The Complete Aristotle (eng.)

resembles the third. For
example let A be evil, B making war against neighbours, C Athenians
against Thebans, D Thebans against Phocians. If then we wish to
prove that to fight with the Thebans is an evil, we must assume
that to fight against neighbours is an evil. Evidence of this is
obtained from similar cases, e.g. that the war against the Phocians
was an evil to the Thebans. Since then to fight against neighbours
is an evil, and to fight against the Thebans is to fight against
neighbours, it is clear that to fight against the Thebans is an
evil. Now it is clear that B belongs to C and to D (for both are
cases of making war upon one’s neighbours) and that A belongs to D
(for the war against the Phocians did not turn out well for the
Thebans): but that A belongs to B will be proved through D.
Similarly if the belief in the relation of the middle term to the
extreme should be produced by several similar cases. Clearly then
to argue by example is neither like reasoning from part to whole,
nor like reasoning from whole to part, but rather reasoning from
part to part, when both particulars are subordinate to the same
term, and one of them is known. It differs from induction, because
induction starting from all the particular cases proves (as we saw)
that the major term belongs to the middle, and does not apply the
syllogistic conclusion to the minor term, whereas argument by
example does make this application and does not draw its proof from
all the particular cases.
25
    By reduction we mean an argument in which the first term clearly
belongs to the middle, but the relation of the middle to the last
term is uncertain though equally or more probable than the
conclusion; or again an argument in which the terms intermediate
between the last term and the middle are few. For in any of these
cases it turns out that we approach more nearly to knowledge. For
example let A stand for what can be taught, B for knowledge, C for
justice. Now it is clear that knowledge can be taught: but it is
uncertain whether virtue is knowledge. If now the statement BC is
equally or more probable than AC, we have a reduction: for we are
nearer to knowledge, since we have taken a new term, being so far
without knowledge that A belongs to C. Or again suppose that the
terms intermediate between B and C are few: for thus too we are
nearer knowledge. For example let D stand for squaring, E for
rectilinear figure, F for circle. If there were only one term
intermediate between E and F (viz. that the circle is made equal to
a rectilinear figure by the help of lunules), we should be near to
knowledge. But when BC is not more probable than AC, and the
intermediate terms are not few, I do not call this reduction: nor
again when the statement BC is immediate: for such a statement is
knowledge.
26
    An objection is a premiss contrary to a premiss. It differs from
a premiss, because it may be particular, but a premiss either
cannot be particular at all or not in universal syllogisms. An
objection is brought in two ways and through two figures; in two
ways because every objection is either universal or particular, by
two figures because objections are brought in opposition to the
premiss, and opposites can be proved only in the first and third
figures. If a man maintains a universal affirmative, we reply with
a universal or a particular negative; the former is proved from the
first figure, the latter from the third. For example let stand for
there being a single science, B for contraries. If a man premises
that contraries are subjects of a single science, the objection may
be either that opposites are never subjects of a single science,
and contraries are opposites, so that we get the first figure, or
that the knowable and the unknowable are not subjects of a single
science: this proof is in the third figure: for it is true of C
(the knowable and the unknowable) that they are contraries, and it
is false that they are the subjects of a single science.
    Similarly if the premiss objected to is negative. For if a man
maintains that contraries are not subjects of a single science, we
reply either that all opposites or that certain contraries, e.g.
what is healthy and what is sickly, are subjects of the same
science: the former argument issues from the first, the latter from
the third figure.
    In general if a man urges a universal objection he must frame
his contradiction with reference to the universal of the terms
taken by his opponent, e.g. if a man maintains