using the word there to designate an event that satisfies his definition. But in other places
he uses comparative expressions such as “greater miracle” and “more miraculous.” I don't
see any way of making sense of the argument here without understanding these
comparative expressions to be simply stylistic substitutions for the terms “probable” and
“improbable.” A “greater miracle” would be, then, an event that had a lower probability.
Initially at least, Hume's procedure seems to have some plausibility. Faced with
competing and incompatible hypotheses, it seems plausible to accept the candidate that
has a higher probability of being true (if one is going to accept either of the candidates at
all). And it seems implausible to accept the one that has the lower probability, at least
after one has decided that it does have the lower probability.
It is important, however, to be clear about just what the candidates are, and about just
what the item is to which one is assigning a probability. For example, is the birth of
quintuplets (in humans) probable or improbable? Well, quintuplets are very rare. So the
probability that a randomly selected childbirth—say, the first
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delivery in San Francisco in 2007—will be the birth of quintuplets is very low. On the
other hand, the probability that there have been some quintuplet births in the history of
the world is very, very high. (And that, course, is because there are well-attested accounts
of such births.) The probability that there will be at least one quintuplet birth in the
United States within the next ten years is not quite that high, but it certainly is not low. So
here we have three different propositions about quintuplet births, and it seems that they
have three quite different probabilities. And all of these probabilities are based on
experience.
Armed with this warning, we can consider the Lottery Surprise.
An organization that sponsors a very large prize lottery in the United States recently
informed potential entrants that the chance of winning the grand prize was approximately
one in 100 million. I suppose that this is based on an estimate of the number of entries
that will be received, or something like that. So if I were to submit an entry for this
lottery the probability of my winning the grand prize would be approximately
0.00000001. That is, of course, a very low probability, and I would be very surprised if I
won. Assuming that the lottery is fairly drawn, every other entrant would have that same
probability of winning. Suppose now that the drawing has actually been held, and that we
read a short news story about it. The newspaper reports that a certain man, Henry
Plushbottom of Topeka, Kansas, is the winner of the grand prize. The antecedent
probability—antecedent, that is, to the news story—of Henry's being the winner is
fantastically low. But what is now the consequent probability—consequent to the news
story—that Henry really is the winner?
My own inclination is to say that the news story makes the probability that Henry really
is the winner quite high. Of course, the account in the newspaper does not make it
absolutely certain that Henry won. I know that there are mistakes in newspapers, that
reporters sometimes get the facts wrong, they sometimes lie, and so on. (The New York
Times regularly publishes a list of corrections, with a rate of about one correction for
every fifty news items. And there must be other errors that go uncorrected.) But unless I
have some special reason for doubt in this particular case, I would surely take the