This formulation proves nothing, inasmuch as a different example does
not contradict the one it is intended to substitute. The explanation is
rather as follows: In the first case there is involved the norm of equal
possibilities, and if we apply the Humian principle of increase of
probability through repetition, we find it effective in explaining the
example. We have known until now always that the numbers in the Little
Lottery are drawn equally, and with approximate regularity,--i.e., none
of the single numbers is drawn for a disproportionately long time. And
as this fact is invariable, we may suppose that every individual number
would appear with comparative regularity. But this explanation is in
accord with Hume’s doctrine.
The doctrine clarifies even astonishing statistical miracles. We know,
e.g., that every year there come together in a certain region a large
number of suicides, fractures of arms and legs, assaults, unaddressed
letters, etc. When, now, we discover that the number of suicides in a
certain semester is significantly less than the number in the same
semester of another year, we will postulate that in the next half-year a
comparatively larger number of suicides will take place so that the
number for the whole year will become approximately equal. Suppose we
say: “There were in the months of January, February, March, April, May
and June an average of x cases. Because we have observed the average to
happen six times, we conclude that it will not happen in the other
months but that instead, x+y cases will occur in those months, since
otherwise the average annual count will not be attained.” This would be
a mistaken abstraction of the principle of equal distribution from the
general Humian law, for the Humian law applied to this case indicates:
“For a long series of years we have observed that in this region there
occur annually so and so many suicides; we conclude therefore that in
this year also there will occur a similar number of suicides.”
The principle of equal distribution presents itself therefore as a
subordinate rule which must not be separated from the principal law. It
is, indeed, valid for the simplest events. When I resolve to walk in x
street, which I know well, and when I recall whether to-day is Sunday or
a week day, what time it is and what the weather is like, I know quite
accurately how the street will look with regard to the people that may
be met there, although a large number of these people have chosen the
time accidentally and might as well have passed through another street.
If, for once, there were more people in the street, I should immediately
ask myself what unusual event had taken place.
Public-domain text, read in full here on John Shaqi.
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