| Should it be said, that though in an opposition of chances it is impossible to determine with certainty, on which side the event will fall, yet we can pronounce with certainty, that it is more likely and probable, it will be on that side where there is a superior number of chances, than where there is an inferior: should this be said, I would ask, what is here meant by likelihood and probability? The likelihood and probability of chances is a superior number of equal chances; and consequently when we say it is likely the event win fall on the side, which is superior, rather than on the inferior, we do no more than affirm, that where there is a superior number of chances there is actually a superior, and where there is an inferior there is an inferior; which are identical propositions, and of no consequence. |
| The question is, by what means a superior number of equal chances operates upon the mind, and produces belief or assent; since it appears, that it is neither by arguments derived from demonstration, nor from probability. |
| In order to clear up this difficulty, we shall suppose a person to take a dye, formed after such a manner as that four of its sides are marked with one figure, or one number of spots, and two with another; and to put this dye into the box with an intention of throwing it: It is plain, he must conclude the one figure to be more probable than the other, and give the preference to that which is inscribed on the greatest number of sides. |
| He in a manner believes, that this will lie uppermost; though still with hesitation and doubt, in proportion to the number of chances, which are contrary: And according as these contrary chances diminish, and the superiority encreases on the other side, his belief acquires new degrees of stability and assurance. |
| This belief arises from an operation of the mind upon the simple and limited object before us; and therefore its nature will be the more easily discovered and explained. |
| We have nothing but one single dye to contemplate, in order to comprehend one of the most curious operations of the understanding. |
| This dye, formed as above, contains three circumstances worthy of our attention. |
| First, Certain causes, such as gravity, solidity, a cubical figure, &c. |
| which determine it to fall, to preserve its form in its fall, and to turn up one of its sides. |
| Secondly, A certain number of sides, which are supposed indifferent. |
| Thirdly, A certain figure inscribed on each side. |
| These three particulars form the whole nature of the dye, so far as relates to our present purpose; and consequently are the only circumstances regarded by the mind in its forming a judgment concerning the result of such a throw. |
| Let us, therefore, consider gradually and carefully what must be the influence of these circumstances on the thought and imagination. |
| First, We have already observed, that the mind is determined by custom to pass from any cause to its effect, and that upon the appearance of the one, it is almost impossible for it not to form an idea of the other. |
| Their constant conjunction in past instances has produced such a habit in the mind, that it always conjoins them in its thought, and infers the existence of the one from that of its usual attendant. |
| When it considers the dye as no longer supported by the box, it can not without violence regard it as suspended in the air; but naturally places it on the table, and views it as turning up one of its sides. |
| This is the effect of the intermingled causes, which are requisite to our forming any calculation concerning chances. |
| Secondly, It is supposed, that though the dye be necessarily determined to fall, and turn up one of its sides, yet there is nothing to fix the particular side, but that this is determined entirely by chance. |
| The very nature and essence of chance is a negation of causes, and the leaving the mind in a perfect indifference among those events, which are supposed contingent. |
| When therefore the thought is determined by the causes to consider the dye as falling and turning up one of its sides, the chances present all these sides as equal, and make us consider every one of them, one after another, as alike probable and possible. |
| The imagination passes from the cause, viz. the throwing of the dye, to the effect, viz. the turning up one of the six sides; and feels a kind of impossibility both of stopping short in the way, and of forming any other idea. |