Thus, if the axioms of mathematics are innate, nature would seem to have
taken unnecessary trouble; since the ordinary process of association
appears to be amply sufficient to confer upon them all the universality
and necessity which they actually possess.
Whatever needless admissions Hume may have made respecting other
necessary truths he is quite clear about the axiom of causation, "That
whatever event has a beginning must have a cause;" whether and in what
sense it is a necessary truth; and, that question being decided, whence
it is derived.
With respect to the first question, Hume denies that it is a necessary
truth, in the sense that we are unable to conceive the contrary. The
evidence by which he supports this conclusion in the _Inquiry_, however,
is not strictly relevant to the issue.
"No object ever discovers, by the qualities which appear to the
senses, either the cause which produced it, or the effects which
will arise from it; nor can our reason, unassisted by experience,
ever draw any inference concerning real existence and matter of
fact."--(IV. p. 35.)
Abundant illustrations are given of this assertion, which indeed cannot
be seriously doubted; but it does not follow that, because we are
totally unable to say what cause preceded, or what effect will succeed,
any event, we do not necessarily suppose that the event had a cause and
will be succeeded by an effect. The scientific investigator who notes a
new phenomenon may be utterly ignorant of its cause, but he will,
without hesitation, seek for that cause.
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