### Aristotle - The Organon ANALYTICA PRIORIA Book 1 Part 21

## One premiss pure, the other problematic

1.
If one premiss is pure, the other problematic, the conclusion will
be problematic, not pure;
and a syllogism will be possible under the
same arrangement of the terms as before. First let the premisses be
affirmative: suppose that A belongs to all C, and B may possibly
belong to all C. If the proposition BC is converted, we
shall have the
first figure, and the conclusion that A may possibly belong
to some of
the Bs. For when one of the premisses in the first figure is
problematic, the conclusion also (as we saw) is problematic.
Similarly
if the proposition BC is pure, AC problematic; or if AC is negative,
BC affirmative, no matter which of the two is pure; in both cases
the conclusion will be problematic: for the first figure is obtained
once more, and it has been proved that if one premiss is problematic
in that figure the conclusion also will be problematic. But if the
minor premiss BC is negative, or if both premisses are negative, no
syllogistic conclusion can be drawn from the premisses as they
stand, but if they are converted a syllogism is obtained as before.

2.
If one of the premisses is universal, the other particular, then
when both are affirmative, or when the universal is negative, the
particular affirmative, we shall have the same sort of
syllogisms:
for
all are completed by means of the first figure. So it is
clear that we
shall have not a pure but a problematic syllogistic
conclusion. But if
the affirmative premiss is universal, the negative particular, the
proof will proceed by a reductio ad impossibile. Suppose that B
belongs to all C, and A may possibly not belong to some C: it
follows that may possibly not belong to some B. For if A necessarily
belongs to all B, and B (as has been assumed) belongs to all
C, A will
necessarily belong to all C: for this has been proved before. But it
was assumed at the outset that A may possibly not belong to some C.

3.
Whenever both premisses are indefinite or particular, no syllogism
will be possible.
The demonstration is the same as was given in the
case of universal premisses, and proceeds by means of the same terms.

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