dilemma

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dilemma

Logic a form of argument one of whose premises is the conjunction of two conditional statements and the other of which affirms the disjunction of their antecedents, and whose conclusion is the disjunction of their consequents. Its form is if p then q and if r then s; either p or r so either q or s

Dilemma

a particular form of inference with hypothetical (conditional) and alternative (disjunctive) premises. Two types are distinguished: the constructive (the affirmative form, the modus ponens dilemma) and the destructive (the negative form, the modus tollens dilemma), each of which, in turn, can be simple or complex. Complex constructive dilemmas are of the form “if A, then B; if C, then D; A or C; therefore, B or D” (where A,B,C,D are arbitrary judgments); simple constructive dilemmas are of the form “If A, then B; if C, then B; A or C; therefore, B” (the consequences of the conditional premises coincide). Complex destructive dilemmas are of the form “If A, then B; if C, then D; not-B or not-D; therefore, not-A or not-C”; simple destructive dilemmas are of the form “If A, then B; if A, then C; not-B or not-C; therefore, not-A” (where A, B, C, D are any judgments and the particle “not” negates the judgment before which it stands). The logical form of the dilemma finds an application in debates and discussions; in particular, logical refutations are often constructed according to the form of the simple constructive dilemma. Like any inference in logic, a dilemma guarantees a true consequence only if the premises are true.

In the figurative sense, a dilemma is a difficult situation in which a person finds himself when he must make a choice between two equally unpleasant possibilities.

REFERENCES

Church, A. Vvedenie v matematicheskuiu logiku, vol. 1. Moscow, 1960. Pages 98, 394. (Translated from English.)
Getmanova, A. D. Vyrazhenie deduktivnykh umozakliuchenii traditsionnoi logiki v simvolicheskoi logike. Murmansk, 1962.

B. V. BIRIUKOV

Dilemma

Buridan’s ass
placed exactly between two equal haystacks, could not decide which to turn to in his hunger. [Fr. Philos.: Brewer Dictionary, 154]
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It is a dilemna that Palios desperately hopes will not materialise as he would be forced to point out that Beckham's dispute with Sky was a personal matter which should be resolved away from England duty.
SCHOOL league tables are an extremely useful device, providing information which can help parents faced with the agonising dilemna of trying to choose the best schools for their children.
12) The striking adaptation that Arnold makes of Carlyle's complex account of poetic history is detailed in my Revolution as Tragedy: The Dilemna of the Moderate from Scott to Arnold (Ithaca: Cornell Univ.
Three folks have written with their own perspectives on this dilemna, and they all reiterate the same thing--if we don't have the basic necessities, we're in no better shape than our 20,000 close friends waiting with us in line for water bottles.
Unfortunate decisions by the Croatian state contributed to their dilemna.
Meanwhile Luxembourg's Jean Asselborn summed up the dilemna facing the EU, which is seeking a common foreign policy but threw its divisions into the open already in May, when Britain and France, determined to arm Syria's rebels, effectively put an end to an EU arms embargo.

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