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
24. It may perhaps be supposed that such an example
as this is a _reductio ad absurdum_ of the principle upon which
Life and other Insurances are founded. But a moment's
consideration will show that this is quite a mistake, and
that the principle of insurance is just as applicable to
examples of this kind as to any other. An office need find
no difficulty in the case supposed. They _might_ (for a reason
to be mentioned presently, they probably _would_ not) insure
the individual without inconsistency at a rate determined
by either average. They might say to him, "You are an
Englishman. Out of the multitude of English who come to
us nine in ten die if they go to Madeira. We will insure
you at a rate assigned by these statistics, knowing that in
the long run all will come right so far as we are concerned.
You are also consumptive, it is true, and we do not know
what proportion of the English are consumptive, nor what
proportion of English consumptives die in Madeira. But
this does not really matter for our purpose. The formula,
nine in ten die, is in reality calculated by taking into account
these unknown proportions; for, though we do not know
them in themselves, statistics tell us all that we care to
know about their results. In other words, whatever unknown
elements may exist, must, in regard to all the effects
which they can produce, have been already taken into
account, so that our ignorance about them cannot in the
least degree invalidate such conclusions as we are able to
draw. And this is sufficient for our purpose." But precisely
the same language might be held to him if he presented
himself as a consumptive man; that is to say, the office
could safely carry on its proceedings upon either alternative.
This would, of course, be a very imperfect state for the
matter to be left in. The only rational plan would be to
isolate the case of consumptive Englishmen, so as to make
a separate calculation for their circumstances. This calculation
would then at once supersede all other tables so
far as they were concerned; for though, _in the end_, it could
not arrogate to itself any superiority over the others, it
would in the mean time be marked by fewer and slighter
aberrations from the truth.
25. The real reason why the Insurance office could
not long work on the above terms is of a very different
kind from that which some readers might contemplate, and
belongs to a class of considerations which have been much
neglected in the attempts to construct sciences of the different
branches of human conduct. It is nothing else than
that annoying contingency to which prophets since the time
of Jonah have been subject, of uttering _suicidal_ prophecies;
of publishing conclusions which are perfectly certain when
every condition and cause but one have been taken into
account, that one being the effect of the prophecy itself
upon those to whom it refers.
Public-domain text, read in full here on John Shaqi.
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