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
Or suppose I am one of a regiment into which a shot
flies, and it strikes me, and me only. At this I am surprised,
and why? Our common language will guide us to the
reason. 'How strange that it should just have hit _me_ of all
men!' We are thinking of the very natural two-fold division
of mankind into, ourselves, and everybody else; our surprise
is again, as it were, retrospective, and in reference to this
division. No anticipation was distinctly formed, because
we did not think beforehand of the event, but the event,
when it has happened, is at once assigned to its appropriate
class.
11. This view is confirmed by the following considerations.
Tell the story to a friend, and he will be a little
surprised, but less so than we were, _his_ division in this
particular case being,--his friends (of whom we are but one),
and the rest of mankind. It is not a necessary division, but
it is the one which will be most likely suggested to him.
Tell it again to a perfect stranger, and his division being
different (viz. we falling into the majority) we shall fail to
make him perceive that there is anything at all remarkable
in the event.
It is not of course attempted in these remarks to justify
our surprise in every case in which it exists. Different
persons might be differently affected in the cases supposed,
and the examples are therefore given mainly for illustration.
Still on principles already discussed (Ch. VI. §32) we might
expect to find something like a general justification of the
amount of surprise.
12. The answer commonly given in these cases is
confined to attempting to show that the surprise should not
arise, rather than to explaining how it does arise. It takes
the following form,--'You have no right to be surprised, for
nothing remarkable has really occurred. If this particular
thing had not happened something equally improbable
must. If the shot had not hit you or your friend, it must
have hit some one else who was _à priori_ as unlikely to be
hit.'
For one thing this answer does not explain the fact
that almost every one _is_ surprised in such cases, and surprised
somewhat in the different proportions mentioned
above. Moreover it has the inherent unsatisfactoriness
of admitting that something improbable has really happened,
but getting over the difficulty by saying that all the
other alternatives were equally improbable. A natural inference
from this is that there is a class of things, in themselves
really improbable, which can yet be established upon
very slight evidence. Butler accepted this inference, and
worked it out to the strange conclusion given above. Mill
attempts to avoid it by the consideration of the very different
values to be assigned to improbability before and after
the event. Some further discussion of this point will be
found in the chapter on Fallacies, and in that on the Credibility
of Extraordinary Stories.
Public-domain text, read in full here on John Shaqi.
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