In order to be conclusive a dilemma must meet two requirements. First, there must be only two possibilities in the case; the alternative must include these exactly. Second, both members of the alternative, or “horns” of the dilemma must be untenable. To ignore or fail to comply with either of these requirements is fatal to this method of refutation. Lincoln, in the following quotation, shows that Douglas has violated the first of these requirements. He refuses to accept either of the horns of the dilemma which Douglas has sought to force upon him, by pointing out a third possibility. On this third possibility, overlooked by Douglas, he can stand with safety. He says:—
“Judge Douglas finds the Republicans insisting that the Declaration of Independence includes all men, black as well as white, and forthwith he boldly denies that it includes negroes at all, and proceeds to argue gravely that all who contend it does, do so only because they went to vote, to eat and sleep, and marry with negroes. He will have it that they cannot be consistent else. Now I protest against this counterfeit logic which concludes that because I do not want a black woman for a slave I must necessarily want her for a wife. I need not have her for either. I can just leave her alone.”
IV. Residues.
The method of residues consists in stating all the possible conclusions regarding the controverted subject and then destroying all of these except one which is then regarded as the true conclusion. For example, there are three possibilities, A, B, and C. A and B are false. Therefore the presumption is that C is true. It will be seen that this process is destructive and hence belongs with refutation. This method of refutation must be used with great care. It is absolutely essential that every possibility be included in the process. If one possibility is overlooked the refutation is worthless. This is true because no one can tell whether the known possibility is the true one or whether the possibility which has been omitted is the true one. In such a case no conclusion is reached. Even when it is apparent that the entire field has been covered, and that every possibility has been stated the residuary part should be supported by direct positive proof. This will offset the suspicion, which is otherwise ever present in the minds of those who are listening to or reading the argument, that perhaps one possibility has been overlooked.
Foster in his Argumentation and Debate quotes two excellent examples of this method of refutation. The first of these is taken from Burke’s Speech on Conciliation. After showing that a fierce spirit of liberty has developed in the American colonies Burke asks what is to be done with that spirit. Answering his own question he says:—
“‘As far as I am capable of discerning there are but three ways of proceeding relative to this stubborn spirit which prevails in your colonies, and disturbs your government. These are—to change that spirit, as inconvenient, by removing the cause; to prosecute it as criminal; or to cope with it as necessary. I would not be guilty of an imperfect enumeration; I can think of but these three. Another has indeed been started,—that of giving up the colonies; but it met so slight a reception that I do not think myself obliged to dwell a great while upon it. It is nothing but a little sally of anger, like the frowardness of peevish children, who when they cannot get all they would have, are resolved to take nothing.’
“Burke then proceeds to show that the first and second of these plans are impracticable, and concludes with the following characteristic, logical summary:—
“‘If, then, the removal of the causes of this spirit of American liberty be for the greater part, or rather entirely, impracticable; if the ideas of criminal process be inapplicable—or if applicable, are in the highest degree inexpedient—what way yet remains? No way is open but the third and last—to comply with the American spirit as necessary; or, if you please, to submit to it as a necessary evil.’
“Huxley, in his first lecture on Evolution, presented three hypotheses regarding the origin of the universe:—
“‘So far as I know, there are only three hypotheses which ever have been entertained, or which well can be entertained, respecting the past history of Nature. I will, in the first place, state the hypotheses, and then I will consider what evidence bearing upon them is in our possession, and by what light of criticism that evidence is to be interpreted.