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. ii., 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 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

added to render our knowledge more adequate. When I am convinced that the three angles of a triangle are equal to two right angles, nothing can be added to the proposition by which my knowledge can be increased. If I fully comprehend the terms, I have precisely the same knowledge of the truth as Newton himself. He might have seen consequences derivable from it that I do not see; but our knowledge of the proposition itself is precisely the same. In the case of the other proposition, that at a given time and place, there was an eclipse of the sun, it is not so. We all may be equally confident in the main fact; but of various circumstances respecting it, our knowledge may be dissimilar and unequal. Men who observed the eclipse may have been more or less influenced by their imaginations; they may have dissimilar appreciations of the temperature, of the degree of darkness, of the time and duration of the event. Hence their narratives may in these respects differ, and it may require much labor to obtain a complete idea of the eclipse, and there may, after all, remain many circumstances which we know but imperfectly. All this may be granted, and yet it does not in the least affect our belief of the main fact. Nay, all these variations must exist if the main fact were true. They follow from the differences in the subjective nature of man. Hence the rule in testimony is that the best evidence to any fact is, agreement of witnesses as to the main event, and difference as to the minor particulars.

The following striking illustration of these remarks is worthy of notice. I presume that no one can doubt that the battle of Waterloo was fought on the eighteenth of June, 1815, between the French and the allies, under the commands respectively of Napoleon and Wellington. It may certainly be taken for granted that men believe this fact as undoubtingly as they do any proposition in geometry. Yet the time of the commencement of the battle cannot even now

be settled with precision. In Maxwell's life of Wellington, I find the following statement:

"The time when the battle began has been stated with marked contrariety. The Duke of Wellington says it commenced about ten o'clock, and further observes that when his troops discontinued the pursuit, at night, they had been engaged twelve hours. In this General Gneisenau concurs, but, of course, only from information he had received. General Alava, who was by the side of the duke the whole day, fixes it at half-past eleven. Napoleon and General Drouet state twelve as the hour; while Marshal Ney names one o'clock. Without tracing minuter contradictions, this may suffice to show the difficulty of attaining exact knowledge when it might have been presumed no difficulty could exist. With one exception, which I think ought to be decisive, I was equally bewildered by the intelligence I received from officers whom I had an opportunity of consulting. By one I was told that the battle began soon after mid-day, by another exactly twenty minutes past eleven, and by a third at ten o clock. But Sir George Wood--- and his information is what I conceive cannot be disputed — gave me the following statement. The action commenced about half-past ten or a quarter to eleven. There had been skirmishing, before, all the morning. A column of the enemy was advancing against Hougomont, and the first gun that was fired was from our lines against that column. I gave the order by the command of the duke. The gun did immediate execution, and killed six or eight. This column then retired, and went round the wood."- Maxwell's Life of Wellington, vol. 3, note to page 479.

We perceive, from this incident, how dissimilar is the adequateness of our knowledge in a matter of fact, from that in an abstract geometrical proposition; and yet our