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
very many of the circumstances which do admit of such
measurement have been measured, and found to display
the characteristics in question. Hence, from the known
analogy and correlation between our various organs, there
can be no reasonable doubt that if we could arrange human
constitutions in general, or the various elements which compose
them in particular, in the order of their strength, we
should find just such an aggregate regularity and just such
groupings about the mean, as the final result (viz. in this
case the length of their lives) presents to our notice.
3. It will be observed therefore that for this purpose
the existence of natural kinds or groups is necessary.
In our games of chance of course the same die may be
thrown, or a card be drawn from the same pack, as often
as we please; but many of the events which occur to
human beings either cannot be repeated at all, or not often
enough to secure in the case of the single individual any
sufficient statistical uniformity. Such regularity as we trace
in nature is owing, much more than is often suspected,
to the arrangement of things in natural kinds, each of
them containing a large number of individuals. Were each
kind of animals or vegetables limited to a single pair, or
even to but a few pairs, there would not be much scope
left for the collection of statistical tables amongst them.
Or to take a less violent supposition, if the numbers
in each natural class of objects were much smaller than
they are at present, or the differences between their varieties
and sub-species much more marked, the consequent
difficulty of extracting from them any sufficient length of
statistical tables, though not fatal, might be very serious.
A large number of objects in the class, together with that
general similarity which entitles the objects to be fairly
comprised in one class, seem to be important conditions
for the applicability of the theory of Probability to any
phenomenon. Something analogous to this excessive paucity
of objects in a class would be found in the attempt to
apply special Insurance offices to the case of those trades
where the numbers are very limited, and the employment
so dangerous as to put them in a class by themselves. If
an insurance society were started for the workmen in
gunpowder mills alone, a premium would have to be charged
to avoid possible ruin, so high as to illustrate the extreme
paucity of appropriate statistics.
Public-domain text, read in full here on John Shaqi.
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