The Complete Aristotle (eng.)

belong to
no A and to some B. But if the negative statement is particular, no
resolution will be possible: for the particular negative does not
admit of conversion.
    It is clear then that the same syllogisms cannot be resolved in
these figures which could not be resolved into the first figure,
and that when syllogisms are reduced to the first figure these
alone are confirmed by reduction to what is impossible.
    It is clear from what we have said how we ought to reduce
syllogisms, and that the figures may be resolved into one
another.
46
    In establishing or refuting, it makes some difference whether we
suppose the expressions ‘not to be this’ and ‘to be not-this’ are
identical or different in meaning, e.g. ‘not to be white’ and ‘to
be not-white’. For they do not mean the same thing, nor is ‘to be
not-white’ the negation of ‘to be white’, but ‘not to be white’.
The reason for this is as follows. The relation of ‘he can walk’ to
‘he can not-walk’ is similar to the relation of ‘it is white’ to
‘it is not-white’; so is that of ‘he knows what is good’ to ‘he
knows what is not-good’. For there is no difference between the
expressions ‘he knows what is good’ and ‘he is knowing what is
good’, or ‘he can walk’ and ‘he is able to walk’: therefore there
is no difference between their contraries ‘he cannot walk’-’he is
not able to walk’. If then ‘he is not able to walk’ means the same
as ‘he is able not to walk’, capacity to walk and incapacity to
walk will belong at the same time to the same person (for the same
man can both walk and not-walk, and is possessed of knowledge of
what is good and of what is not-good), but an affirmation and a
denial which are opposed to one another do not belong at the same
time to the same thing. As then ‘not to know what is good’ is not
the same as ‘to know what is not good’, so ‘to be not-good’ is not
the same as ‘not to be good’. For when two pairs correspond, if the
one pair are different from one another, the other pair also must
be different. Nor is ‘to be not-equal’ the same as ‘not to be
equal’: for there is something underlying the one, viz. that which
is not-equal, and this is the unequal, but there is nothing
underlying the other. Wherefore not everything is either equal or
unequal, but everything is equal or is not equal. Further the
expressions ‘it is a not-white log’ and ‘it is not a white log’ do
not imply one another’s truth. For if ‘it is a not-white log’, it
must be a log: but that which is not a white log need not be a log
at all. Therefore it is clear that ‘it is not-good’ is not the
denial of ‘it is good’. If then every single statement may truly be
said to be either an affirmation or a negation, if it is not a
negation clearly it must in a sense be an affirmation. But every
affirmation has a corresponding negation. The negation then of ‘it
is not-good’ is ‘it is not not-good’. The relation of these
statements to one another is as follows. Let A stand for ‘to be
good’, B for ‘not to be good’, let C stand for ‘to be not-good’ and
be placed under B, and let D stand for not to be not-good’ and be
placed under A. Then either A or B will belong to everything, but
they will never belong to the same thing; and either C or D will
belong to everything, but they will never belong to the same thing.
And B must belong to everything to which C belongs. For if it is
true to say ‘it is a not-white’, it is true also to say ‘it is not
white’: for it is impossible that a thing should simultaneously be
white and be not-white, or be a not-white log and be a white log;
consequently if the affirmation does not belong, the denial must
belong. But C does not always belong to B: for what is not a log at
all, cannot be a not-white log either. On the other hand D belongs
to everything to which A belongs. For either C or D belongs to
everything to which A belongs. But since a thing cannot be
simultaneously not-white and white, D must belong to everything to
which A belongs. For of that which is white it is true to say that
it is not not-white. But A is not true of all D. For of that which
is not a log at all it is not true to say A, viz. that it is a
white log. Consequently D is true, but A is not true, i.e. that it
is a white log. It is clear also that A and C cannot together
belong to the same thing, and that B and D may possibly belong to
the