true and the other false. We have pointed out, moreover, what the

reason of this is and under what circumstances the truth of the one

involves the falsity of the other.



8



An affirmation or denial is single, if it indicates some one fact

about some one subject; it matters not whether the subject is

universal and whether the statement has a universal character, or

whether this is not so. Such single propositions are: 'every man is

white', 'not every man is white';'man is white','man is not white';

'no man is white', 'some men are white'; provided the word 'white' has

one meaning. If, on the other hand, one word has two meanings which do

not combine to form one, the affirmation is not single. For

instance, if a man should establish the symbol 'garment' as

significant both of a horse and of a man, the proposition 'garment

is white' would not be a single affirmation, nor its opposite a single

denial. For it is equivalent to the proposition 'horse and man are

white', which, again, is equivalent to the two propositions 'horse

is white', 'man is white'. If, then, these two propositions have

more than a single significance, and do not form a single proposition,

it is plain that the first proposition either has more than one

significance or else has none; for a particular man is not a horse.

This, then, is another instance of those propositions of which

both the positive and the negative forms may be true or false

simultaneously.



9



In the case of that which is or which has taken place, propositions,

whether positive or negative, must be true or false. Again, in the

case of a pair of contradictories, either when the subject is