Page:Philosophical Transactions - Volume 053.djvu/437

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circumſtances, it has happened a certain number of times, and failed a certain other number of times. He adds, that he ſoon perceived that it would not be very difficult to do this, provided ſome rule could be found according to which we ought to eſtimate the chance that the probability for the happening of an event perfectly unknown, ſhould lie between any two named degrees of probability, antecedently to any experiments made about it; and that it appeared to him that the rule muſt be to ſuppoſe the chance the ſame that it ſhould lie between any two equidifferent degrees; which, if it were allowed, all the reſt might be eaſily calculated in the common method of proceeding in the doctrine of chances. Accordingly, I find among his papers a very ingenious ſolution of this problem in this way. But he afterwards conſidered, that the poſtulate on which he had argued might not perhaps be looked upon by all as reaſonable; and therefore he choſe to lay down in another form the propoſition in which he thought the ſolution of the problem is contained, and in a ʃcholium to ſubjoin the reaſons why he thought ſo, rather than to take into his mathematical reaſoning any thing that might admit diſpute. This, you will obſerve, is the method which he has purſued in this eſſay.

Every judicious perſon will be ſenſible that the problem now mentioned is by no means merely a curious ſpeculation in the doctrine of chances, but neceſſary to be ſolved in order to a ſure foundation for all our reaſonings concerning paſt facts, and what is likely to be hereafter. Common ſenſe is indeed ſufficient to ſhew us that, from the obſervation of what has in former inſtances been the conſequence of a certain