# 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*Dictionary*, 154]