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Sect. II. Of deductive evidence.

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 one 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 twelve”. The degree of probability is here determined demonstratively. It is indeed true, that such mathemetical 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,

* 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 I.
The chances for II are
A 6. B 5.
A 5. B 6.

The only chance for 12 is A 6. B 6. The 1st is to the 2d, as 6 to 2; to the 3d, as 6 to 1.

Part IV. The superiority of scientific evidence re-examined.

and several other commercial articles. In such cases, a great number of instances 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 shew 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.

Ir was observed of memory, that as it instantly succeeds sensation, it is the repository of all the stores VoI. I. I

Sect. II. Of deductive evidence.

from which our experience is collected, and that with-out 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 imbecillity in the very foundation of moral reasoning. But is it less so in demonstrative reasoning 2 This point deserves a careful examination.

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. Nor 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 satisfaçtion 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 contem

Part IV. "The superiority of seientific evidence re-examined.

plating 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 oftecollecting the several steps, wheneverit 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 Priestly, than what was af.

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Sect. II. of deductive evidence.

firmed 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, disco-
vers a new theorem, which, having made a diagram
for the purpose, he attempts to demonstrate, and
succeeds in the attempt. . The figure he hath con-
structed is very comple: 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 2 Whence arises this diffidence 2 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 testimonies of

his memory, in support of the truth of its former tes, timony ? I acknowledge, that after a hundred at

tempts 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,

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