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
2. (I.) One of the most fertile sources of error and
confusion upon the subject has been already several times
alluded to, and in part discussed in a previous chapter.
This consists in choosing the class to which to refer an
event, and therefore judging of the rarity of the event and
the consequent improbability of foretelling it, _after it has
happened_, and then transferring the impressions we experience
to a supposed contemplation of the event beforehand.
The process in itself is perfectly legitimate (however unnecessary
it may be), since time does not in strictness enter
at all into questions of Probability. No error therefore
need arise in this way, if we were careful as to the class
which we thus selected; but such carefulness is often neglected.
An illustration may afford help here. A man once
pointed to a small target chalked upon a door, the target
having a bullet hole through the centre of it, and surprised
some spectators by declaring that he had fired that shot
from an old fowling-piece at a distance of a hundred yards,
His statement was true enough, but he suppressed a rather
important fact. The shot had really been aimed in a general
way at the barn-door, and had hit it; the target was afterwards
chalked round the spot where the bullet struck. A
deception analogous to this is, I think, often practised unconsciously
in other matters. We judge of events on a similar
principle, feeling and expressing surprise in an equally unreasonable
way, and deciding as to their occurrence on
grounds which are really merely a subsequent adjunct of our
own. Butler's remarks about 'the story of Cæsar,' discussed
already in the twelfth chapter, are of this character. He
selects a series of events from history, and then imagines a
person guessing them correctly who at the time had not the
history before him. As I have already pointed out, it is one
thing to be unlikely to guess an event rightly without
specific evidence; it is another and very different thing to
appreciate the truth of a story which is founded partly or
entirely upon evidence. But it is a great mistake to transfer
to one of these ways of viewing the matter the mental impressions
which properly belong to the other. It is like
drawing the target afterwards, and then being surprised to
find that the shot lies in the centre of it.
3. One aspect of this fallacy has been already discussed,
but it will serve to clear up difficulties which are
often felt upon the subject if we reexamine the question
under a somewhat more general form.
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