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