
Prior Analytics  Book II
(2) Also if each premiss is partly false, the conclusion may be
true. For nothing prevents both A and B from belonging to some C while
A belongs to some B, e.g. white and beautiful belong to some
animals, and white to some beautiful things. If then it is stated that
A and B belong to all C, the premisses are partially false, but the
conclusion is true. Similarly if the premiss AC is stated as negative.
For nothing prevents A from not belonging, and B from belonging, to
some C, while A does not belong to all B, e.g. white does not belong
to some animals, beautiful belongs to some animals, and white does not
belong to everything beautiful. Consequently if it is assumed that A
belongs to no C, and B to all C, both premisses are partly false,
but the conclusion is true.
(3) Similarly if one of the premisses assumed is wholly false, the
other wholly true. For it is possible that both A and B should
follow all C, though A does not belong to some B, e.g. animal and
white follow every swan, though animal does not belong to everything
white. Taking these then as terms, if one assumes that B belongs to
the whole of C, but A does not belong to C at all, the premiss BC will
be wholly true, the premiss AC wholly false, and the conclusion
true. Similarly if the statement BC is false, the statement AC true,
the conclusion may be true. The same terms will serve for the proof.
Also if both the premisses assumed are affirmative, the conclusion may
be true. For nothing prevents B from following all C, and A from not
belonging to C at all, though A belongs to some B, e.g. animal belongs
to every swan, black to no swan, and black to some animals.
Consequently if it is assumed that A and B belong to every C, the
premiss BC is wholly true, the premiss AC is wholly false, and the
conclusion is true. Similarly if the premiss AC which is assumed is
true: the proof can be made through the same terms.
(4) Again if one premiss is wholly true, the other partly false, the
conclusion may be true. For it is possible that B should belong to all
C, and A to some C, while A belongs to some B, e.g. biped belongs to
