The common proposition that two negatives make an affirmative, is true only upon the supposition that there are but two possible things, one of which is denied. Grant that a man must be either able or unable to do a particular thing, and then _not unable_ and able are the same things. But if we suppose various degrees of performance, and therefore degrees of ability, it is false, in the common sense of the words, that two negatives make an affirmative. Thus, it would be erroneous to say, ‘John is able to translate Virgil, and Thomas is not unable; therefore, what John can do Thomas can do,’ for it is evident that the premises mean that John is so near to the best sort of translation that an affirmation of his ability may be made, while Thomas is considerably lower than John, but not so near to absolute deficiency that his ability may be altogether denied. It will generally be found that two negatives imply an affirmative of a weaker degree than the positive affirmation. Each of the propositions, ‘A is B,’ and ‘A is not B,’ may be subdivided into two species: the _universal_, in which every possible case is included; and the _particular_, in which it is not meant to be asserted that the affirmation or negation is universal. The four species of propositions are then as follows, each being marked with the letter by which writers on logic have always distinguished it. A _Universal Affirmative_ Every A is B E _Universal Negative_ No A is B I _Particular Affirmative_ Some A is B O _Particular Negative_ Some A is not B In common conversation the affirmation of a part is meant to imply the denial of the remainder. Thus, by ‘some of the apples are ripe,’ it is always intended to signify that some are not ripe. This is not the case in logical language, but every proposition is intended to make its amount of affirmation or denial, and no more. When we say, ‘Some A is B,’ or, more grammatically, ‘Some As are Bs,’ we do not mean to imply that some are not: this may or may not be. Again, the word some means, ‘one or more, possibly all.’ The following table will shew the bearing of each proposition on the rest. _Every A is B_ affirms and contains _Some A is B_ and│_No A is B_ denies │_Some A is not B_ _No A is B_ affirms and contains _Some A is not B_ │_Every A is B_ and denies │_Some A is B_ _Some A is B_ does not │_Every A is B_ │but denies _No A is B_ contradict │_Some A is not B_│ _Some A is not B_ does not │_No A is B_ │but denies _Every A is B_ contradict │_Some A is B_ │