The Complete Aristotle (eng.)

terms in this way, but it cannot be
reached as C is established by means of A and B. Suppose that the
proposition E is inferred from the premisses A, B, C, and D. It is
necessary then that of these one should be related to another as
whole to part: for it has already been proved that if a syllogism
is formed some of its terms must be related in this way. Suppose
then that A stands in this relation to B. Some conclusion then
follows from them. It must either be E or one or other of C and D,
or something other than these.
    (1) If it is E the syllogism will have A and B for its sole
premisses. But if C and D are so related that one is whole, the
other part, some conclusion will follow from them also; and it must
be either E, or one or other of the propositions A and B, or
something other than these. And if it is (i) E, or (ii) A or B,
either (i) the syllogisms will be more than one, or (ii) the same
thing happens to be inferred by means of several terms only in the
sense which we saw to be possible. But if (iii) the conclusion is
other than E or A or B, the syllogisms will be many, and
unconnected with one another. But if C is not so related to D as to
make a syllogism, the propositions will have been assumed to no
purpose, unless for the sake of induction or of obscuring the
argument or something of the sort.
    (2) But if from the propositions A and B there follows not E but
some other conclusion, and if from C and D either A or B follows or
something else, then there are several syllogisms, and they do not
establish the conclusion proposed: for we assumed that the
syllogism proved E. And if no conclusion follows from C and D, it
turns out that these propositions have been assumed to no purpose,
and the syllogism does not prove the original proposition.
    So it is clear that every demonstration and every syllogism will
proceed through three terms only.
    This being evident, it is clear that a syllogistic conclusion
follows from two premisses and not from more than two. For the
three terms make two premisses, unless a new premiss is assumed, as
was said at the beginning, to perfect the syllogisms. It is clear
therefore that in whatever syllogistic argument the premisses
through which the main conclusion follows (for some of the
preceding conclusions must be premisses) are not even in number,
this argument either has not been drawn syllogistically or it has
assumed more than was necessary to establish its thesis.
    If then syllogisms are taken with respect to their main
premisses, every syllogism will consist of an even number of
premisses and an odd number of terms (for the terms exceed the
premisses by one), and the conclusions will be half the number of
the premisses. But whenever a conclusion is reached by means of
prosyllogisms or by means of several continuous middle terms, e.g.
the proposition AB by means of the middle terms C and D, the number
of the terms will similarly exceed that of the premisses by one
(for the extra term must either be added outside or inserted: but
in either case it follows that the relations of predication are one
fewer than the terms related), and the premisses will be equal in
number to the relations of predication. The premisses however will
not always be even, the terms odd; but they will alternate-when the
premisses are even, the terms must be odd; when the terms are even,
the premisses must be odd: for along with one term one premiss is
added, if a term is added from any quarter. Consequently since the
premisses were (as we saw) even, and the terms odd, we must make
them alternately even and odd at each addition. But the conclusions
will not follow the same arrangement either in respect to the terms
or to the premisses. For if one term is added, conclusions will be
added less by one than the pre-existing terms: for the conclusion
is drawn not in relation to the single term last added, but in
relation to all the rest, e.g. if to ABC the term D is added, two
conclusions are thereby added, one in relation to A, the other in
relation to B. Similarly with any further additions. And similarly
too if the term is inserted in the middle: for in relation to one
term only, a syllogism will not be constructed. Consequently the
conclusions will be much more numerous than the terms or the
premisses.
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    Since we understand the subjects with which syllogisms are
concerned, what sort of conclusion is established in each figure,
and in how many moods this is done, it is evident to us both what
sort of