The Complete Aristotle (eng.)

problematic, whenever
the minor premiss is problematic a syllogism always results, only
sometimes it results from the premisses that are taken, sometimes
it requires the conversion of one premiss. We have stated when each
of these happens and the reason why. But if one of the relations is
universal, the other particular, then whenever the major premiss is
universal and problematic, whether affirmative or negative, and the
particular is affirmative and assertoric, there will be a perfect
syllogism, just as when the terms are universal. The demonstration
is the same as before. But whenever the major premiss is universal,
but assertoric, not problematic, and the minor is particular and
problematic, whether both premisses are negative or affirmative, or
one is negative, the other affirmative, in all cases there will be
an imperfect syllogism. Only some of them will be proved per
impossibile, others by the conversion of the problematic premiss,
as has been shown above. And a syllogism will be possible by means
of conversion when the major premiss is universal and assertoric,
whether positive or negative, and the minor particular, negative,
and problematic, e.g. if A belongs to all B or to no B, and B may
possibly not belong to some C. For if the premiss BC is converted
in respect of possibility, a syllogism results. But whenever the
particular premiss is assertoric and negative, there cannot be a
syllogism. As instances of the positive relation we may take the
terms white-animal-snow; of the negative, white-animal-pitch. For
the demonstration must be made through the indefinite nature of the
particular premiss. But if the minor premiss is universal, and the
major particular, whether either premiss is negative or
affirmative, problematic or assertoric, nohow is a syllogism
possible. Nor is a syllogism possible when the premisses are
particular or indefinite, whether problematic or assertoric, or the
one problematic, the other assertoric. The demonstration is the
same as above. As instances of the necessary and positive relation
we may take the terms animal-white-man; of the necessary and
negative relation, animal-white-garment. It is evident then that if
the major premiss is universal, a syllogism always results, but if
the minor is universal nothing at all can ever be proved.
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    Whenever one premiss is necessary, the other problematic, there
will be a syllogism when the terms are related as before; and a
perfect syllogism when the minor premiss is necessary. If the
premisses are affirmative the conclusion will be problematic, not
assertoric, whether the premisses are universal or not: but if one
is affirmative, the other negative, when the affirmative is
necessary the conclusion will be problematic, not negative
assertoric; but when the negative is necessary the conclusion will
be problematic negative, and assertoric negative, whether the
premisses are universal or not. Possibility in the conclusion must
be understood in the same manner as before. There cannot be an
inference to the necessary negative proposition: for ‘not
necessarily to belong’ is different from ‘necessarily not to
belong’.
    If the premisses are affirmative, clearly the conclusion which
follows is not necessary. Suppose A necessarily belongs to all B,
and let B be possible for all C. We shall have an imperfect
syllogism to prove that A may belong to all C. That it is imperfect
is clear from the proof: for it will be proved in the same manner
as above. Again, let A be possible for all B, and let B necessarily
belong to all C. We shall then have a syllogism to prove that A may
belong to all C, not that A does belong to all C: and it is
perfect, not imperfect: for it is completed directly through the
original premisses.
    But if the premisses are not similar in quality, suppose first
that the negative premiss is necessary, and let necessarily A not
be possible for any B, but let B be possible for all C. It is
necessary then that A belongs to no C. For suppose A to belong to
all C or to some C. Now we assumed that A is not possible for any
B. Since then the negative proposition is convertible, B is not
possible for any A. But A is supposed to belong to all C or to some
C. Consequently B will not be possible for any C or for all C. But
it was originally laid down that B is possible for all C. And it is
clear that the possibility of belonging can be inferred, since the
fact of not belonging is inferred. Again, let the affirmative
premiss be necessary,