Tuesday, February 21, 2012

Dilemmas & Quandaries

Last week, I had to deal with a series of dilemmas both constructive and destructive. We’ve moved past truth tables in the logic class. We also found a new category of lawyer-jokes.

A dilemma, officially defined, is a valid argument presenting a choice between two conditionals. In non-technical language, a dilemma is a situation which presents two options. One option will produce certain results, while the alternative produces radically different results. Most reasonable people would want to avoid either option, but the dilemma forces them to make the choice—in theory.

In practice, however, much depends on the way that the dilemma is phrased.

In many cases, you can phrase a dilemma to point out the horrible consequences that result when you choose one of the options. On the other hand, you can also rephrase these dilemmas to emphasize the wonderful benefits of not choosing one option.

You can either be a pessimist in logic, or an optimist.

One particular dilemma, slightly paraphrased, illustrates this difference. I heard it on the video lessons accompanying the workbook Intermediate Logic by James Nance:

One young Roman, after settling on his career, explained to his mother that he wanted to become a lawyer. “But,” she protested, “as a lawyer, if you tell the truth, then men will hate you. And if you don’t tell the truth, then that is unjust and the gods will hate you. You should not become a lawyer, because either way, you will be hated.”

“But mom,” the boy answered, giving the matter a more positive spin, “if I tell the truth, then the gods will love me. And if I tell lies, then men will love me. So either way, I will be loved!”

Don’t you think the boy made the right career choice?

Of course, when you have a dilemma that produces a contradiction, you have a paradox (or a quandary or a headache). In this situation, choosing either option produces X, while also denying the production of X. The example “Hanging or beheading” came from the lengthy collection of paradoxes and logic puzzles at http://www.paradoxes.co.uk:

“Poaching on the hunting preserves of a powerful prince was punishable by death, but the prince further decreed that anyone caught poaching was to be given the privilege of deciding whether he should be hanged or beheaded. The culprit was permitted to make a statement - if it were false, he was to be hanged; if it were true, he was to be beheaded. One logical rogue availed himself of this dubious prerogative - to be hanged if he didn't and to be beheaded if he did - by stating: ‘I shall be hanged.’ Here was a dilemma not anticipated. For, as the poacher put it, ‘If you now hang me, you break the laws made by the prince, for my statement is true, and I ought to be beheaded, but if you behead me, you are also breaking the laws, for then what I said was false and I should therefore be hanged.’”

I can't say much for the prince's powers of perspicacity, but there's also the case of the Greek pupil, also a lawyer who promised to pay his teacher after he won his first case. When, following graduation, he neglected to take any cases, his teacher took him to court claiming that if he won the judge would be ordering the student to pay. If he lost, however, his student would have to won his first case and be required to pay—as stated in their agreement.

A no-lose situation?

Yet the student responded that if he lost, he would not have to pay, since he had not won his first case yet, as their agreement stated. If he won, he still would not have to pay, since the court would have ruled againt the teacher.

Is your mind numb yet?

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