The Complete Aristotle (eng.)

false. Again, in fact it is false to assume that that which
is an attribute of all B is an attribute of no A, for if it be an
attribute of all B, it must be an attribute of some A. If then C is
nevertheless assumed to be an attribute of all B but of no A, C-B
will be true but C-A false.
    It is thus clear that in the case of atomic propositions
erroneous inference will be possible not only when both premisses
are false but also when only one is false.
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    In the case of attributes not atomically connected with or
disconnected from their subjects, (a) (i) as long as the false
conclusion is inferred through the ‘appropriate’ middle, only the
major and not both premisses can be false. By ‘appropriate middle’
I mean the middle term through which the contradictory-i.e. the
true-conclusion is inferrible. Thus, let A be attributable to B
through a middle term C: then, since to produce a conclusion the
premiss C-B must be taken affirmatively, it is clear that this
premiss must always be true, for its quality is not changed. But
the major A-C is false, for it is by a change in the quality of A-C
that the conclusion becomes its contradictory-i.e. true. Similarly
(ii) if the middle is taken from another series of predication;
e.g. suppose D to be not only contained within A as a part within
its whole but also predicable of all B. Then the premiss D-B must
remain unchanged, but the quality of A-D must be changed; so that
D-B is always true, A-D always false. Such error is practically
identical with that which is inferred through the ‘appropriate’
middle. On the other hand, (b) if the conclusion is not inferred
through the ‘appropriate’ middle-(i) when the middle is subordinate
to A but is predicable of no B, both premisses must be false,
because if there is to be a conclusion both must be posited as
asserting the contrary of what is actually the fact, and so posited
both become false: e.g. suppose that actually all D is A but no B
is D; then if these premisses are changed in quality, a conclusion
will follow and both of the new premisses will be false. When,
however, (ii) the middle D is not subordinate to A, A-D will be
true, D-B false-A-D true because A was not subordinate to D, D-B
false because if it had been true, the conclusion too would have
been true; but it is ex hypothesi false.
    When the erroneous inference is in the second figure, both
premisses cannot be entirely false; since if B is subordinate to A,
there can be no middle predicable of all of one extreme and of none
of the other, as was stated before. One premiss, however, may be
false, and it may be either of them. Thus, if C is actually an
attribute of both A and B, but is assumed to be an attribute of A
only and not of B, C-A will be true, C-B false: or again if C be
assumed to be attributable to B but to no A, C-B will be true, C-A
false.
    We have stated when and through what kinds of premisses error
will result in cases where the erroneous conclusion is negative. If
the conclusion is affirmative, (a) (i) it may be inferred through
the ‘appropriate’ middle term. In this case both premisses cannot
be false since, as we said before, C-B must remain unchanged if
there is to be a conclusion, and consequently A-C, the quality of
which is changed, will always be false. This is equally true if
(ii) the middle is taken from another series of predication, as was
stated to be the case also with regard to negative error; for D-B
must remain unchanged, while the quality of A-D must be converted,
and the type of error is the same as before.
    (b) The middle may be inappropriate. Then (i) if D is
subordinate to A, A-D will be true, but D-B false; since A may
quite well be predicable of several terms no one of which can be
subordinated to another. If, however, (ii) D is not subordinate to
A, obviously A-D, since it is affirmed, will always be false, while
D-B may be either true or false; for A may very well be an
attribute of no D, whereas all B is D, e.g. no science is animal,
all music is science. Equally well A may be an attribute of no D,
and D of no B. It emerges, then, that if the middle term is not
subordinate to the major, not only both premisses but either singly
may be false.
    Thus we have made it clear how many varieties of erroneous
inference are liable to happen and through what kinds of premisses
they occur, in the case both of immediate and of demonstrable
truths.
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    It is also clear that the loss of any one of the senses entails
the loss of