these conclusions, the demonstration of them is before us. But if an argument be founded on the principle that the heavenly bodies attract onę another with a force which is directly as their quantity of matter, and inversely as the square of their distance; this great principle must be received on the authority of the eminent men by whom it was ascertained, the mass of mankind having neither the power nor the means of verifying it.

3. All the terms are fully and distinctly defined, and there is no room for obscurity or ambiguity in regard to them.

4. The various steps in a process of mathematical reasoning follow each other so closely and consecutively, as to carry a constant conviction of absolute certainty; and, provided we are in possession of the necessary premises, each single step is short, and the result obvious.

5. The proper objects of mathematical reasoning are quantity and its relations; and these are capable of being defined and measured with a precision of which the objects of other kinds of reasoning are entirely unsusceptible. It is, indeed, always to be kept in mind, that mathematical reasoning is only applicable to subjects which can be defined and measured in this manner, and that all attempts to extend it to subjects of other kinds have led to the greatest absurdities.

ン

Notwithstanding the high degree of precision which thus distinguishes mathematical reasoning, the study of mathematics does not, as is commonly supposed, necessarily lead to precision in other species of reasoning, and still less to correct investigation in physical science. The explanation that is given of the fact seems to be satisfactory. The mathematician argues certain conclusions from certain assumptions, rather than from actual ascertained facts; and the facts to which he may have occasion to refer are so simple, and so free from all extraneous matter, that their truth is obvious, or is ascertained without difficulty. By being conversant with truths of this nature, he does not learn that kind of caution and severe examination which is required in physi cal science,―for enabling us to judge whether the statements on which we proceed are true, and whether they include the whole truth which ought to enter into the investigation. He thus acquires a habit of too great facility in the admission of data or premises, which is the part of every investigation which the physical inquirer scrutinizes with the most anxious care, and too great confidence in the mere force of reasoning, without adequate attention to the previous processes of investigation on which all reasoning must be founded. It has been, accord ingly, remarked by Mr. Stewart, and other accurate observers of intellectual character, that mathemati cians are apt to be exceedingly credulous, in regard both to opinions and to matters of testimony; while, on the other hand, persons who are chiefly conver sant with the uncertain sciences, acquire a kind of skepticism in regard to statements, which is apt to lead them into the opposite error. These observations, of course, apply only to what we may call a mere mathematician,-a character which is now robably rare, since the close connexion was estab shed between the mathematical and physical sciices in the philosophy of Newton.

In the various steps constituting a process of reasoning, or a process of investigation, in any department of knowledge, our guide is reason or judgment. Its peculiar province is to give to each fact or each principle, a proper place and due influence in the inquiry, and to trace the real and true tendency of it in the conclusion. It is, of course, assisted by other mental operations, as memory, conception, and abstraction, but especially by attention,-or a deliberate and careful application of the mind to each fact and each consideration which ought to have a place in the inquiry. This is entirely a voluntary exercise of the mind, strengthened and made easy by habit, or frequent exercise, and weakened or impaired by disuse or misapplication; and there is, perhaps, nothing which has a greater influence in the formation of character, or in determining the place which a man is to assume among his fellow

men.

This sound exercise of judgment is widely distinct from the art of ingenious disputation. The object of the former is to weigh, fully and candidly, all the relations of things, and to give to each fact its proper weight in the inquiry: the aim of the latter is to seize with rapidity particular relations, and to find facts bearing upon a particular view of a subject. This habit when much exercised tends rather to withdraw the attention from the cultivation of the former. Thus, it has not unfrequently happened, that an ingenious pleader has made a bad judge; and that acute and powerful disputants have perplexed themselves by their own subtleties, till they have ended by doubting of every thing. The same observation applies to controversial writing; and hence the hesitation with which we receive the arguments and statements of a keen controvertist, and the necessity for hearing both sides. In making use of this caution, we may not accuse the reasoner S

of any unsound arguments or false statements. We only charge him with acting the part of an ingenious pleader, who brings forward the statements and arguments calculated to favour one side of a question, and leaves those of the opposite side out of view. The candid inquirer, like the just judge, considers both sides, and endeavours, according to the best of his judgment, to decide between them. To the same principle we trace the suspicion with which we receive the statements of an author, who first brings forward his doctrine, and then proceeds to collect facts in support of it. To a similar process we may ascribe the paradoxical opinions in which sophistical writers have landed themselves, often on subjects of the highest importance, and which they have continued to advocate, with much appear. ance of an honest conviction of their truth. It would be unjust to suppose that these writers have always intended to impose upon others; they have very often imposed upon themselves; but they have done so by their own voluntary act, in a misapplication of their reasoning powers. They have directed their attention, exclusively or chiefly, to one view of a subject, and have neglected to direct it, with the same care, to the facts and considerations which tend to support the opposite conclusions.

In regard to the sound exercise of judgment, it is farther to be remarked, that it may exist without the habit of observing the various steps in the mental process which is connected with it. Thus we find men of that character to which we give the name of strong sound sense, who form just and comprehensive conclusions on a subject, without being able to explain to others the chain of thought by which they arrived at them; and who, when they attempt to do so, are apt to bewilder themselves, and fall into absurdities. Such persons, accordingly, are adapted for situations requiring both