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
Suppose, for instance, a man is seized with a fit in a
house where he has gone to dine, and dies there; and some
one remarks that that was the very house in which he was
born. We begin to wonder if this was an odd coincidence
and nothing more. But if our informant goes on to tell us
that the house was an old family one, and was occupied by
the brother of the deceased, we should feel at once that
these facts put the matter in a rather different light. Or
again, as Cournot suggests, if we hear that two brothers
have been killed in battle on the same day, it makes a great
difference in our estimation of the case whether they were
killed fighting in the same engagement or whether one fell
in the north of France and the other in the south. The
latter we should at once class with mere coincidences, whereas
the former might admit of explanation.
10. The problem, as thus conceived, seems to be one
rather of Inductive Logic than of Probability, because there
is not the slightest attempt to calculate chances. But it
deserves some notice here. Of course no accurate thinker
who was under the sway of modern physical notions would
for a moment doubt that each of the two elements in question
had its own 'cause' behind it, from which (assuming perfect
knowledge) it might have been confidently inferred. No
more would he doubt, I apprehend, that if we could take a
sufficiently minute and comprehensive view, and penetrate
sufficiently far back into the past, we should reach a stage at
which (again assuming perfect knowledge) the co-existence of
the two events could equally have been foreseen. The
employment of the word _casual_ therefore does not imply any
rejection of a cause; but it does nevertheless correspond to a
distinction of some practical importance. We call a coincidence
casual, I apprehend, when we mean to imply that no
knowledge of one of the two elements, which we can suppose
to be practically attainable, would enable us to expect the
other. We know of no generalization which covers them
both, except of course such as are taken for granted to be
inoperative. In such an application it seems that the word
'casual' is not used in antithesis to 'causal' or to 'designed',
but rather to that broader conception of order or regularity
to which I should apply the term Uniformity. The casual
coincidence is one which we cannot bring under any special
generalization; certain, probable, or even plausible.
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