Dilemma is a kind of mixed syllogism in which the major premise is a compound hypothetical proposition, the minor premise is a disjunctive proposition and the conclusion is either a categorical or a disjunctive proposition.
The dilemma is a combination of two hypothetical-categorical syllogisms. So, like mixed-hypothetical syllogism a dilemma has two forms (i) Constructive Dilemma and (ii) Destructive Dilemma. Furthermore, a dilemma is known to be simple, if the conclusion is a categorical proposition and it is called complex, if the conclusion is a disjunctive proposition.
Thus we get four types of dilemma viz. (i) Simple constructive, (ii) Simple destructive, (iii) Complex constructive and (iv) Complex destructive.
i) Simple Constructive Dilemma:
It is a kind of mixed syllogism in which the major premise is a compound-hypothetical proposition, (i.e. a conjunction of two hypothetical propositions), and the minor premise is a disjunctive proposition in which the antecedents of the major premise are affirmed disjunctively, and the conclusion is a categorical proposition. Symbolically it is of the following form:
If A is B, C is D and if E is F, C is D
Either A is B or E is F
Therefore, C is D
If a person arranges a grand marriage reception, he is subject to criticism and
If he arranges a modest reception, he is also subject to criticism.
Either the person will arrange a grand reception or a modest reception.
Therefore, in any case, he is subject to criticism
ii) Simple Destructive Dilemma:
In a simple destructive dilemmatic argument the consequents of the compound hypothetical major are alternatively denied in the minor premise and the conclusion is a categorical proposition.
In other words, it is a kind of mixed syllogism in which the major premise is a compound hypothetical proposition and the minor premise is a disjunctive proposition in which the consequents of the major premise are alternatively denied.
Finally, the conclusion is a denial of a categorical proposition. Symbolically it is of following form:
If A is B then C is D and if A is B then E is F
Either C is not D or E is not F
Therefore, A is not B
If Hari has to achieve success, then he must toil hard and if he has to achieve
Success, he must be fortunate.
Either Hari does not toil hard or he is not fortunate
Therefore, Hari will not achieve success.
iii) Complex Constructive Dilemma:
Complex constructive dilemma is an argument, where the major premise is a compound hypothetical, in the minor premise the antecedents of the major premise are disjunctively affirmed and the conclusion is a disjunctive proposition. It is of the following form:
If A is B then C is D and if E is F then G is H
Either A is B or E is F
Therefore, either C is D or G is H
If Rakesh is in Mumbai, he is in Maharashtra and if he is in Kolkata, then he is in Bengal
Rakesh is either in Mumbai or in Kolkata
Therefore, he is either in Maharashtra or in Bengal.
iv) Complex Destructive Dilemma:
In this kind of dilemma, the major premise is a compound-hypothetical proposition; the minor premise and the conclusion are disjunctive propositions. Moreover, in the minor premise, the consequents of the major premise are disjunctively denied.
It is of the following symbolic form:
If A is B then C is D, and if E is F then G is H.
Either C is not D or G is not H.
Therefore, either A is not B or E is not F.
If Rakesh is in Mumbai, then he is in Maharashtra and if he is in Kolkata, then he is Bengal.
Either he is not in Maharashtra or he is not in Kolkata.
Therefore, either Rakesh is not in Mumbai or he is not in Kolkata.
Refutation of Dilemma:
Normally, the formal validity of dilemmatic argument is not in question. Since a dilemma is a complex form of hypothetical-categorical syllogism, no new principles are involved in determining the formal validity of dilemmatic arguments. If one is in doubt regarding the validity of a dilemmatic argument, then the argument can be analysed into its constituent hypothetical-categorical syllogism to check whether the rules have been obeyed or not.
But in most cases, dilemmatic arguments are based on assumptions which are not correct. There are mainly three ways of evading the conclusion of a dilemma. These three ways have been given special names. These are
a) Escaping between the horns
b) Taking the dilemma by the horns
c) Rebutting the dilemma by a counter dilemma.
(a) Escaping between the horns:
In this method, one refutes a given dilemma by showing that the alternatives given in the minor premise are not exhaustive and there is a third alternative which goes in favour of the opponent. Let us take the example of the dilemma presented by an Athenian mother to restrain her son from going outside the house in the following manner.
If the day is hot, you should not go out to avoid exhaustion and if the day is cold, you should not go out to avoid exposure to cold. Either the day is hot or cold. Therefore, you should not go outside to avoid exhaustion or exposure.
The son could escape between the horns by showing a third possibility. Since some parts of the day are neither hot nor cold and during that period he could go out, which will not be harmful for his health.
(b) Taking by the horns:
Here we may point out that either one consequent or both consequents do not follow from their antecedents. Thus the dilemma is wrong and the conclusion cannot be established. Let us examine a simple constructive dilemma.
If the son is efficient, then the father’s saving is unnecessary and if the son is misfit, then the father’s saving is unnecessary. Either the son is efficient or is a misfit. Therefore, in any case the father’s saving is unnecessary.
In the above dilemma, both the alternatives in the major premise are weak. There is no justification in comparing the father’s saving with the efficiency or misfitness of the son. Furthermore, it is not justified to say that father’s saving is only meant for son’s benefit. Thus both the horns of the dilemma are weak and it will be easier to take the dilemma by horns.
(c) Rebutting a dilemma by a counter dilemma:
It is one of the most ingenious method by which a dilemma can be rebutted by constructing another counter dilemma whose conclusion is opposed to the original conclusion. Let us take a classical example of an Athenian mother persuading her son not to join politics in the following manner.
If you say what is just, men will hate you and if you say what is unjust, Gods will hate you. But you must either say the one or the other. Therefore, your will be hated.
The son rebutted the dilemma in the following manner:
If I say what is just, the Gods will love me and if I say what is unjust, men will love me. I must say either the one or the other. Therefore, I shall be loved.
The conclusion of the first dilemma (by the mother) is changed in the conclusion of the rebutted dilemma.