The Logic of Chance, 3rd edition: An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to StatisticsVenn, John
Philosophy
The Logic of Chance, 3rd edition: An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to Statistics
Venn, John
Chance; Logic, Symbolic and mathematical; Probabilities; Science -- Methodology
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. ch. XXV. §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."
5. That there is some difficulty about such problems
as these must be admitted. The fact that so many people
find them a source of perplexity, and that such various
explanations are offered to solve the perplexity, are a sufficient
proof of this.[3] The considerations of the last chapter,
however, over-technical and even scholastic as some of the
language in which it was expressed may have seemed to the
reader, will I hope guide us to a more satisfactory way of
regarding the matter.
Public-domain text, read in full here on John Shaqi.
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