Prior Analytics - Book II   

universal premiss is true, the particular false, and the conclusion

true.

(6) It is clear too that though both premisses are false they may

yield a true conclusion, since it is possible that A should belong

both to B and to C as wholes, though B does not follow some C. For

if it is assumed that A belongs to no B and to some C, the premisses

are both false, but the conclusion is true. Similarly if the universal

premiss is affirmative and the particular negative. For it is possible

that A should follow no B and all C, though B does not belong to

some C, e.g. animal follows no science but every man, though science

does not follow every man. If then A is assumed to belong to the whole

of B, and not to follow some C, the premisses are false but the

conclusion is true.



4



In the last figure a true conclusion may come through what is false,

alike when both premisses are wholly false, when each is partly false,

when one premiss is wholly true, the other false, when one premiss

is partly false, the other wholly true, and vice versa, and in every

other way in which it is possible to alter the premisses. For (1)

nothing prevents neither A nor B from belonging to any C, while A

belongs to some B, e.g. neither man nor footed follows anything

lifeless, though man belongs to some footed things. If then it is

assumed that A and B belong to all C, the premisses will be wholly

false, but the conclusion true. Similarly if one premiss is

negative, the other affirmative. For it is possible that B should

belong to no C, but A to all C, and that should not belong to some

B, e.g. black belongs to no swan, animal to every swan, and animal not

to everything black. Consequently if it is assumed that B belongs to

all C, and A to no C, A will not belong to some B: and the

conclusion is true, though the premisses are false.