Such is here the natural subordination, however rational and purely intellectual the former may be accounted, however mysterious and inexplicable the latter. For it is manifest, that without a perfect acquiescence in such representations, the mathematician could not advance a single step beyond his definitions and axioms. Nothing therefore is more certain, however inconceivable it appeared to Dr Priestley, than what was affirmed by Dr Oswald, that, the possibility of error attends the most complete demonstration.

If from theory we recur to fact, we shall quickly find, that those most deeply versed in this sort of reasoning, are conscious of the justness of the remark now made. A geometrician, I shall suppose, discovers a new theorem, which, having made a diagram for the purpose, he attempts to demonstrate, and succeeds in the attempt. The figure he hath constructed is very complex, and the demonstration long. Allow me now to ask, Will he be so perfectly satisfied on the first trial, as not to think it of importance to make a second, perhaps a third, and a fourth? Whence arises this diffidence? Purely from the consciousness of the fallibility of his own faculties. But to what purpose, it may be said, the reiterations of the attempt, since it is impossible for him, by any efforts, to shake off his dependence on the accuracy of his attention, and fidelity of his memory? Or, what can he have more than reiterated testi

monies of his memory, in support of the truth of its former testimony? 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 oversights committed by the mind in one operation, are sometimes, on a review, corrected in a second, or perhaps in a third. Besides, the repetition, when no error is discovered, enlivens the remembrance, and so strengthens the conviction. But, for this conviction, it is plain that we are in a great measure indebted to memory, and in some measure even to experience.

Arithmetical operations, as well as geometrical, are in their nature scientific; yet the most accurate accountants are very sensible of the possibility of committing a blunder, and therefore rarely fail, for securing the matter, when it is of importance, to prove what they have done, by trying to effect the same thing another way. You have employed yourself, I suppose, in resolving some difficult problem by algebra, and are convinced that your solution is just. One whom you know to be an expert algebraist, carefully peruses the whole operation, and acquaints you that he hath discovered an error in your procedure. You are that instant sensible that your conviction was not of such an impregnable nature, but that his single testimony, in consequence of the confidence you repose in his experienced veracity and skill, makes a considerable abatement in it.

Many cases might be supposed, of belief founded only on moral evidence, which it would be impossible thus to shake. A man of known probity and good sense, and (if you think it makes an addition of any moment in this case) an astronomer and philosopher, bids you look at the sun as it goes down, and tells you, with a serious countenance, that the sun which sets to-day will never again rise 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 soundness of the man's intellects, but not as to the truth of what he said. Thus, if we regard only the effect, demonstration itself doth not always produce such immoveable certainty, as is sometimes consequent on merely moral evidence. And if there are, on the other hand, some well-known demonstrations, of so great authority, that it would equally look like lunacy to impugn, it may deserve the attention of the curious, to inquire how far, with respect to the bulk of mankind, these circumstances, their having stood the test of ages, their having obtained the universal suffrage 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 result of both kinds, is reduced to this narrow point. In mathematical reasoning, provided you

are ascertained of the regular procedure of the mind, to affirm that the conclusion is false, implies a contradiction; in moral reasoning, though the procedure of the mind were quite unexceptionable, there still remains a physical possibility of the falsity of the conclusion. But how small this difference is in reality, any judicious person who but attends a little may easily discover. The geometrician, for instance, can no more doubt, whether the book called Euclid's Elements is a human composition, whether its contents were discovered and digested into the order in which they are there disposed, by human genius and art, than he can doubt the truth of the propositions therein demonstrated. Is he in the smallest degree surer of any of the properties of the circle, than that if he take away his hand from the compasses, with which he is describing it on the wall, they will immediately fall to the ground. These things affect his mind, and influence his practice, precisely in the same manner.

So much for the various kinds of evidence, whether intuitive or deductive; intuitive evidence, as divided into that of pure intellection, of consciousness, and of common sense, under the last of which that of memory is included; deductive evidence, as divided into scientific and moral, with the subdivisions of the latter into experience, analogy, and testimony, to which hath been added, the consideration of a mixed

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species concerning chances. So much for the various subjects of discourse, and the sorts of eviction of which they are respectively susceptible. This, though peculiarly the logician's province, is the foundation of all conviction, and consequently of persuasion too. To attain either of these ends, the speaker must always assume the character of the close and candid reasoner: for though he may be an acute logician who is no orator, he will never be a consummate orator who is no logician.

Of the nature and use of the scholastic art of syllogizing.

. HAVING in the preceding chapter endeavoured to trace the outlines of natural logic, perhaps with more minuteness than in such an inquiry as this was strictly necessary, it might appear strange to pass over in silence the dialectic of the schools; an art which, though now fallen into disrepute, maintained for a tract of ages, the highest reputation among the learned. What was so long regarded, as teaching the only legitimate use and application of our rational powers. in the acquisition of knowledge, ought not surewhen we are employed in investigating the

ly,