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nydus/The Logic of Chance, 3rd EditionPublic

This work examines the physical foundations of probability by analyzing the formation and behavior of statistical series. It explores the nature of laws of error, the processes of causation, and the empirical methods required to establish and prove probabilistic data.

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Table of Contents

CONSEQUENCES OF THE FOREGOING DISTINCTIONS.

conclude them to be false. And the like may be said of a single common fact.”

§ 4. These remarks have been a good deal criticized, and they certainly seem to me misleading and obscure in their reference. If one may judge by the context, and by another passage in which the same argument is afterwards referred to,[1] it would certainly appear that Butler drew no distinction between miraculous accounts, and other accounts which, to use any of the various expressions in common use, are unlikely or improbable or have a presumption against them; and concluded that since some of the latter were instantly accepted upon somewhat mediocre testimony, it was altogether irrational to reject the former when similarly or better supported.[2] This subject will come again under our notice, and demand fuller discussion, in the chapter on the Credibility of extraordinary stories. It will suffice here to

remark that, however satisfactory such a view of the matter might be to some theologians, no antagonist of miracles would for a moment accept it. He would naturally object that, instead of the miraculous element being (as Butler considers) “a small additional presumption” against the narrative, it involved the events in a totally distinct class of incredibility; that it multiplied, rather than merely added to, the difficulties and objections in the way of accepting the account.

Mill's remarks (Logic, Bk. III.[ TN: space] ch. XXV.[ TN: space] § 4) are of a different character. Discussing the grounds of disbelief he speaks of people making the mistake of “overlooking the distinction between (what may be called) improbability before the fact, and improbability after it, two different properties, the latter of which is always a ground of disbelief, the former not always.” He instances the throwing of a die. It is improbable beforehand that it should turn up ace, and yet afterwards, “there is no reason for disbelieving it if any credible witness asserts it.” So again, “the chances are greatly against A. B.'s dying, yet if any one tells us that he died yesterday we believe it.”

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