The Complete Aristotle (eng.)

of
‘to all’ to ‘not to all’, and of ‘to some’ to ‘to none’; by
contrary opposition I mean the opposition of ‘to all’ to ‘to none’,
and of ‘to some’ to ‘not to some’. Suppose that A been proved of C,
through B as middle term. If then it should be assumed that A
belongs to no C, but to all B, B will belong to no C. And if A
belongs to no C, and B to all C, A will belong, not to no B at all,
but not to all B. For (as we saw) the universal is not proved
through the last figure. In a word it is not possible to refute
universally by conversion the premiss which concerns the major
extreme: for the refutation always proceeds through the third since
it is necessary to take both premisses in reference to the minor
extreme. Similarly if the syllogism is negative. Suppose it has
been proved that A belongs to no C through B. Then if it is assumed
that A belongs to all C, and to no B, B will belong to none of the
Cs. And if A and B belong to all C, A will belong to some B: but in
the original premiss it belonged to no B.
    If the conclusion is converted into its contradictory, the
syllogisms will be contradictory and not universal. For one premiss
is particular, so that the conclusion also will be particular. Let
the syllogism be affirmative, and let it be converted as stated.
Then if A belongs not to all C, but to all B, B will belong not to
all C. And if A belongs not to all C, but B belongs to all C, A
will belong not to all B. Similarly if the syllogism is negative.
For if A belongs to some C, and to no B, B will belong, not to no C
at all, but-not to some C. And if A belongs to some C, and B to all
C, as was originally assumed, A will belong to some B.
    In particular syllogisms when the conclusion is converted into
its contradictory, both premisses may be refuted, but when it is
converted into its contrary, neither. For the result is no longer,
as in the universal syllogisms, refutation in which the conclusion
reached by O, conversion lacks universality, but no refutation at
all. Suppose that A has been proved of some C. If then it is
assumed that A belongs to no C, and B to some C, A will not belong
to some B: and if A belongs to no C, but to all B, B will belong to
no C. Thus both premisses are refuted. But neither can be refuted
if the conclusion is converted into its contrary. For if A does not
belong to some C, but to all B, then B will not belong to some C.
But the original premiss is not yet refuted: for it is possible
that B should belong to some C, and should not belong to some C.
The universal premiss AB cannot be affected by a syllogism at all:
for if A does not belong to some of the Cs, but B belongs to some
of the Cs, neither of the premisses is universal. Similarly if the
syllogism is negative: for if it should be assumed that A belongs
to all C, both premisses are refuted: but if the assumption is that
A belongs to some C, neither premiss is refuted. The proof is the
same as before.
9
    In the second figure it is not possible to refute the premiss
which concerns the major extreme by establishing something contrary
to it, whichever form the conversion of the conclusion may take.
For the conclusion of the refutation will always be in the third
figure, and in this figure (as we saw) there is no universal
syllogism. The other premiss can be refuted in a manner similar to
the conversion: I mean, if the conclusion of the first syllogism is
converted into its contrary, the conclusion of the refutation will
be the contrary of the minor premiss of the first, if into its
contradictory, the contradictory. Let A belong to all B and to no
C: conclusion BC. If then it is assumed that B belongs to all C,
and the proposition AB stands, A will belong to all C, since the
first figure is produced. If B belongs to all C, and A to no C,
then A belongs not to all B: the figure is the last. But if the
conclusion BC is converted into its contradictory, the premiss AB
will be refuted as before, the premiss, AC by its contradictory.
For if B belongs to some C, and A to no C, then A will not belong
to some B. Again if B belongs to some C, and A to all B, A will
belong to some C, so that the syllogism results in the
contradictory of the minor premiss. A similar proof can be given if
the premisses are transposed in respect of their quality.
    If the syllogism is particular, when the conclusion is converted
into its contrary neither premiss can be refuted, as also happened
in the first figure,’ if the