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
14. Such distinctions as those just insisted on may
seem to some persons to be needless, but serious errors have
occasionally arisen from the neglect of them. The immediate
products of man's mind, so far indeed as we can make
an attempt to obtain them, do not seem to possess this
essential characteristic of Probability. Their characteristic
seems rather to be, either perfect mathematical accuracy or
utter want of it, either law unfailing or mere caprice. If,
e.g., we find the trees in a forest growing in straight lines,
we unhesitatingly conclude that they were planted by man
as they stand. It is true on the other hand, that if we find
them not regularly planted, we cannot conclude that they
were not planted by man; partly because the planter may
have worked without a plan, partly because the subsequent
irregularities brought on by nature may have obscured the
plan. Practically the mind has to work by the aid of imperfect
instruments, and is subjected to many hindrances
through various and conflicting agencies, and by these means
the work loses its original properties. Suppose, for instance,
that a man, instead of producing numerical results by imperfect
observations or by the cast of dice, were to select
them at first hand for himself by simply thinking of them
at once; what sort of series would he obtain? It would be
about as difficult to obtain in this way any such series as
those appropriate to Probability as it would be to keep his
heart or pulse working regularly by direct acts of volition,
supposing that he had the requisite control over these organs.
But the mere suggestion is absurd. A man must have an
object in thinking, he must think according to a rule or formula;
but unless he takes some natural series as a copy, he
will never be able to construct one mentally which shall permanently
imitate the originals. Or take another product of
human efforts, in which the intention can be executed with
tolerable success. When any one builds a house, there are
many slight disturbing influences at work, such as shrinking
of bricks and mortar, settling of foundations, &c. But the
effect which these disturbances are able to produce is so inappreciably
small, that we may fairly consider that the result
obtained is the direct product of the mind, the accurate
realization of its intention. What is the consequence?
Every house in the row, if designed by one man and at one
time, is of exactly the same height, width, &c. as its
neighbours; or if there are variations they are few, definite,
and regular. The result offers no resemblance whatever to
the heights, weights, &c. of a number of men selected at
random. The builder probably had some regular design in
contemplation, and he has succeeded in executing it.
Public-domain text, read in full here on John Shaqi.
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