The Complete Aristotle (eng.)

not belong to
some’ is indefinite, it may be used truly of that also which
belongs to none. But if R belongs to no S, no syllogism is
possible, as has been shown. Clearly then no syllogism will be
possible here.
    But if the negative term is universal, whenever the major is
negative and the minor affirmative there will be a syllogism. For
if P belongs to no S, and R belongs to some S, P will not belong to
some R: for we shall have the first figure again, if the premiss RS
is converted.
    But when the minor is negative, there will be no syllogism.
Terms for the positive relation are animal, man, wild: for the
negative relation, animal, science, wild-the middle in both being
the term wild.
    Nor is a syllogism possible when both are stated in the
negative, but one is universal, the other particular. When the
minor is related universally to the middle, take the terms animal,
science, wild; animal, man, wild. When the major is related
universally to the middle, take as terms for a negative relation
raven, snow, white. For a positive relation terms cannot be found,
if R belongs to some S, and does not belong to some S. For if P
belongs to all R, and R to some S, then P belongs to some S: but we
assumed that it belongs to no S. Our point, then, must be proved
from the indefinite nature of the particular statement.
    Nor is a syllogism possible anyhow, if each of the extremes
belongs to some of the middle or does not belong, or one belongs
and the other does not to some of the middle, or one belongs to
some of the middle, the other not to all, or if the premisses are
indefinite. Common terms for all are animal, man, white: animal,
inanimate, white.
    It is clear then in this figure also when a syllogism will be
possible, and when not; and that if the terms are as stated, a
syllogism results of necessity, and if there is a syllogism, the
terms must be so related. It is clear also that all the syllogisms
in this figure are imperfect (for all are made perfect by certain
supplementary assumptions), and that it will not be possible to
reach a universal conclusion by means of this figure, whether
negative or affirmative.
7
    It is evident also that in all the figures, whenever a proper
syllogism does not result, if both the terms are affirmative or
negative nothing necessary follows at all, but if one is
affirmative, the other negative, and if the negative is stated
universally, a syllogism always results relating the minor to the
major term, e.g. if A belongs to all or some B, and B belongs to no
C: for if the premisses are converted it is necessary that C does
not belong to some A. Similarly also in the other figures: a
syllogism always results by means of conversion. It is evident also
that the substitution of an indefinite for a particular affirmative
will effect the same syllogism in all the figures.
    It is clear too that all the imperfect syllogisms are made
perfect by means of the first figure. For all are brought to a
conclusion either ostensively or per impossibile. In both ways the
first figure is formed: if they are made perfect ostensively,
because (as we saw) all are brought to a conclusion by means of
conversion, and conversion produces the first figure: if they are
proved per impossibile, because on the assumption of the false
statement the syllogism comes about by means of the first figure,
e.g. in the last figure, if A and B belong to all C, it follows
that A belongs to some B: for if A belonged to no B, and B belongs
to all C, A would belong to no C: but (as we stated) it belongs to
all C. Similarly also with the rest.
    It is possible also to reduce all syllogisms to the universal
syllogisms in the first figure. Those in the second figure are
clearly made perfect by these, though not all in the same way; the
universal syllogisms are made perfect by converting the negative
premiss, each of the particular syllogisms by reductio ad
impossibile. In the first figure particular syllogisms are indeed
made perfect by themselves, but it is possible also to prove them
by means of the second figure, reducing them ad impossibile, e.g.
if A belongs to all B, and B to some C, it follows that A belongs
to some C. For if it belonged to no C, and belongs to all B, then B
will belong to no C: this we know by means of the second figure.
Similarly also demonstration will be possible in the case of the
negative. For if A belongs to no B, and B belongs to some C, A will
not belong to some C: for if it belonged to all C, and belongs to
no