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
If this remark had been made about the succession of
heads and tails in the throwing up of a penny, it would
have been intelligible. It would simply mean this: that the
constitution of the body was such that we could anticipate
with some confidence what the result would be when it was
treated in a certain way, and that experience would justify
our anticipation in the long run. But applied as it is in a
more general form to the facts of nature, it seems really to
have but little meaning in it. Let us test it by an instance.
Amidst the irregularity of individual births, we find that the
male children are to the female, in the long run, in about
the proportion of 106 to 100. Now if we were told that
there is nothing in this but "the development of their respective
probabilities," would there be anything in such a
statement but a somewhat pretentious re-statement of the
fact already asserted? The probability _is_ nothing but that
proportion, and is unquestionably in this case derived from
no other source but the statistics themselves; in the above
remark the attempt seems to be made to invert this process,
and to derive the sequence of events from the mere numerical
statement of the proportions in which they occur.
15. It will very likely be replied that by the probability
above mentioned is meant, not the mere numerical
proportion between, the births, but some fact in our constitution
upon which this proportion depends; that just as
there was a relation of equality between the two sides of the
penny, which produced the ultimate equality in the number
of heads and tails, so there may be something in our constitution
or circumstances in the proportion of 106 to 100,
which produces the observed statistical result. When this
something, whatever it might be, was discovered, the observed
numbers might be supposed capable of being determined
beforehand. Even if this were the case, however, it
must not be forgotten that there could hardly fail to be, in
combination with such causes, other concurrent conditions in
order to produce the ultimate result; just as besides the shape
of the penny, we had also to take into account the nature of
the 'randomness' with which it was tossed. What these
may be, no one at present can undertake to say, for the best
physiologists seem indisposed to hazard even a guess upon
the subject.[7] But without going into particulars, one may
assert with some confidence that these conditions cannot well
be altogether independent of the health, circumstances, manners
and customs, &c. (to express oneself in the vaguest way)
of the parents; and if once these influencing elements are
introduced, even as very minute factors, the results cease to
be dependent only on fixed and permanent conditions. We
are at once letting in other conditions, which, if they also
possess the characteristics that distinguish Probability (an
exceedingly questionable assumption), must have that fact
specially proved about them. That this should be the case
Public-domain text, read in full here on John Shaqi.
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