The Art of Logical Thinking; Or, The Laws of ReasoningAtkinson, William Walker
Philosophy
The Art of Logical Thinking; Or, The Laws of Reasoning
Atkinson, William Walker
Logic; Reasoning
Brooks says regarding the probability of hypotheses: "The probability of
a hypothesis is in proportion to the number of facts and phenomena it
will explain. The larger the number of facts and phenomena that it will
satisfactorily account for, the greater our faith in the correctness of
our supposition.... If there is more than one hypothesis in respect to
the facts under consideration, that one which accounts for the greatest
number of facts is the most probable.... In order to verify a hypothesis
it must be shown that it will account for all the facts and phenomena.
If these facts are numerous and varied, and the subject is so thoroughly
investigated that it is quite certain that no important class of facts
has been overlooked, the supposition is regarded as true, and the
hypothesis is said to be verified. Thus the hypothesis of the 'daily
rotation' of the earth on its axis to account for the succession of day
and night is accepted as absolutely true. This is the view taken by Dr.
Whewell and many other thinkers in respect to the verification of a
hypothesis. Some writers, however, as Mill and his school, maintain that
in order to verify a hypothesis, we must show not only that it explains
all the facts and phenomena, but that there is no other possible
hypothesis which will account for them.... The former view of
verification is regarded as the correct one. By the latter view, it is
evident that a hypothesis could never be verified."
Jevons says: "In the fourth step (verification), we proceed to compare
these deductions with the facts already collected, or when necessary and
practicable, we make new observations and plan new experiments, so as to
find out whether the hypothesis agrees with nature. If we meet with
several distinct disagreements between our deductions and our
observations, it will become likely that the hypothesis is wrong, and we
must then invent a new one. In order to produce agreement it will
sometimes be enough to change the hypothesis in a small degree. When we
get hold of a hypothesis which seems to give results agreeing with a few
facts, we must not at once assume that it is certainly correct. We must
go on making other deductions from it under various circumstances, and,
whenever it is possible, we ought to verify these results, that is,
compare them with facts observed through the senses. When a hypothesis
is shown in this way to be true in a great many of its results,
especially when it enables us to predict what we should never otherwise
have believed or discovered, it becomes certain that the hypothesis
itself is a true one.... Sometimes it will happen that two or even three
quite different hypotheses all seem to agree with certain facts, so that
we are puzzled which to select.... When there are thus two hypotheses,
one as good as the other, we need to discover some fact or thing which
will agree with one hypothesis and not with the other, because this
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