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
So long therefore as we make the logically possible
though practically absurd supposition that some men will
continue to pay a higher rate than they need, there is nothing
to prevent the English consumptives (some or all) from
insuring in each category and paying its appropriate premium.
As soon as they gave any thought to the matter, of
course they would, in the case supposed, all prefer to insure
as consumptives. But their doing this would disturb each set
of statistics. The English mortality in Madeira would instantly
become heavier, so far as the Insurance company was
concerned, by the loss of all their best lives; whilst the consumptive
statistics (unless _all_ the English consumptives had
already been taken for insurance) would be in the same way
deteriorated.[5] A slight readjustment therefore of each scale
of insurance would then be needed; this is the disturbance
mentioned just above. It must be clearly understood, however,
that it is not our original statistics which have proved
to be inconsistent, but simply that there were practical
obstacles to carrying out a system of insurance upon them.
28. Examples subject to the difficulty now under
consideration will doubtless seem perplexing to the student
unacquainted with the subject. They are difficult to reconcile
with any other view of the science than that insisted on
throughout this Essay, viz. that we are only concerned with
averages. It will perhaps be urged that there are two
different values of the man's life in these cases, and that
they cannot both be true. Why not? The 'value' of his
life is simply the number of years to which men in his
circumstances do, on the average, attain; we have the man
set before us under two different circumstances; what wonder,
therefore, that these should offer different averages? In such
an objection it is forgotten that we have had to substitute
for the unattainable result about the individual, the really
attainable result about a set of men as much like him as
possible. The difficulty and apparent contradiction only
arise when people will try to find some justification for their
belief in the individual case. What can we possibly conclude,
it may be asked, about this particular man John
Smith's prospects when we are thus offered two different
values for his life? Nothing whatever, it must be replied;
nor could we in reality draw a conclusion, be it remembered,
in the former case, when we were practically confined to one
set of statistics. There also we had what we called the
'value' of his life, and since we only knew of one such value,
we came to regard it as in some sense appropriate to him as
an individual. Here, on the other hand, we have two values,
belonging to different series, and as these values are really
different it may be complained that they are discordant, but
such a complaint can only be made when we do what we
have no right to do, viz. assign a value to the individual
which shall admit of individual justification.
Public-domain text, read in full here on John Shaqi.
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