Prior Analytics - Book II   

hypothesi is true. And the premiss AB is true, the premiss BC false.

(10) Also if the premiss AB is partially false, and the premiss BC

is false too, the conclusion may be true. For nothing prevents A

belonging to some B and to some C, though B belongs to no C, e.g. if B

is the contrary of C, and both are accidents of the same genus: for

animal belongs to some white things and to some black things, but

white belongs to no black thing. If then it is assumed that A

belongs to all B, and B to some C, the conclusion will be true.

Similarly if the premiss AB is negative: for the same terms arranged

in the same way will serve for the proof.

(11) Also though both premisses are false the conclusion may be

true. For it is possible that A may belong to no B and to some C,

while B belongs to no C, e.g. a genus in relation to the species of

another genus, and to the accident of its own species: for animal

belongs to no number, but to some white things, and number to

nothing white. If then it is assumed that A belongs to all B and B

to some C, the conclusion will be true, though both premisses are

false. Similarly also if the premiss AB is negative. For nothing

prevents A belonging to the whole of B, and not to some C, while B

belongs to no C, e.g. animal belongs to every swan, and not to some

black things, and swan belongs to nothing black. Consequently if it is

assumed that A belongs to no B, and B to some C, then A does not

belong to some C. The conclusion then is true, but the premisses arc

false.



3



In the middle figure it is possible in every way to reach a true

conclusion through false premisses, whether the syllogisms are

universal or particular, viz. when both premisses are wholly false;

when each is partially false; when one is true, the other wholly false

(it does not matter which of the two premisses is false); if both