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that instant, perceive the whole intuitively. Our remembrance, on the contrary, amounts to no more than this, that the perception of the truth of the axiom to which we have ad. vanced in the proof, is accompanied with a strong impression on the memory of the satisfaction that the mind received from the justness and regularity of what preceded. And in this we are under a necessity of acquiescing; for the understanding is no more capable of contemplating and perceiving, at once, the truth of all the propositions in the series, than the tongue is capable of uttering them at once. Before we make great progress in geometry, we come to demonstrations wherein there is a reference to preceding demonstrations ; and in these, perhaps, to others that preceded them. The bare reflection that as to these we once were satisfied, is accounted by every learner, and teacher too, as sufficient. And, if it were not so, no advancement at all could be made in this science. Yet here, again, the whole evidence is reduced to the testimony of memory.
It may be said that, along with the remembrance now mentioned, there is often in the mind a conscious power of recollecting the several steps, whenever it pleases; but the power of recollecting them severally and successively, and the actual instantaneous recollection of the whole, are widely different. Now what is the consequence of this induction ? It is plainly this, that in spite of the pride of mathesis, no demonstration whatever can produce, or reasonably ought to produce, a higher degree of certainty than that which resulis from the vivid representations of memory, on which the other is obliged to lean. 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 dependance on the accuracy of his attention, and fidelity of his memory? Or, what can he have more than reiterated testimonies 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 astrono. mer 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 rise again 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 intellect, but not as to the truth of what he said. Thus, if we regard only the effect, demonstration itself doth not al. ways produce such immovable 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 contribCuted 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 man
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 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 SYLLO
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, surely, when we are employed in investigating the nature and the different sorts of evidence, to be altogether overlooked.
It is long since I was convinced, by what Mr. Locke hath said on the subject, that the syllogistic art, with its figures and moods, serves more to display the ingenuity of the inventor, and to exercise the address and fluency of the learner, than to assist the diligent inquirer in his researches after truth. The method of proving by syllogism appears, even on a superficial review, both unnatural and prolix. The rules laid down for distinguishing the conclusive from the inconclusive forms of argument, the true syllogism from the various kinds of sophism, are at once cumbersome to the memory, and unnecessary in practice. No person, one may venture to pronounce, will ever be made a reasoner who stands in need of them. In a word, the whole bears the manifest indications of an artful and ostentatious parade of learning, calculated for giving the appearance of great profundity to what, in fact, is very shallow. Such, I acknowledge, have been, of a long time, my sentiments on the subject. On a nearer inspection, I cannot say I have found reason to alter them, though I think I have seen a little farther into the nature of the disputative science, and, consequently, into the grounds of its futility. I shall, therefore, as briefly as possible, lay before the reader a few observations on the subject, and so dismiss this article.
Permit me only to premise in general, that I proceed all along on the supposition that the reader hath some previous acquaintance with school logic. It would be extremely superfluous, in a work like this, to give even the shortest abridgment that could be made of an art so well known, and which is still to be found in many thousand volumes. On the other hand, it is not necessary that he be an adept in it; a mere smattering will sufficiently serve the present purpose.
My first observation is, that this method of arguing has not the least affinity to moral reasoning, the procedure in the one being the very reverse of that employed in the other. In moral reasoning we proceed by analysis, and ascend from particulars to universals; in syllogizing we proceed by synthesis, and descend from universals to particulars. The analytic is the only method which we can follow in the acquisi. tion of natural knowledge, or of whatever regards actual ex
istences; the synthetic is more properly the method that ought to be pursued in the application of knowledge already acquired. It is for this reason it has been called the didactic method, as being the shortest way of communicating the principles of a science. But even in teaching, as often as we attempt, not barely to inform, but to convince, there is a necessity of recurring to the tract in which the knowledge we would convey was first attained. Now the method of reasoning by syllogism more resembles mathematical demonstration, wherein, from universal principles, called axioms, we deduce many truths, which, though general in their nature, may, when compared with those first principles, be justly styled particular. " Whereas, in all kinds of knowledge wherein experience is our only guide, we can proceed to general truths solely by an induction of particulars.
Agreeably to this remark, if a syllogism be regular in mood and figure, and if the premises be true, the conclusion is infallible. The whole foundation of thc syllogistic art lies in these two axioms: “Things which coincide with the same thing, coincide with one another;” and “ Two things, whereof one does, and one does not coincide with the same thing, do not coincide with one another.” On the former rest all the affirmative syllogisms, on the latter all the negative. Accordingly, there is no more mention here of probability and of degrees of evidence, than in the operations of geometry and algebra. It is true, indeed, that the term probable may be admitted into a syllogism, and make an essential part of the conclusion, and so it may also in an arithmetical computa
but this does not in the least affect what was advanced just now; for, in all such cases, the probability itself is assumed in one of the premises : whereas, in the inductive method of reasoning, it often happens that from certain facts we can deduce only probable consequences.
I observe, secondly, that though this manner of arguing has more of the nature of scientific reasoning than of moral, it has, nevertheless, not been thought worthy of being adopted by mathematicians as a proper method of demonstrating their theorems. I am satisfied that mathematical demonstration is capable of being moulded into the syllogistic form, having made the trial with success on some propositions. But that this form is a very incommodious one, and has many disadvantages, but not one advantage of that commonly practised, will be manifest to every one who makes the experiment. It is at once more indirect, more tedious, and more obscure. I may add, that if into those abstract sciences one were to introduce some specious fallacies, such fallacies could be much more easily sheltered under the awkward verbosity of this artificial method, than under the elegant simplicity of that which has hitherto been used.