Dilemma. Different things are intended by this word. We may distinguish between
1st. The logical dilemma.
2nd. The rhetorical dilemma.
3rd. The sophism commonly called the crocodolinus or the cornutus, to which the name dilemma has been given.
4th. The conversational use of the word.
1st. The logical dilemma. This exactly answers to one probable etymology of the word, double λῆμμα or sumption. It is not necessary, however, that there should be only two. The kind of reasoning will admit three or more sumptions as readily as two, and it has accordingly been proposed to speak of a trilemma, a tetralemma, &c. The dilemma, however, will adequately represent the whole procedure. It consists in the combination of two hypotheses, with a complex disjunction. If A is B, or C is D, E is F; but either A is B, or C is D, ∴ E is F. The hypotheses or λῆμματα, as we have seen, may be more than two, and the kind of reasoning will be the same; the same too should the conclusion be, itself disjunctive, as in the following: If A is B, E is F, and if C is D, G is H. But either A is B, or C is D, ∴ either E is F, or G is H. Further, the disjunction may be not in the antecedents but the consequents, and in this form we can arrive at negative conclusions; e. g. if A is B, either C is D, or E is F, but neither C is D, nor E is F, ∴ A is not B. Negative dilemmas are destructive, or in the modus tollens; and affirmative ones are called constructive, or in the modus ponens.
The dilemma is generally classed in logical manuals under the head of syllogism, as one form of that. A very little consideration, however, will show that we have here no distinct form of reasoning, and that, taken by itself, the dilemma is not a syllogism at all. It is combined of two or more hypotheses, each of which has to be confirmed in its own way, and a disjunction of them, the adequacy of which must be ascertained. All this done, we have an immediate, as distinguished from a mediate or syllogistic, inference.
2ndly. The rhetorical dilemma consists in presenting the adversary with a choice of alternatives, each of which involves consequences inconvenient to him or a gain of our point to ourselves. This is called impaling him on the horns of a dilemma. It is obviously different from the logical procedure, though it can by manipulation be brought to the form of that. It has been well observed that we have a sacred example of the rhetorical dilemma in our Lord’s question to the Pharisees respecting the baptism of John.
3rdly. The name dilemma has been given to the sophism called the Crocodolinus, the Litigiosus, the Reciprocus, and by many names besides. It consists of drawing contradictory consequents from the members of the same disjunction, and thus rendering a conclusion impossible. The best known example of it is the story from which it has procured the name Litigiosus. His master received the half of the sum due from his pupil for instructions in pleading, and engaged to wait for the remaining half till the latter should have won his first cause. This the pupil showed no haste to do; whereupon the master, losing patience, sued him for the sum, and the other appeared in court to defend himself in person. «0 foolish youth,» said the master, before the trial commenced, «dost thou not see that in any event thou must lose? If the decision be in my favour, I have gained my cause, and thou must pay; if in thine, thou shalt have won thy first cause, and by the terms of our agreement must pay.» » 0, wisest of masters,» rejoined the pupil, «dost thou not see that in any event thou must lose? If the court decides for me, I need not pay; if against me, I shall not yet have won a suit, and, by the terms of our agreement, am still free.» It is easy to see that the puzzle in this and similar examples results from ambiguity of terms. In the present case we have confounded the compulsory authority of the court and the moral obligation of an agreement. If the latter was to be brought under legal jurisdiction, it could only be by the defeated party bringing a fresh action founded on the issue of the preceding one, the master pleading in this second suit that his pupil had won a case, and was therefore bound to pay him; or the pupil that he had lost his first suit, and therefore was still free from the master’s claim.
4thly. In common conversation by a dilemma is frequently meant a situation in which ill consequences may be apprehended from whatever we do. We thus come to a sense of the word involving results the very opposite of those which follow from the logical dilemma. Here we do not know what to do. There we are brought to a conclusion with warrant more than common. Instead of an inconvenience, there can be nothing more welcome to an inquirer than a dilemma, in which he is sure that his disjunction is complete, and that his consequents really follow from the antecedents.
