The whole subject of syllogisms, their nature and classification, the rules to which they are subjected, and the distinction between true and false syllogisms, is treated of in the science of logic. To these the reader is referred for a further development of the doctrines here briefly alluded to. I ask leave to commend this study to all persons who aim at the attainment of mental acuteness, and the thorough cultivation of their reasoning power.

REFERENCES.

Reasoning, its nature - - Reid, Essay 7, chap. 1.

Reasoning, instinctive - Reid, Essay 7, chap. 1.

Reasoning rests on first truths-Reid, Essay 1, chap. 2; Essay 6, chap. 2.

This denied Locke, Book 4, chap. 2, secs. 7, 8; chap. 7, secs. 8, 10, 19, 20.

Cousin's Review of Locke-chap. 9.

Buffier, first truths.

Test of first truths - Reid, Essay 6, chap. 4.

Classification of first truths-Reid, Essay 1, chap. 2; Essay 6, chaps.

5, 6.

Judgment, its nature - Reid, Essay 6, chap. 1.

Judgment distinguished from testimony and conceptions - Reid, Essay 6, chap. 1.

Judgments necessary and contingent — Reid, Essay 6, chap. 1.
Common Sense, Reid, Essay 6, chap. 2.

Syllogism not the great instrument of reasoning-Locke, Book 4, chap. 17, secs. 4-7; Cousin, chap. 9.

Aristotle's logic examined - Stewart, vol. ii., chap. 3, sec. 1.

Effects of study of logic on intellectual habits-Stewart, vol. ii., chap. 3, sec. 2.

Use of definitions-Stewart, vol. ii., chap. 2, sec. 3.

Nugatory propositions - Locke, Book 4, chap. 8, sec. 4.

Propositions true or false — Locke, Book 2, chap. 32, secs. 1-4.

SECTION II.- OF THE DIFFERENT KINDS OF CERTAINTY AT WHICH WE ARRIVE BY REASONING.

I HAVE remarked that by the process of reasoning, if properly conducted, we always render the conclusion as certain as the premises. This is the sole object of syllogism, and this it invariably accomplishes. I have also observed that our conclusions may be either certain, or only probable, according to the nature of the premises from which they proceed.

Dismissing the consideration of the cases in which we establish probability, and confining our attention to that in which we arrive at certainty, we perceive that this certainty is of two kinds. We may arrive, first, at metaphysical or absolute, or, secondly, at practical certainty. Let us attempt to distinguish these from each other, and show the peculiarities of each.

I. Of metaphysical and absolute certainty.

When we arrive at this kind of certainty, the matter of our reasoning is wholly conceptions, or the notions which we form in our own minds, representing no actual reality. These are, of course, precisely what we make them, neither greater nor less, nor in any possible respect different from our thoughts; for they are our thoughts themselves, and nothing else. Hence, when they are distinctly comprehended, and formed into syllogism according to the rules of logic, they must lead to a conception of the same character as the premises, and be inevitably as true. There is no liability for misconception or ambiguity. The result must be as true as our thoughts themselves.

The most remarkable example of this mode of reasoning is found in the pure mathematics. Here the matter about which we reason is pure conceptions. We demonstrate truth

about lines, angles, triangles, circles, etc., not as actual existences, but merely as conceptions. By our definitions, we announce distinctly the ideas intended by the terms which we employ. These ideas we continue to use without change throughout our reasonings, and the results to which we arrive are concerning these alone.

I have said that in this mode of reasoning we have nothing to do with actual existences. This is evident from the fact that the pure mathematics might have been carried to any conceivable degree of perfection, had a material universe never been created. All that is required for this mode of reasoning is a thinking mind. Hence we never, in geometry, attempt to prove anything respecting an existing figure. We may use a diagram for the sake of concentrating our attention, but our reasoning is not concerning it, or any other thing visible or tangible. No actual figure exactly corresponds with our definitions, and, if it did, we have no faculties by which to ascertain the correspondence. We say the angles at the base of an isosceles triangle are equal. This we show to be unconditionally true. But it is true of our conceptions only, and not of the diagram on the blackboard. We do not know that the lines of that triangle are perfectly straight, or the sides equal; nay, we know that it is beyond our power to make them so. But this in no manner affects our demonstration. If any one should attempt to convict us of error, by measuring the triangle and showing that one angle was greater than the other, we should smile at his ignorance. We know that our proposition is true concerning the conception existing in our minds, and this is all we ever attempted to prove.

I have said that the most striking example of this species of reasoning is observed in the case of the pure mathematics. I know of no reason, however, why it should not exist in any other case in which the matter of our argu

ment is pure conception. All that is necessary is that our terms be accurately defined and clearly apprehended, and that they be subjected to the laws of syllogistic reasoning. The result must be as purely truth in the one case as the other. Thus,

1. All accountable beings are entitled to freedom.

2. Sylphs and gnomes are accountable beings.
3. Sylphs and gnomes are entitled to freedom.
Suppose the first proposition clearly understood.

Sylphs and gnomes are imaginary beings, of which I form a conception just as I please. The conclusion must follow as clearly and inevitably as in mathematical demonstration.

It must, however, be manifest that the range of subjects of this character is extremely limited, and, therefore, its utility by no means extensive. We live in a matter-of-fact world. We desire to enlarge our knowledge, not of mere conceptions, but of realities. We wish to know the laws of things actually existing, and so to use them as to ascertain other laws of which we are ignorant. In order to do this, we must come forth from the region of conceptions into that of realities. Thus, the pure mathematics themselves would be utterly useless, except as a discipline, unless we combined them with existing facts, when they assume the form of mixed mathematics. Here, however, we arrive not at absolute, but practical certainty. Let us observe the manner in which this kind of certainty is attained.

In this kind of reasoning, either one or both of our prem→ ises is some general law, or particular fact, established by observation or experiment. Our conclusion, then, approaches no nearer to absolute truth, than our fact or observation represents the pure and absolute verity. But no one pretends that our faculties are capable of arriving at pure and absolute truth. It has often been remarked that a perfect

circle, or triangle, or square, never was constructed, and that no instrument ever made, could claim to be absolutely accurate. Our processes may be as perfect as the present condition of the arts will allow, but we can go no further. Progress in the arts may enable us to exclude additional causes of error, and thus arrive at greater accuracy. But when we have done all, our powers are limited and imperfect; and, to use the words of Johnson, "a fallible being must fail somewhere." The eye is incapable of observing objects below a certain magnitude, or differences which do not exceed a certain degree. The sensation of touch can only detect impressions when their impulse attains to a certain force. Our nerves are easily fatigued, and fatigue impairs their accuracy of observation, and their control over our muscles. The various passions to which we are subject influence our whole sentient organism, and frequently unfit us for observation at a time when their perfect accuracy is the most needed. It is said that when Sir I. Newton had arrived very nearly at the close of that calculation which has made his name immortal, and saw the result to which he was tending, he was seized with so violent a fit of trembling, that, unable to complete the work, he surrendered his papers to a friend, by whom it was finished. It is told of one of the observers sent many years ago to the Pacific Ocean to observe the transit of Venus, that, at the precise moment when the transit occurred, he fainted from excess of excitement. Perfect accuracy can, therefore, never be predicated of a being in whose organization are involved so many liabilities to error.

Thus, for instance, in the mixed mathematics we arrive at only practical certainty. Here we first establish the relations existing between the lines of a figure of which we have conceived. This is pure mathematics, and our result is absolute truth. We then apply these relations to a figure