### Aristotle - The Organon ANALYTICA PRIORIA Book 2 Part 9

## ... in the second figure

1.
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.

2.
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 conclusion is converted into its
contradictory, both premisses can be refuted.
Suppose that A belongs
to no B, and to some C: the conclusion is BC. If then it is assumed
that B belongs to some C, and the statement AB stands, the
conclusion will be that A does not belong to some C. But the
original statement has not been refuted: for it is possible that A
should belong to some C and also not to some C. Again if B belongs
to some C and A to some C, no syllogism will be possible: for
neither of the premisses taken is universal.
Consequently the
proposition AB is not refuted. But if the conclusion is
converted into
its contradictory, both premisses can be refuted. For if B belongs
to all C, and A to no B, A will belong to no C: but it was assumed
to belong to some C. Again if B belongs to all C and A to some C, A
will belong to some B. The same proof can be given if the universal
statement is affirmative.

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