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. So much (at present) for the objects. If we turn
to what we have termed the agencies, we find much the
same thing again here. By the adjustment of their relative
intensity, and the respective frequency of their occurrence,
the total effects which they produce are found to be also
tolerably uniform. It is of course conceivable that this
should have been otherwise. It might have been found
that the second group of conditions so exactly corrected the
former as to convert the merely general uniformity into
an absolute one; or it might have been found, on the
other hand, that the second group should aggravate or
disturb the influence of the former to such an extent
as to destroy all the uniformity of its effects. Practically
neither is the case. The second condition simply varies the
details, leaving the uniformity on the whole of precisely
the same general description as it was before. Or if the
objects were supposed to be absolutely alike, as in the case
of successive throws of a penny, it may serve to bring about
a uniformity. Analysis will show these agencies to be
thus made up of an almost infinite number of different
components, but it will detect the same peculiarity that
we have so often had occasion to refer to, pervading almost
all these components. The proportions in which they are
combined will be found to be nearly, though not quite, the
same; the intensity with which they act will be nearly
though not quite equal. And they will all unite and blend
into a more and more perfect regularity as we proceed to
take the average of a larger number of instances.
Take, for instance, the length of life. As we have seen,
the constitutions of a very large number of persons selected
at random will be found to present much the same feature;
general uniformity accompanied by individual irregularity.
Now when these persons go out into the world, they are
exposed to a variety of agencies, the collective influence
of which will assign to each the length of life allotted to
him. These agencies are of course innumerable, and their
mutual interaction complicated beyond all power of analysis
to extricate. Each effect becomes in its turn a cause, is
interwoven inextricably with an indefinite number of other
causes, and reacts upon the final result. Climate, food,
clothing, are some of these agencies, or rather comprise
aggregate groups of them. The nature of a man's work
is also important. One man overworks himself, another
follows an unhealthy trade, a third exposes himself to infection,
and so on.
The result of all this interaction between what we have
thus called objects and agencies is that the final outcome
presents the same general characteristics of uniformity as may
be detected separately in the two constituent elements. Or
rather, as we shall proceed presently to show, it does so
in the great majority of cases.
Public-domain text, read in full here on John Shaqi.
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