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
18. We shall find it advisable to commence by ascertaining
how such enquiries as the above would be answered
in the case of ordinary full belief. Such a step would not
offer the slightest difficulty. Suppose, to take a simple
example, that we have obtained the following proposition,--whether
by induction, or by the rules of ordinary deductive
logic, does not matter for our present purpose,--that a certain
mixture of oxygen and hydrogen is explosive. Here we have
an inference, and consequent belief of a proposition. Now
suppose there were any enquiry as to whether our belief
were correct, what should we do? The simplest way of
settling the matter would be to find out by a distinct appeal
to experience whether the proposition was true. Since we
are reasoning about things, the justification of the belief, that
is, the test of its correctness, would be most readily found in
the truth of the proposition. If by any process of inference
I have come to believe that a certain mixture will explode, I
consider my belief to be justified, that is to be correct, if
under proper circumstances the explosion always does occur;
if it does not occur the belief was wrong.
Such an answer, no doubt, goes but a little way, or rather
no way at all, towards explaining what is the nature of belief
in itself; but it is sufficient for our present purpose, which is
merely that of determining what is meant by the correctness
of our belief, and by the test of its correctness. In all inferences
about things, in which the _amount_ of our belief is not
taken into account, such an explanation as the above is quite
sufficient; it would be the ordinary one in any question of
science. It is moreover perfectly intelligible, whether the
conclusion is particular or universal. Whether we believe
that 'some men die', or that 'all men die', our belief may with
equal ease be tested by the appropriate train of experience.
Public-domain text, read in full here on John Shaqi.
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