tion of the whole, are widely different. Now what is the confequence of this induction? It is plainly this, that, in fpite of the pride of mathefis, no demonftration whatever can produce, or reasonably ought to produce, a higher degree of certainty, than that which refults from the vivid representations of memory, on which the other is obliged to lean. Such is here the natural fubordination, however rational and purely intellectual the former may be accounted, however myfterious and inexplicable the latter. For it is manifeft, that without a perfect acquiefcence in fuch representations, the mathematician could not advance a fingle step beyond his definitions and axioms. Nothing therefore is more certain, however inconceivable it appeared to Dr. Prieftley, than what was affirmed by Dr. Ofwald, that, the poffibility of error attends the most complete demonftration.

IF from theory we recur to fact, we shall quickly find, that those most deeply verfed in this fort of reafoning, are confcious of the juftnefs of the remark now made. A geometrician, I fhall fuppofe, difcovers a new theorem, which, having made a diagram for the purpose, he attempts to demonftrate, and fucceeds in the attempt.

The

The figure he hath conftructed is very complex, and the demonftration long. Allow me now to afk, Will he be so perfectly satisfied on the first trial, as not to think it of importance to make a fecond, perhaps a third, and a fourth? Whence arifes this diffidence? Purely from the confcioufnefs of the fallibility of his own faculties. But, to what purpose, it may be faid, the reiterations of the attempt, fince it is impoffible for him, by any efforts, to fhake off his dependence on the accuracy of his attention, and fidelity of his memory? Or, what can he have more than reiterated teftimonies of his memory, in fupport of the truth of its former teftimony? I acknowledge, that after a hundred attempts he can have no more. But even this is a great deal. We learn from experience, that the mistakes or overfights committed by the mind in one operation, are fometimes, on a review, corrected in a fecond, or perhaps in a third. Befides, the repetition, when no error is difcovered, enlivens the remembrance, and fo ftrengthens the conviction. But for this conviction, it is plain that we are in a great measure indebted to memory, and in fome meafure even to experience.

ARITH

t

ARITHMETICAL operations, as well as gedmetrical, are in this nature fcientific; yet the moft accurate accountants are very fenfible of the poffibility of committing a blunder, and therefore rarely fail, for fecuring the matter, when it is of importance, to prove what they have done, by trying to effect the fame thing another way. You have employed yourself, I fuppofe, in refolving fome difficult problem by algebra, and are convinced that your folution is juft. One whom you know to be an expert algebraift, carefully perufes the whole operation, and acquaints you that he hath discovered an error in your procedure. You are that inftant fenfible that your conviction was not of fuch an impregnable nature, but that his fingle teftimony, in confequence of the confidence you repofe in his experienced veracity and fkill, makes a confiderable abatement in it.

MANY cafes might be fuppofed, of belief founded only on moral evidence, which it would be impoffible thus to fhake. A man of known probity and good fenfe, and (if you think it makes an addition of any moment in this case) an aftronomer and philofopher, bids you look at the fun as it goes down, and tells you with a fe

rious countenance, that the fun which fets today will never again rife upon the earth. What would be the effect of this declaration? Would it create in you any doubts? I believe it might, as to the foundnefs of the man's intellects, but not as to the truth of what he said. Thus, if we regard only the effect, demonftration itself doth not always produce fuch immoveable certainty, as is fometimes confequent on merely moral evidence. And if there are, on the other hand, fome well-known demonftrations, of fo great authority, that it would equally look like lunacy to impugn, it may deferve the attention of the curious, to inquire how far, with respect to the bulk of mankind, these circunftances, their having ftood the test of ages, their having obtained the univerfal fuffrage of those who are qualified to examine them (things purely of the nature of moral evidence), have contributed to that unshaken faith with which they are received.

THE principal difference then, in respect of the refult of both kinds, is reduced to this narrow point. In mathematical reafoning, provided you are afcertained of the regular procedure of the mind, to affirm that the conclufion is falfe, implies a contradiction; in moral reafoning, though the pro

VOL. I.

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cedure

cedure of the mind were quite unexceptionable, there ftill remains a phyfical poffibility of the falfity of the conclufion. But how fmall this difference is in reality, any judicious person who but attends a little, may cafily discover. The geometrician, for inftance, can no more doubt, whether the book called Euclid's Elements is a human compofition, whether its contents were discovered and digefted into the order in which they are there difpofed, by human genius and art, than he can doubt the truth of the propofitions therein demonftrated. Is he in the smallest degree furer of any of the properties of the circle, than that if he take away his hand from the compaffes, with which he is defcribing it on the wall, they will immediately fall to the ground. These things affect his mind, and influence his practice, precisely in the fame manner.

So much for the various kinds of evidence, whether intuitive or deductive; intuitive evidence, as divided into that of pure intellection, of confciousness, and of common fenfe, under the laft of which that of memory is included; deductive evidence, as divided into scientific and moral, with the fubdivifions of the latter into experience, analogy, and teftimony, to which hath

been