The Complete Aristotle (eng.)

it
is true, positive error may befall one in alternative ways; for it
may arise where one directly believes a connexion or disconnexion
as well as where one’s belief is acquired by inference. The error,
however, that consists in a direct belief is without complication;
but the error resulting from inference-which here concerns us-takes
many forms. Thus, let A be atomically disconnected from all B: then
the conclusion inferred through a middle term C, that all B is A,
will be a case of error produced by syllogism. Now, two cases are
possible. Either (a) both premisses, or (b) one premiss only, may
be false. (a) If neither A is an attribute of any C nor C of any B,
whereas the contrary was posited in both cases, both premisses will
be false. (C may quite well be so related to A and B that C is
neither subordinate to A nor a universal attribute of B: for B,
since A was said to be primarily disconnected from B, cannot have a
genus, and A need not necessarily be a universal attribute of all
things. Consequently both premisses may be false.) On the other
hand, (b) one of the premisses may be true, though not either
indifferently but only the major A-C since, B having no genus, the
premiss C-B will always be false, while A-C may be true. This is
the case if, for example, A is related atomically to both C and B;
because when the same term is related atomically to more terms than
one, neither of those terms will belong to the other. It is, of
course, equally the case if A-C is not atomic.
    Error of attribution, then, occurs through these causes and in
this form only-for we found that no syllogism of universal
attribution was possible in any figure but the first. On the other
hand, an error of non-attribution may occur either in the first or
in the second figure. Let us therefore first explain the various
forms it takes in the first figure and the character of the
premisses in each case.
    (c) It may occur when both premisses are false; e.g. supposing A
atomically connected with both C and B, if it be then assumed that
no C is and all B is C, both premisses are false.
    (d) It is also possible when one is false. This may be either
premiss indifferently. A-C may be true, C-B false-A-C true because
A is not an attribute of all things, C-B false because C, which
never has the attribute A, cannot be an attribute of B; for if C-B
were true, the premiss A-C would no longer be true, and besides if
both premisses were true, the conclusion would be true. Or again,
C-B may be true and A-C false; e.g. if both C and A contain B as
genera, one of them must be subordinate to the other, so that if
the premiss takes the form No C is A, it will be false. This makes
it clear that whether either or both premisses are false, the
conclusion will equally be false.
    In the second figure the premisses cannot both be wholly false;
for if all B is A, no middle term can be with truth universally
affirmed of one extreme and universally denied of the other: but
premisses in which the middle is affirmed of one extreme and denied
of the other are the necessary condition if one is to get a valid
inference at all. Therefore if, taken in this way, they are wholly
false, their contraries conversely should be wholly true. But this
is impossible. On the other hand, there is nothing to prevent both
premisses being partially false; e.g. if actually some A is C and
some B is C, then if it is premised that all A is C and no B is C,
both premisses are false, yet partially, not wholly, false. The
same is true if the major is made negative instead of the minor. Or
one premiss may be wholly false, and it may be either of them.
Thus, supposing that actually an attribute of all A must also be an
attribute of all B, then if C is yet taken to be a universal
attribute of all but universally non-attributable to B, C-A will be
true but C-B false. Again, actually that which is an attribute of
no B will not be an attribute of all A either; for if it be an
attribute of all A, it will also be an attribute of all B, which is
contrary to supposition; but if C be nevertheless assumed to be a
universal attribute of A, but an attribute of no B, then the
premiss C-B is true but the major is false. The case is similar if
the major is made the negative premiss. For in fact what is an
attribute of no A will not be an attribute of any B either; and if
it be yet assumed that C is universally non-attributable to A, but
a universal attribute of B, the premiss C-A is true but the minor
wholly