may exist which have never been discovered. Be it so. But, inasmuch as we have been unable to discover them, we have arrived at the nearest approximation to truth which our faculties admit, and we must rely on such faculties as we possess. When, in the full and free exercise of our intellectual powers, we can discover no error in our premises, and no error in our reasoning, we must receive as true the conclusions which they necessitate. We have no other resource. If we deny this, there is an end to all reasoning, and everything beyond our own observation is a delusion.

If we now compare these two kinds of reasoning, we observe the following facts:

1. The process which we employ is, in both cases, precisely the same. When we attempt to discover truth by reasoning, we use syllogism; for this is the mode of action imposed upon our reasoning faculty. We use this, for we have no other to use.

2. The one kind of reasoning treats only of conceptions both in its premises and its conclusions. With actual existences, res gesta, it has nothing to do. Of course, it is excluded from all cases which involve matters of fact. The other has to do with actual existences, and to them its conclusions refer. Hence, this is the mode of reasoning which we must, of necessity, employ in all the business of life, and in all those investigations of science which contemplate things as actual existences.

3. By the one we arrive at absolute certainty respecting things not existing except in our conceptions. By the other we arrive at practical certainty respecting things as existing wholly distinct and separate from ourselves. In the one case we arrive at absolute truth; in the other, we approach as near to absolute truth as the limited and imperfect nature of our faculties admits. We approach so near to it that we are unable to detect any error.

It will be observed that these two kinds of reasoning correspond in general to those commonly termed demonstrative and moral reasoning. I have used different terms from those commonly employed, because I suppose them better adapted to the subject. It will be seen, if what I have said be true, that the difference between these two kinds of reasoning is much less than has frequently been supposed, both as to the mode in which they are conducted, and the results at which they arrive.

From what has been said, I think it will appear that but little ground exists for the superiority which has been claimed for demonstrative reasoning, or that which treats purely of conceptions. It is granted that in this species of reasoning we arrive at absolute truth; but then, from its conditions, it excludes all actual existences, and can, therefore, furnish no guide to conduct. As soon as demonstrative reasoning has to do with matters of fact, it reposes, by necessity, upon moral reasoning, and, specially, on the evidence of testimony. Thus, suppose I have demonstrated the distance of the sun from the earth. It is evident that the facts which form the elements of my reasoning must be established by what is called moral evidence. I am told that such and such observations have been made by different men, through a succession of years. Now, here is a two-fold liability of error. In the first place, how do I know that these observations were ever made at all? I have nothing here to rely on but the testimony of men, which is said to be so vastly inferior in certainty to demonstration. In the second place, what assurance have I that these observations were correctly made? How shall I be sure that all the instruments were perfect, or that proper skill was employed in the use of them? Important errors have frequently been made by scientific men. Sir Isaac Newton's discoveries were for several years postponed by an error in measuring a degree of the

earth's surface. What shall guard us against similar error? Now, if these are not reliable grounds of belief, all our demonstration is useless; for, on the facts which they deliver to us, all our calculations rely. Our demonstrations, then, as soon as they affect any matter of fact, are limited in their certainty by moral evidence, and they attain to no higher certainty than moral evidence confers. By the evidence of testimony, however, we are assured that these observations were made. From the known characters of the observers, we have every reason to believe that they were made correctly. On these assurances our calculations proceed, and they arrive at a degree of accuracy so great that neither we nor any one else can discover any error.

From these remarks we perceive the absurdity of demanding what is called demonstrative evidence to substantiate a matter of fact. Men sometimes tell us, for instance, that a revelation from God, being a matter of so great importance, should have been attested by mathematical demonstration. We see that to ask this is to demand what is absolutely impossible. Being a matter of fact, it must come under the laws of evidence which belong to matters of fact. To attempt to prove a fact by mathematical demonstration is as absurd as to attempt to prove a mathematical proposition by testimony.

REFERENCES.

Conclusions either certain or probable - Reid, Essay 6, chapter 4; Essay 7, chap. 1.

Metaphysical and mathematical reasoning-Reid, Essay 7, chapter 1; Locke, Book 4, chapter 4, section 6.

Nature of demonstrative evidence-Stewart, vol. ii., chap. 2, secs. 3, 4. Superiority of mathematical reasoning - Stewart, vol. ii., chapter 2, section 3; Reid, Essay 7, chap, 2.

Morality capable of demonstration - Locke, Book 4, chap. 2, sections 16, 18; chap. 3, section 18; chap. 4, section 7.

Conclusions in mixed mathematics as sure as data Stewart, vol. it. chap. 2, section 4.

SECTION III. OF THE EVIDENCE OF TESTIMONY.

IN demonstrative reasoning our premises rest upon truths intuitively perceived by every intellect in a normal condition, or else upon truths proceeding from these by necessity. In reasoning concerning matters of fact, many of our premises are general laws, established by observation and experience. But this observation and experience must be established by many witnesses. A single individual can observe but little. We must all rely upon the labors of others. But how shall we distinguish true from false testimony? Many things have been recorded as true, which have subsequently been found to be false. We need, therefore, to ascertain the laws by which testimony may be established, so that we may be able to proceed with certainty in our reasonings. It is, therefore, proper to examine this part of our subject, and determine, if possible, the principles on which the evidence of testimony rests. Testimony is of two kinds, direct and indirect.

I. Of direct testimony.

It must be admitted that the testimony of man is a source of as certain knowledge as any that we possess. If we refer to our own consciousness, we find no difference between the strength of our belief in matters of fact and matters of demonstration. We as perfectly believe that such persons as Julius Cæsar, Cicero, Alexander, Martin Luther, Washington, and Napoleon, existed; that the battles of Marathon, Bunker Hill, Austerlitz and Waterloo, were fought; and that there are now standing the cities of London, Paris, and Vienna, as we believe that the three angles of a triangle are equal to two right angles. If we ask ourselves which do we most confidently believe, we can discover no shade of difference. In any practical matter we should proceed upon

the belief of one as readily as upon that of the other. This is true of mankind universally. If this be so, then both of these grounds of belief must rest equally upon the laws of human thought. There must exist elementary first truths, acknowledged by all men, on which our confidence ultimately reposes. That this is true of mathematical reasoning is universally admitted. It must, however, be equally true of any other mode of proof which produces the same results.

Let us take another case. We are told that, a few years since, an eclipse of the sun occurred on a Sunday, a little after noon. It had been predicted by astronomers, and their predictions concerning it had been extensively published. Men in every place on this continent declared that they witnessed it. The daily newspapers, immediately after it is said to have occurred, were filled with accounts of the phenomena that were said to have been observed. Every fact respecting it was minutely recorded, and the statements of its various phases were inserted in the transactions of learned societies throughout the world. Now, granting these facts to be so, could we any more doubt that an eclipse really occurred, at the time and in the manner specified, than we could doubt a proposition in geometry? Suppose that one man, under these circumstances, should doubt the fact of the eclipse, and another should doubt a demonstration in mathematics, should we not decide that the mind of the one was in as abnormal a state as that of the other?

Yet I am aware that there are differences in the belief in the two cases. In the one case our belief is in the truth as universal, as true at all times and in all places. In the other, it is particular; that is, it is not true of every time and every place, but only of this time and this place. In the one case our knowledge is perfect and complete; that is, we know the whole of the truth affirmed, and nothing can be