| These agreeing images unite together, and render the idea more strong and lively, not only than a mere fiction of the imagination, but also than any idea, which is supported by a lesser number of experiments. |
| Each new experiment is as a new stroke of the pencil, which bestows an additional vivacity on the colours without either multiplying or enlarging the figure. |
| This operation of the mind has been so fully explained in treating of the probability of chance, that I need not here endeavour to render it more intelligible. |
| Every past experiment may be considered as a kind of chance; I it being uncertain to us, whether the object will exist conformable to one experiment or another. |
| And for this reason every thing that has been said on the one subject is applicable to both. |
| Thus upon the whole, contrary experiments produce an imperfect belief, either by weakening the habit, or by dividing and afterwards joining in different parts, that perfect habit, which makes us conclude in general, that instances, of which we have no experience, must necessarily resemble those of which we have. |
| To justify still farther this account of the second species of probability, where we reason with knowledge and reflection from a contrariety of past experiments, I shall propose the following considerations, without fearing to give offence by that air of subtilty, which attends them. |
| Just reasoning ought still, perhaps, to retain its force, however subtile; in the same manner as matter preserves its solidity in the air, and fire, and animal spirits, as well as in the grosser and more sensible forms. |
| First, We may observe, that there is no probability so great as not to allow of a contrary possibility; because otherwise it would cease to be a probability, and would become a certainty. |
| That probability of causes, which is most extensive, and which we at present examine, depends on a contrariety of experiments: and it is evident An experiment in the past proves at least a possibility for the future. |
| Secondly, The component parts of this possibility and probability are of the same nature, and differ in number only, but not in kind. |
| It has been observed, that all single chances are entirely equal, and that the only circumstance, which can give any event, that is contingent, a superiority over another is a superior number of chances. |
| In like manner, as the uncertainty of causes is discovery by experience, which presents us with a view of contrary events, it is plain, that when we transfer the past to the future, the known to the unknown, every past experiment has the same weight, and that it is only a superior number of them, which can throw the ballance on any side. |
| The possibility, therefore, which enters into every reasoning of this kind, is composed of parts, which are of the same nature both among themselves, and with those, that compose the opposite probability. |
| Thirdly, We may establish it as a certain maxim, that in all moral as well as natural phaenomena, wherever any cause consists of a number of parts, and the effect encreases or diminishes, according to the variation of that number, the effects properly speaking, is a compounded one, and arises from the union of the several effects, that proceed from each part of the cause. |
| Thus, because the gravity of a body encreases or diminishes by the encrease or diminution of its parts, we conclude that each part contains this quality and contributes to the gravity of the whole. |
| The absence or presence of a part of the cause is attended with that of a proportionable part of the effect. |
| This connexion or constant conjunction sufficiently proves the one part to be the cause of the other. |
| As the belief which we have of any event, encreases or diminishes according to the number of chances or past experiments, it is to be considered as a compounded effect, of which each part arises from a proportionable number of chances or experiments. |
| Let us now join these three observations, and see what conclusion we can draw from them. |
| To every probability there is an opposite possibility. |