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
Now when we speak of either class as a whole and say
that nine-tenths die, the most natural and soundest meaning
is that that would be the proportion if all without
exception went abroad, or (what comes to the same thing) if
each of these various subdivisions was represented in fair
proportion to its numbers. Or it might only be meant that
they go in some other proportion, depending upon their
tastes, pursuits, and so on. But whatever meaning be adopted
one condition is necessary, viz. that the proportion of each
class that went at the time the statistics were drawn up
must be adhered to throughout. When the class is homogeneous
this is not needed, but when it is heterogeneous the
statistics would be interfered with unless this condition were
secured.
We are here supposed to have two sets of statistics, one
for the English and one for the consumptives, so that the
consumptive English are in a sense counted twice over. If
their mortality is of an intermediate amount, therefore, they
serve to keep down the mortality of one class and to keep
up that of the other. If the statistics are supposed to be
exhaustive, by referring to the whole of each class, it follows
that actually the same individuals must be counted each
time; but if representatives only of each class are taken, the
same individuals need not be inserted in each set of tables.
27. When therefore they come to insure (our remarks
are still confined to our supposed Madeira case), we have
some English consumptives counted as English, and paying
the high rate; and others counted as consumptives and paying
the low rate. Logically indeed we may suppose them all
entered in each class, and paying therefore each rate. What
we have said above is that any individual may be conceived
to present himself for either of these classes. Conceive that
some one else pays his premium for him, so that it is a
matter of indifference to him personally at which rate he
insures, and there is nothing to prevent some of the class (or
for that matter all) going to one class, and others (or all
again) going to the other class.
Public-domain text, read in full here on John Shaqi.
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