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
7. There is another and practical way of getting rid
of the perplexities of modal reasoning which must be noticed
here. It is the resource of ordinary reasoners rather than the
decision of professed logicians,[7] and, like the first method of
evasion already pointed out in this chapter, is of very partial
application. It consists in treating the premises, during the
process of reasoning, as if they were pure, and then reintroducing
the modality into the conclusion, as a sort of
qualification of its full certainty. When each of the premises
is nearly certain, or when from any cause we are not
concerned with the extent of their departure from full certainty,
this rough expedient will answer well enough. It is,
I apprehend, the process which passes through the minds of
most persons in such cases, in so far as they reason consciously.
They would, presumably, in such an example as that previously
given (§4), proceed as if the premises that 'those
who take arsenic will die,' and that 'the man in question
has taken it,' were quite true, instead of being only probably
true, and they would consequently draw the conclusion that
'he would die.' But bearing in mind that the premises are
not certain, they would remember that the conclusion was
only to be held with a qualified assent. This they would
express quite correctly, if the mere nature and not the
degree of that assent is taken into account, by saying that
'he is likely to die.' In this case the modality is rejected
temporarily from the premises to be reintroduced into the
conclusion.
It is obvious that such a process as this is of a very
rough and imperfect kind. It does, in fact, omit from accurate
consideration just the one point now under discussion.
It takes no account of the varying shades of expression by
which the degree of departure from perfect conviction is
indicated, which is of course the very thing with which
modality is intended to occupy itself. At best, therefore, it
could only claim to be an extremely rude way of deciding
questions, the accurate and scientific methods of treating
which are demanded of us.
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