### Aristotle - The Organon ANALYTICA PRIORIA Book 1 Part 18

## One premiss assertoric, the other problematic

1.
But if one premiss is assertoric, the other problematic, if the
affirmative is assertoric and the negative problematic no syllogism
will be possible, whether the premisses are universal or particular.
The proof is the same as above, and by means of the same terms. But
when the affirmative premiss is problematic, and the negative
assertoric, we shall have a syllogism. Suppose A belongs to no B,
but can belong to all C. If the negative proposition is converted, B
will belong to no A. But ex hypothesi can belong to all C: so a
syllogism is made, proving by means of the first figure that B may
belong to no C. Similarly also if the minor premiss is negative. But
if both premisses are negative, one being assertoric, the other
problematic, nothing follows necessarily from these premisses as
they stand, but if the problematic premiss is converted into its
complementary affirmative a syllogism is formed to prove that B may
belong to no C, as before: for we shall again have the first figure.
But if both premisses are affirmative, no syllogism will be
possible. This arrangement of terms is possible both when
the relation
is positive, e.g. health, animal, man, and when it is negative, e.g.
health, horse, man.

2.
The same will hold good if the syllogisms are particular.
Whenever
the affirmative proposition is assertoric, whether universal or
particular,
no syllogism is possible (this is proved similarly and
by the same examples as above), but when the negative proposition is
assertoric, a conclusion can be drawn by means of conversion, as
before. Again if both the relations are negative, and the assertoric
proposition is universal, although no conclusion follows from the
actual premisses, a syllogism can be obtained by converting the
problematic premiss into its complementary affirmative as before.
But if the negative proposition is assertoric, but particular, no
syllogism is possible, whether the other premiss is affirmative or
negative. Nor can a conclusion be drawn when both premisses are
indefinite, whether affirmative or negative, or particular. The
proof is the same and by the same terms.

HTML edition © created 1996/11/25 modified 2009/04/26