teftimony, the poffible or probable design in giving it, the difpofition of the hearers to whom it was given, and feveral other circumftances, have all confiderable influence in fixing the degree of credibility. But of thefe I thall have occafion to take notice afterwards. It deferves likewife to be attended to on this fubject, that in a number of concurrent teftimonies, (in cafes wherein there could have been no previous concert) there is a probability diftinct from that which may be termed the fum of the probabilities refulting from the teftimonies of the witneffes, a probability which would remain even though the witneffes were of fuch a character as to merit no faith at all. This probability arifeth purely from the concurrence itfelf. That fuch a concurrence fhould fpring from chance, is as one to infinite; that is, in other words, morally impoffible. If therefore concert be excluded, there remains no other caufe but the reality of the fact.

Now to this fpecies of evidence, teftimony, we are first immediately indebted for all the branches of philology, fuch as hiftory, civil, ecclefiaftic, and literary, grammar, languages, jurifprudence, and criticism; to which I may add revealed religion, as far as it is to be confidered

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fidered as a fubject of historical and critical inquiry, and fo discoverable by natural means: and fecondly, to the fame fource we owe, as was hinted above, a great part of that light which is commonly known under the name of experience, but which is, in fact, not founded on our own perfonal obfervations, or the notices originally given by our own fenfes, but on the attefted experiences and obfervations of others. So that as hence we derive entirely our knowledge of the actions and productions of men, efpecially in other regions, and in former ages; hence alfo we derive, in a much greater measure than is commonly imagined, our acquaintance with Nature and her works.--Logic, rhetoric, ethics, œconomics, and politics, are properly branches of pneumatology, though very closely connected with the philological ftudies above enumerated.

IV. Calculations of chances.

THE laft kind of evidence I propofed to confider, was that refulting from calculations of chances. Chance is not commonly understood either in philofophic or in vulgar language to imply the exclufion of a caufe, but our ignorance of the caufe. It is often employed to de

note a bare poffibility of an event, when nothing is known either to produce or to hinder it. But in this meaning it can never be made the subject of calculation. It then only affords fcope to the calculator, when a caufe is known for the production of an effect, and when that effect muft neceffarily be attended with this or that or the other circumftance; but no caufe is known to determine us to regard one particular circumftance, in preference to the reft, as that which fhall accompany the fuppofed effect. The effect is then confidered as neceffary, but the circumftance as only cafual or contingent. When a die is thrown out of the hand, we know that its gravity will make it fall; we know alfo, that this, together with its cubical figure, will make it lie fo, when intercepted by the table, as to have one fide facing upwards. Thus far we proceed on the certain principles of a uniform experience; but there is no principle which can lead me to conclude, that one fide rather than another will be turned up. I know that this circumftance is not without a caufe; but is, on the contrary, as really effected by the previous toffing 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 mo

tions given it, in this manner, do inevitably escape my notice; and fo are held for nothing, I fay, therefore, that the chance is equal for every one of the fix fides. Now, if five of these were marked with the fame figure, fuppofe a dagger [+], and only one with an afterisk [*], I should, in that cafe, fay, there were five chances that the die would turn up the dagger, for one that it would turn up the afterifk. For the turning up each of the fix fides being equally poffible, there are five cafes in which the dagger, and only one in which the afterifk, would be uppermoft.

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 poffibilities on both fides. But though different from experience, it is fo fimilar, that we cannot wonder that it should produce a fimilar effect upon the mind. Thefe different pofitions being confidered as equal, if any of five thall produce one effect, and but the fixth another, the mind weighing the different events, refteth in an expectation of that in which the greater number of chances concur; but ftill accompanied with a degree of hefitancy, which appears propor

tioned to the number of chances on the oppofite fide. It is much after the fame manner that the mind, on comparing its own experiences, when five inftances favour one fide, to one that favours the contrary, determines the greater credibility of the former. Hence in all complicated cafes, the very degree of probability may be arithmetically afcertained. That two dice marked in the common way will turn up feven, is thrice as probable as that they will turn up eleven, and fix times as probable as that they will turn up twelve*. The degree of probability is here determined demonstratively. It is indeed true, that fuch 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, infurances, and feyeral other commercial articles. In fuch cases, a great number of inftances is neceffary, the greatest exactness in collecting them on each fide, and due care that there be no difcoverable peculiarity in any

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

The only chance for 12 is A 6. B 6. The 1ft is to the zd, as

6 to 2; to the 3d, as 6 to 1.

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