In discussing Conditional Propositions, the conditional sentence of a Hypothetical, or the first alternative of a Disjunctive, is called the Antecedent; the indicative sentence of a Hypothetical, or the second alternative of a Disjunctive, is called the Consequent. Hypotheticals, like Categoricals, have been classed according to Quantity and Quality. Premising that the quantity of a Hypothetical depends on the quantity of its Antecedent (which determines its limitation), whilst its quality depends on the quality of its consequent (which makes the predication), we may exhibit four forms: A. _If A is B, C is D;_ I. _Sometimes when A is B, C is D;_ E. _If A is B, C is not D;_ O. _Sometimes when A is B, C is not D._ But I. and O. are rarely used. As for Disjunctives, it is easy to distinguish the two quantities thus: A. _Either A is B, or C is D;_ I. _Sometimes either A is B or C is D._ But I. is rarely used. The distinction of quality, however, cannot be made: there are no true negative forms; for if we write-- _Neither is A B, nor C D,_ there is here no alternative predication, but only an Exponible equivalent to _No A is B, and No C is D_. And if we write-- _Either A is not B, or C is not D,_ this is affirmative as to the alternation, and is for all methods of treatment equivalent to A. Logicians are divided in opinion as to the interpretation of the conjunction 'either, or'; some holding that it means 'not both,' others that it means 'it may be both.' Grammatical usage, upon which the question is sometimes argued, does not seem to be established in favour of either view. If we say _A man so precise in his walk and conversation is either a saint or a consummate hypocrite_; or, again, _One who is happy in a solitary life is either more or less than man_; we cannot in such cases mean that the subject may be both. On the other hand, if it be said that _the author of 'A Tale of a Tub' is either a misanthrope or a dyspeptic_, the alternatives are not incompatible. Or, again, given that _X. is a lunatic, or a lover, or a poet_, the three predicates have much congruity. It has been urged that in Logic, language should be made as exact and definite as possible, and that this requires the exclusive interpretation 'not both.' But it seems a better argument, that Logic (1) should be able to express all meanings, and (2), as the science of evidence, must not assume more than is given; to be on the safe side, it must in doubtful cases assume the least, just as it generally assumes a preindesignate term to be of particular quantity; and, therefore 'either, or' means 'one, or the other, or both.'