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 it be asked again, Into what may these agencies
themselves be ultimately analysed? the answer to this
question, in so far as it involves any detailed examination
of them, would be foreign to the plan of this essay. In so
far as any general remarks, applicable to nearly all classes
alike of such agencies, are called for, we are led back to
the point from which we started in the previous chapter,
when we were discussing whether there is necessarily one
fixed law according to which all our series are formed. We
there saw that every event might be regarded as being
brought about by a comparatively few important causes, of
the kind which comprises all of which ordinary observation
takes any notice, and an indefinitely numerous group of
small causes, too numerous, minute, and uncertain in their
action for us to be able to estimate them or indeed to take
them individually into account at all. The important ones,
it is true, may also in turn be themselves conceived to be
made up of aggregates of small components, but they are
still best regarded as being by comparison simple and distinct,
for their component parts act mostly in groups collectively,
appearing and disappearing together, so that they
possess the essential characteristics of unity.
7. Now, broadly speaking, it appears to me that the
most suitable conditions for Probability are these: that the
important causes should be by comparison fixed and permanent,
and that the remaining ones should on the average
continue to act as often in one direction as in the other.
This they may do in two ways. In the first place we
may be able to predicate nothing more of them than the
mere fact that they act[1] as often in one direction as the
other; what we should then obtain would be merely the
simple statistical uniformity that is described in the first
chapter. But it may be the case, and in practice generally
is so more or less approximately, that these minor causes
act also in independence of one another. What we then
get is a group of uniformities such as was explained and
illustrated in the second chapter. Every possible combination
of these causes then occurring with a regular degree
of frequency, we find one peculiar kind of uniformity
exhibited, not merely in the mere fact of excess and defect
(of whatever may be the variable quality in question), but
also in every particular amount of excess and defect.
Hence, in this case, we get what some writers term a
'mean' or 'type,' instead of a simple average. For instance,
suppose a man throwing a quoit at a mark. Here
our fixed causes are his strength, the weight of the quoit,
and the intention of aiming at a given point. These we
must of course suppose to remain unchanged, if we are
to obtain any such uniformity as we are seeking. The
minor and variable causes are all those innumerable little
disturbing influences referred to in the last chapter. It
might conceivably be the case that we were only able to
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