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
29. Is it then perfectly arbitrary what series or class
of instances we select by which to judge? By no means; it
has been stated repeatedly that in choosing a series, we must
seek for one the members of which shall resemble our individual
in as many of his attributes as possible, subject only
to the restriction that it must be a sufficiently extensive
series. What is meant is, that in the above case, where we
have two series, we cannot fairly call them contradictory; the
only valid charge is one of incompleteness or insufficiency for
their purpose, a charge which applies in exactly the same
sense, be it remembered, to all statistics which comprise
genera unnecessarily wider than the species with which we
are concerned. The only difference between the two different
classes of cases is, that in the one instance we are on a
path which we know will lead at the last, through many
errors, towards the truth (in the sense in which truth can be
attained here), and we took it for want of a better. In the
other instance we have two such paths, perfectly different
paths, either of which however will lead us towards the truth
as before. Contradiction can only seem to arise when it is
attempted to justify each separate step on our paths, as well
as their ultimate tendency.
Still it cannot be denied that these objections are a
serious drawback to the completeness and validity of any
anticipations which are merely founded upon statistical frequency,
at any rate in an early stage of experience, when
but few statistics have been collected. Such knowledge as
Probability can give is not in any individual case of a high
order, being subject to the characteristic infirmity of repeated
error; but even when measured by its own standard
it commences at a very low stage of proficiency. The
errors are then relatively very numerous and large compared
with what they may ultimately be reduced to.
Public-domain text, read in full here on John Shaqi.
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