In the reduced form the inductive syllogism was described by Aldrich as
"_Syllogismus in Barbara cujus minor_ (i.e. every M is S) _reticetur_."
Whately, on the other hand, proposed an inductive syllogism with the
major suppressed, that is, instead of the minor premise above, he
supposed a major premise, "Whatever belongs to A, B, C magnets belongs
to all." Mill thereupon supposed a still more general premise, an
assumption of the uniformity of nature. Since Mill's time, however, the
logic of induction tends to revert towards syllogisms more like that of
Aristotle. Jevons supposed induction to be inverse deduction,
distinguished from direct deduction as analysis from synthesis, e.g. as
division from multiplication; but he really meant that it is a deduction
from a hypothesis of the law of a cause to particular effects which,
being true, verify the hypothesis. Sigwart declares himself in agreement
with Jevons; except that, being aware of the difference between
hypothetical deduction and mathematical analysis, and seeing that,
whereas analysis (e.g. in division) leads to certain conclusions,
hypothetical deduction is not certain of the hypothesis, he arrives at
the more definite view that induction is not analysis proper but
hypothetical deduction, or "reduction," as he proposes to call it.
Reduction he defines as "the framing of possible premises for given
propositions, or the construction of a syllogism when the conclusion and
one premise is given." On this view induction becomes a reduction in the
form: all M is P (hypothesis), S is M (given), :. S is P (given). The
views of Jevons and Sigwart are in agreement in two main points.
According to both, induction, instead of inferring from A, B, C magnets
the conclusion "Therefore all magnets attract iron," infers from the
hypothesis, "Let every magnet attract iron," to A, B, C magnets, whose
given attraction verifies the hypothesis. According to both, again, the
hypothesis of a law with which the process starts contains more than is
present in the particular data: according to Jevons, it is the
hypothesis of a law of a cause from which induction deduces particular
effects; and according to Sigwart, it is a hypothesis of the ground from
which the particular data necessarily follow according to universal
laws. Lastly, Wundt's view is an interesting piece of eclecticism, for
he supposes that induction begins in the form of Aristotle's inductive
syllogism, S-P, S-M, M-P, and becomes an inductive method in the form of
Jevons's inverse deduction, or hypothetical deduction, or analysis, M-P,
S-M, S-P. In detail, he supposes that, while an "inference by
comparison," which he erroneously calls an affirmative syllogism in the
second figure, is preliminary to induction, a second "inference by
connexion," which he erroneously calls a syllogism in the third figure
with an indeterminate conclusion, is the inductive syllogism itself.
This is like Aristotle's inductive syllogism in the arrangement of
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