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there is no principle which can lead me to conclude that one side rather than another will be turned up. I know that this circumstance is not without a cause; but is, on the contrary, as really effected by the previous tossing which it receives in the hand or in the box, as its fall and the manner of its lying are by its gravity and figure. But the various turns or motions given it, in this manner, do inevitably escape my notice; and so are held for nothing. I say, therefore, that the chance is equal for every one of the six sides. Now if five of these were marked with same figure, suppose a dagger [+], and only one with an asterisk [*], I should in that case, say, there were five chances that the die would turn up the dagger, for one that it would turn up the asterisk. For the turning up each of the six sides being equally possible, there are five cases in which the dagger, and only one in which the asterisk would be uppermost. This differs from experience, inasmuch as I reckon the probability here, not from numbering and comparing the events after repeated trials, but without any trial, from balancing the possibilities on both sides. But though different from experience, it is so similar, that we cannot wonder that it should produce a similar effect upon the mind. These different positions being considered as equal, if any of five shall produce a similar effect, and but the sixth another, the mind, weighing the different events, resteth in an expectation of that in which the greater number of chances concur; but still accompanied with a degree of hesitancy, which appears proportioned to the number of chances on the opposite side. It is much after the same manner that the mind, on comparing its own experiences, when five instances favour one side to one that favours the contrary, determines the greater credibility of the former. Hence, in all complicated cases, the very degree of probability may be arithmetically ascertained. That two dice marked in the common way will turn up 'seven, is thrice as probable as that they will turn up eleven, and six times as probable as that they will turn up twelve1. The degree of probability is here determined demonstratively. It is indeed true that such mathematical calculations may be founded on experience, as well as upon chances. Examples of this we have in the computations that have been made of the value of annuities, insurances, and several other commercial articles.

In such cases a great number of instances

1 Call one die A, the other B. The chances for 7 are

A 1. B 6. A 4. B 3.

A 2. B 5. A 5. B 2.

A 3. B 4.A 6. B 1.

The chances for eleven are

A 6. B 5.

A 5. B 6.

The only chance for 12 is A 6. B 6. as 6 to 1.

The 1st is to the 2nd as 6 to 2; to the 3rd,

is necessary, the greatest exactness in collecting them on each side, and due care that there be no discoverable peculiarity in any of them, which would render them unfit for supporting a general conclusion.

PART IV.-The Superiority of Scientific Evidence

re-examined.

After the enumeration made in the first part of this section, of the principal differences between scientific evidence and moral, I signified my intention of resuming the subject afterwards, as far at least as might be necessary to show, that the prerogatives of demonstration are not so considerable, as on a cursory view one is apt to imagine. It will be proper now to execute this intention. I could not attempt it sooner, as the right apprehension of what is to be advanced will depend on a just conception of those things which have lately been explained. In the comparison referred to, I contrasted the two sorts of evidence, as they are in themselves, without considering the influence which the necessary application of our faculties in using both, has, and ought to have, on the effect. The observations then made in that abstracted view of the subject, appear to be well founded. But that view, I acknowledge, doth not comprehend the whole with which we are concerned.

It was observed of memory, that as it instantly succeeds sensation, it is the repository of all the stores from which our experience is collected, and that without an implicit faith in the clear representations of that faculty, we could not advance a step in the acquisition of experimental knowledge. Yet we know that memory is not infallible: nor can we pretend that in any case there is not a physical possibility of her making a false report. Here, it may be said, is an irremediable imbecility in the very foundation of moral reasoning. But is it less so in demonstrative reasoning? This point deserves a careful examination.

Nor

It was remarked concerning the latter, that it is a proof consisting of an uninterrupted series of axioms. The truth of each is intuitively perceived as we proceed. But this process is of necessity gradual, and these axioms are all brought in succession. It must then be solely by the aid of memory, that they are capable of producing conviction in the mind. by this do I mean to affirm, that we can remember the preceding steps with their connexions, so as to have them all present to our view at one instant; for then we should, in 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 are advanced 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 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 results 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 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 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 on the second, or perhaps on 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 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 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 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 candid reasoner: for though he may be an accute logician who is no orator, he will never be a consummate orator who is no logician.

CHAP. VI.

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 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 first convinced, by what Mr. Locke had said on the subject, that the syllogistic art, with its figures

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