=12. Induction.= The form of conclusion previously discussed, _because
it has been so, I expect it will continue to be so in the future_, is
the form through which each science has arisen and has won its real
content, that is, its value for the judgment of the future. It is called
_inference by induction_, and the sciences in which it is
preponderatingly applied are called _inductive sciences_. They are also
called experiential or empirical sciences. At the basis of this
nomenclature is the notion that there are other sciences, the deductive
or rational sciences, in which a reverse logical procedure is applied,
whereby from general principles admitted to be valid in advance,
according to an absolutely sure logical process, conclusions of like
absolute validity are drawn. At the present time people are beginning to
recognize the fact that the deductive sciences must give up these claims
one by one, and that they already have given them up to a certain
extent; partly because on closer study they prove to be inductive
sciences, and partly because they must forego the title and rank of a
science altogether. The latter alternative applies especially to those
provinces of knowledge which have not been used in prophesying the
future or cannot be so used.
To return to the inductive method--it is to be noted that _Aristotle_,
who was the first to describe it, proposed two kinds of induction, the
_complete_ and the _incomplete_. The first has this form: since _all_
things of a certain kind are so, each _individual thing_ is so. While
the incomplete induction merely says: since _many_ things of a certain
kind are so, _presumably_ all things of this kind are so. One instantly
perceives that the two conclusions are essentially different. The first
lays claim to afford an absolutely certain result. But it rests upon the
assumption that _all_ the things of the kind in question are known and
have been tested as to their behavior. This hypothesis is generally
impossible of fulfilment, since we can never prove that there are not
more things of the same kind other than those known to us or tested by
us. Moreover, the conclusion is _superfluous_, as it merely repeats
knowledge that we have already directly acquired, since we have tested
_all_ the things of the one kind, hence the special thing to which the
predication refers.
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