We must see first of all if it is of any use to refer the difficulty of
the matter to the form in which the question is put, and to say: The
difficulty results from the question itself. If it be asked, “Are any of
the thousand marbles in the bag white marbles?” the question is
determined by the first handful, if the latter brings to light a single
white marble. If, however, the problem is phrased so: Does the bag
contain white marbles _only_? then, although 999 marbles might already
have been drawn from the receptacle, it can not be determined that the
last marble of the 1000 is white. In the same way, if people assert that
the form of the question determines the answer, it does not follow that
the form of the question is itself determined or distinguished inasmuch
as the object belongs to the first or the second of the above named
categories.
A safe method of distinction consists in calling the first form of the
question positive and the second negative. The positive refers to a
single unit; the negative to a boundless unit. If then I ask: Are there
any white marbles whatever in the bag? the answer is rendered
affirmative by the discovery of a single white marble. But if the
question is phrased: Are there _only_ white marbles in the bag? merely
its form is positive but its intent is negative. To conform the manner
of the question to its intent, it would be necessary to ask: Are there
no other colors than white among the marbles in the bag? And inasmuch as
the negative under given circumstances is in many ways boundless, the
question admits of no answer until the last marble has been brought to
light. If the total number of marbles is unlimited the question can
receive no complete inductive answer in mathematical form; it can be
solved only approximately. So again, if one asks: Are there any purely
blue birds? the answer is affirmative as soon as a single completely
blue bird is brought to light. But if the question is: Do not also
striped birds exist? no answer is possible until the very last bird on
earth is exhibited. In that way only could the possibility be excluded
that not one of the terrestrial fowls is striped. As a matter of fact we
are satisfied with a much less complete induction. So we say: Almost the
whole earth has been covered by naturalists and not one of them reports
having observed a striped bird; hence there would be none such even in
the unexplored parts of the earth. This is an inductive inference and
its justification is quite another question.
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