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
There are indeed presumptions as to the time after which
a man, if not heard of, is supposed to be dead (capable of
disproof, of course, by his reappearance). If this time varied
with the age of the man in question, we should at once have
some such standard as we desire, for a reference to the Life
tables would fix his probable duration of life, and so determine
indirectly the measure of probability which satisfied
the law. But this is not the case; the period chosen is
entirely irrespective of age. The nearest case in point (and
that does not amount to much) which I have been able to
ascertain is that of the age after which it has been presumed
that a woman was incapable of bearing children.
This was the age of 53. A certain approach to a statistical
assignment of the chances in this case is to be found in
Quetelet's _Physique Sociale_ (Vol. I. p. 184, note). According
to the authorities which he there quotes it would seem that
in about one birth in 5500 the mother was of the age of 50
or upwards. This does not quite assign the degree of what
may be called the _à priori_ chance against the occurrence of a
birth at that age, because the fact of having commenced a
family at an early age represents some diminution of the
probability of continuing it into later life. But it serves to
give some indication of what may be called the odds against
such an event.
It need not be remarked that any such clues as these to
the measure of judicial certainty are far too slight to be of
any real value. They only deserve passing notice as a possible
logical solution of the problem in question, or rather as
an indication of the mode in which, in theory, such a solution
would have to be sought, were the English law, on those
subjects, a perfectly consistent scheme of scientific evidence.
This is the mode in which one would, under those circumstances,
attempt to extract from its proceedings an admission
of the exact measure of that standard of certainty which it
adopted, but which it declined openly to enunciate.
1. _Formal Logic_, p. 232.
2. This appears to be the purport of some statements in a very
confused passage in Whately's _Logic_ (Bk. II., ch. IV. §1). "A
modal proposition may be stated as a pure one by attaching the mode
to one of the terms, and the proposition will in all respects fall
under the foregoing rules;... 'It is probable that all knowledge is
useful;' 'probably useful' is here the predicate." He draws
apparently no such distinction as that between the true and false
modality referred to in the next note. What is really surprising is
that even Hamilton puts the two (the true and the false modality)
upon the same footing. "In regard to these [the former] the case is
precisely the same; the mode is merely a part of the predicate."
_Logic_, I. 257.
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