8-5. Dilemmas
from 8. DeductionClear Thinking by R W Jepson

My second example of false logic concerns the use of the dilemma in argument.

In popular speech, a dilemma is a situation in which there are only two possible courses of action either of which leads to unpleasant consequences. In Logic the term is applied to a form of argument intended to force an opponent to choose one of two alternatives, both unfavourable to him. The medieval schoolmen called it argumentum cornutum—a horned argument—from a fanciful resemblance to the horns of a bull which will toss you whichever horn you lay hold of. Hence the expression "on the horns of a dilemma," and the epithet "gored" for the unfortunate victims.

In Logic the dilemma may take various forms. Let me give a symbolical representation of one or two, and then translate them into concrete terms.

(a) If A, then B; and if C, then B.
But either A or C

(i.e., affirming the antecedents).

Therefore B.

This may be put concretely thus:

If the train is late (A) (I might catch it, but), I shall miss my appointment (B); and if the train is punctual (C), (I shall not be able to catch it and) I shall miss my appointment (B).
But either the train is late (A) or it is punctual (C).
Therefore in either case I shall miss my appointment. The natural corollary is—It's no good my hurrying to catch the train; I may as well finish my breakfast and catch a later one.

(b) If A, then B; and if C, then D.
But either A or C

(i.e., affirming the antecedents).

Therefore either B or D.

Or, in concrete terms,

If you advise a friend what he means to do (A), your advice is superfluous (B); and if you advise him what he does not mean to do (C), your advice is ineffectual(D).
But you must either advise a friend what he means to do (A), or advise him what he does not mean to do (C).
Therefore your advice is either superfluous (B) or ineffectual (D).
And, of course, it follows—Don't offer advice to friends; better save your pains.

You will note that the major premiss takes a hypothetical form, and the minor a disjunctive form. Therefore in using the dilemma, we are liable to make the errors incidental to the use of both these forms of propositions. That is (i) we must not deny the antecedent, or affirm the consequent; and (ii) we must be careful to see that the alternatives are either contradictories or mutually exclusive. They must cover all the possibilities, no cases must be overlooked and no circumstances left out of account. On the assumption that the conditions of (i) are strictly observed, the dilemma can never be more than a formal argument (like those based on the Law of Contradiction and the Law of the Excluded Middle above); and, if the result is inconclusive, as it frequently is, the fault lies in the terms used, or in the omission of one or more relevant circumstances.

In the first example quoted, the conclusion drawn is invalid because I have neglected one possibility at any rate, namely, that the train may not be very late and may easily make up time before reaching its destination, so that I may be able to keep my appointment after all. In the second example, one possible alternative is omitted, namely, that the friend may not mean to take any particular action until you have advised him; the alternatives, too, are not mutually exclusive.

Let us consider other examples, and note in passing that in actual argument the form of the dilemma as stated above is not always strictly adhered to—the minor premiss and/or the conclusion being frequently omitted.

Someone arguing in support of tariffs might say:

"Tariffs will either reduce imports or they will not; if they do (A), they will provide more work for home manufacturers (B); if they don't (not-A), they will increase the revenue from customs (C)."

[i.e., If A, then B; and if not-A, then C.
But either A or not-A.
Therefore either B or C.]

His opponent might object thus:

"Tariffs will either reduce imports or they will not; if they do (A), they will not increase the revenue from customs (not C); if they don't (not-A), they will not provide more work for home manufacturers (not B)."

[i.e., If A, then not C; and if not-A, then not B.
But either A or not-A.
Therefore either not C or not B.]

First of all, let us observe that this attempt at rebutting the argument is worthless, for its conclusion is not opposed to that of the original dilemma which demanded either B or C, not both B and C. But, unfortunately, outside logic, either . . . or is often used as equivalent to alike . . . and or both . . . and (compare I in the next chapter); and it is perhaps not surprising that either not C or not B is often mistaken for neither C nor B, which is not the same thing.

The more important point, however, is that both dilemmas are inconclusive; for what is still needed is a concrete estimate of how much gain and how much loss can reasonably be looked for, how general prosperity and international good feeling will be affected, and a host of other considerations.

The device used by Bishop Morton in the reign of Henry VII to extract "benevolences" from unwilling contributors was a practical application of the dilemma in this case familiarly known as "Morton's fork." According to Bacon, Morton instructed his officers that "if they met with any that were sparing, they must tell them that they must needs have because they laid up; and if they were spenders, they needs must have, because it was seen in their manner of living."

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