# PEARLS OF WISDOM-III

#### The errant spelling dilemna is often seen in common usage. It appears to have been taught in many areas of the United States and all over the world, including (but not limited to) France, England, Jamaica and Australia. There is no prima facie reason for this substitution error and there is no erroneous parallel to be found with the word lemma, from which dilemma derives.Use in logic In formal logic, the definition of a dilemma differs markedly from everyday usage. Two options are still present, but choosing between them is immaterial because they both imply the same conclusion. Symbolically expressed thus: A \vee B, A \Rightarrow C, B \Rightarrow C, \vdash C Which can be translated informally as “one (or both) of A or B is known to be true, but they both imply C, so regardless of the truth values of A and B we can conclude C.” There are also constructive dilemmas and destructive dilemmas.Constructive dilemmas 1. (If X, then Y) and (If W, then Z). 2. X or W. 3. Therefore, Y or Z. 4. All are possible.Destructive dilemmas 1. (If X, then Y) and (If W, then Z). 2. Not Y or not Z. 3. Therefore, not X or not W.

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