Prior Analytics - Book II   

to some C, and B to no C, e.g. animal to some white things and to some

black things, though white belongs to nothing black. If then it is

assumed that A belongs to all B and to no C, both premisses are

partially false, but the conclusion is true. Similarly, if the

negative premiss is transposed, the proof can be made by means of

the same terms.

It is clear also that our thesis holds in particular syllogisms. For

(5) nothing prevents A belonging to all B and to some C, though B does

not belong to some C, e.g. animal to every man and to some white

things, though man will not belong to some white things. If then it is

stated that A belongs to no B and to some C, the universal premiss

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

true. Similarly if the premiss AB is affirmative: for it is possible

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

belong to some C, e.g. animal belongs to nothing lifeless, and does

not belong to some white things, and lifeless will not belong to

some white things. If then it is stated that A belongs to all B and

not to some C, the premiss AB which is universal is wholly false,

the premiss AC is true, and the conclusion is true. Also a true

conclusion is possible when the universal premiss is true, and the

particular is false. For nothing prevents A following neither B nor

C at all, while B does not belong to some C, e.g. animal belongs to no

number nor to anything lifeless, and number does not follow some

lifeless things. If then it is stated that A belongs to no B and to

some C, the conclusion will be true, and the universal premiss true,

but the particular false. Similarly if the premiss which is stated

universally is affirmative. For it is possible that should A belong

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

a genus in relation to its species and difference: for animal

follows every man and footed things as a whole, but man does not

follow every footed thing. Consequently if it is assumed that A

belongs to the whole of B, but does not belong to some C, the