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.