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
That men _do_ not believe in exact accordance with this
theory must have struck almost every one, but this has
probably been considered as mere exception and irregularity;
the assumption being made that on the average, and in far
the majority of cases, they do so believe. As stated above,
it is very doubtful whether the tendency which has just
been discussed is not so widely prevalent that it might with
far more propriety be called the rule than the exception.
And it may be better that this should be so: many good
results may follow from that cheerful disposition which induces
a man sometimes to go on trying after some great
good, the chance of which he overvalues. He will keep on
through trouble and disappointment, without serious harm
perhaps, when the cool and calculating bystander sees plainly
that his 'measure of belief' is much higher than it should
be. So, too, the tendency also so common, of underrating
the chance of a great evil may also work for good. By many
men death might be looked upon as an almost infinite evil,
at least they would so regard it themselves; suppose they
kept this contingency constantly before them at its right
value, how would it be possible to get through the practical
work of life? Men would be stopping indoors because if
they went out they might be murdered or bitten by a mad
dog. To say this is not to advocate a return to our instincts;
indeed when we have once reached the critical and conscious
state, it is hardly possible to do so; but it should be noticed
that the advantage gained by correcting them is at best but
a balanced one.[3] What is most to our present purpose, it
suggests the inexpediency of attempting to found an exact
theory on what may afterwards prove to be a mere instinct,
unauthorized in its full extent by experience.
11. It may be replied, that though people, as a matter
of fact, do not apportion belief in this exact way, yet they
_ought_ to do so. The purport of this remark will be examined
presently; it need only be said here that it grants all that
is now contended for. For it admits that the degree of our
belief is capable of modification, and may need it. But in
accordance with what is the belief to be modified? obviously
in accordance with experience; it cannot be trusted to by
itself, but the fraction at which it is to be rated must be
determined by the comparative frequency of the events to
which it refers. Experience then furnishing the standard, it
is surely most reasonable to start from this experience, and to
found the theory of our processes upon it.
Public-domain text, read in full here on John Shaqi.
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