The Complete Aristotle (eng.)

the expression
‘not-man’ was not a noun, in the proper sense of the word, but an
indefinite noun, denoting as it does in a certain sense a single
thing. Similarly the expression ‘does not enjoy health’ is not a
verb proper, but an indefinite verb. Every affirmation, then, and
every denial, will consist of a noun and a verb, either definite or
indefinite.
    There can be no affirmation or denial without a verb; for the
expressions ‘is’, ‘will be’, ‘was’, ‘is coming to be’, and the like
are verbs according to our definition, since besides their specific
meaning they convey the notion of time. Thus the primary
affirmation and denial are ‘as follows: ‘man is’, ‘man is not’.
Next to these, there are the propositions: ‘not-man is’, ‘not-man
is not’. Again we have the propositions: ‘every man is, ‘every man
is not’, ‘all that is not-man is’, ‘all that is not-man is not’.
The same classification holds good with regard to such periods of
time as lie outside the present.
    When the verb ‘is’ is used as a third element in the sentence,
there can be positive and negative propositions of two sorts. Thus
in the sentence ‘man is just’ the verb ‘is’ is used as a third
element, call it verb or noun, which you will. Four propositions,
therefore, instead of two can be formed with these materials. Two
of the four, as regards their affirmation and denial, correspond in
their logical sequence with the propositions which deal with a
condition of privation; the other two do not correspond with
these.
    I mean that the verb ‘is’ is added either to the term ‘just’ or
to the term ‘not-just’, and two negative propositions are formed in
the same way. Thus we have the four propositions. Reference to the
subjoined table will make matters clear:
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A. Affirmation. Man is just
B. Denial. Man is not just
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D. Denial. Man is not not-just
C. Affirmation. Man is not-just
    Here ‘is’ and ‘is not’ are added either to ‘just’ or to
‘not-just’. This then is the proper scheme for these propositions,
as has been said in the Analytics. The same rule holds good, if the
subject is distributed. Thus we have the table:
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    tbody>
A'. Affirmation. Every man is just
B'. Denial. Not every man is just
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D'. Denial. Not every man is not-just
C'. Affirmation. Every man is not-just.
    Yet here it is not possible, in the same way as in the former
case, that the propositions joined in the table by a diagonal line
should both be true; though under certain circumstances this is the
case.
    We have thus set out two pairs of opposite propositions; there
are moreover two other pairs, if a term be conjoined with
‘not-man’, the latter forming a kind of subject. Thus:
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    tbody>
A". Not-man is just.
B". Not-man is not just
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/
/
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D". Not-man is not not-just.
C". Not-man is not-just.
    This is an exhaustive enumeration of all the pairs of opposite
propositions that can possibly be framed. This last group should
remain distinct from those which preceded it, since it employs as
its subject the expression ‘not-man’.
    When the verb ‘is’ does not fit the structure of the sentence
(for instance, when the verbs ‘walks’, ‘enjoys health’ are used),
that scheme applies, which applied when the word ‘is’ was
added.
    Thus we have the propositions: ‘every man enjoys health’, ‘every
man does-not-enjoy-health’, ‘all that is not-man enjoys health’,
‘all that is not-man does-not-enjoy-health’. We must not in these
propositions use the expression ‘not every man’. The negative must
be attached to the word ‘man’, for the word ‘every’ does not give
to the subject a universal significance, but implies that, as a
subject, it is distributed. This is plain from the following pairs:
‘man enjoys health’, ‘man does not enjoy health’; ‘not-man enjoys
health’, ‘not man does not enjoy health’. These propositions differ
from the former in being indefinite and not universal in character.
Thus the adjectives ‘every’ and no additional significance except
that the subject, whether in a positive or in a negative sentence,
is distributed. The rest of the sentence, therefore, will in each
case be the same.
    Since the contrary of the proposition ‘every animal is just’ is
‘no animal is just’, it is plain that these two propositions will
never both be true at the same time or with reference to the same
subject. Sometimes, however, the