The Complete Aristotle (eng.)

general contraries, may possibly belong to the
same thing, but cannot belong to one another. This is not in
agreement with what was said before: for we stated that when
several things could belong to the same thing, they could belong to
one another.
    It is evident then that in all these cases the fallacy arises
from the setting out of the terms: for if the things that are in
the conditions are substituted, no fallacy arises. It is clear then
that in such premisses what possesses the condition ought always to
be substituted for the condition and taken as the term.
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    We must not always seek to set out the terms a single word: for
we shall often have complexes of words to which a single name is
not given. Hence it is difficult to reduce syllogisms with such
terms. Sometimes too fallacies will result from such a search, e.g.
the belief that syllogism can establish that which has no mean. Let
A stand for two right angles, B for triangle, C for isosceles
triangle. A then belongs to C because of B: but A belongs to B
without the mediation of another term: for the triangle in virtue
of its own nature contains two right angles, consequently there
will be no middle term for the proposition AB, although it is
demonstrable. For it is clear that the middle must not always be
assumed to be an individual thing, but sometimes a complex of
words, as happens in the case mentioned.
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    That the first term belongs to the middle, and the middle to the
extreme, must not be understood in the sense that they can always
be predicated of one another or that the first term will be
predicated of the middle in the same way as the middle is
predicated of the last term. The same holds if the premisses are
negative. But we must suppose the verb ‘to belong’ to have as many
meanings as the senses in which the verb ‘to be’ is used, and in
which the assertion that a thing ‘is’ may be said to be true. Take
for example the statement that there is a single science of
contraries. Let A stand for ‘there being a single science’, and B
for things which are contrary to one another. Then A belongs to B,
not in the sense that contraries are the fact of there being a
single science of them, but in the sense that it is true to say of
the contraries that there is a single science of them.
    It happens sometimes that the first term is stated of the
middle, but the middle is not stated of the third term, e.g. if
wisdom is knowledge, and wisdom is of the good, the conclusion is
that there is knowledge of the good. The good then is not
knowledge, though wisdom is knowledge. Sometimes the middle term is
stated of the third, but the first is not stated of the middle,
e.g. if there is a science of everything that has a quality, or is
a contrary, and the good both is a contrary and has a quality, the
conclusion is that there is a science of the good, but the good is
not science, nor is that which has a quality or is a contrary,
though the good is both of these. Sometimes neither the first term
is stated of the middle, nor the middle of the third, while the
first is sometimes stated of the third, and sometimes not: e.g. if
there is a genus of that of which there is a science, and if there
is a science of the good, we conclude that there is a genus of the
good. But nothing is predicated of anything. And if that of which
there is a science is a genus, and if there is a science of the
good, we conclude that the good is a genus. The first term then is
predicated of the extreme, but in the premisses one thing is not
stated of another.
    The same holds good where the relation is negative. For ‘that
does not belong to this’ does not always mean that ‘this is not
that’, but sometimes that ‘this is not of that’ or ‘for that’, e.g.
‘there is not a motion of a motion or a becoming of a becoming, but
there is a becoming of pleasure: so pleasure is not a becoming.’ Or
again it may be said that there is a sign of laughter, but there is
not a sign of a sign, consequently laughter is not a sign. This
holds in the other cases too, in which the thesis is refuted
because the genus is asserted in a particular way, in relation to
the terms of the thesis. Again take the inference ‘opportunity is
not the right time: for opportunity belongs to God, but the right
time does not, since nothing is useful to God’. We must take as
terms opportunity-right time-God: but the premiss must be
understood according to the case of the noun. For we state this
universally