dilemma

logic

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Related Topics:: inference schema

dilemma, in syllogistic, or traditional, logic, any one of several forms of inference in which there are two major premises of hypothetical form and a disjunctive (“either . . . or”) minor premise. For example:

If we increase the price, sales will slump.

If we decrease the quality, sales will slump.

Either we increase the price or

we decrease the quality.

Therefore, sales will slump.

In logic ⊃ signifies “if . . . then”; ∨ signifies “either . . . or”. Symbolically, therefore, a dilemma is an argument of the form A ⊃ C, B ⊃ C, A ∨ B, therefore C.

It is not necessary that a dilemma should have an unwelcome conclusion; but from its use in rhetoric the word has come to mean a situation in which each of the alternative courses of action (presented as the only ones open) leads to some unsatisfactory consequence. To take a familiar example, a person who is asked, “Have you stopped beating your wife?” is presented with a rhetorical dilemma. In this more complicated version of the dilemma, however, two unwelcome results are presented instead of one (C, above). Thus, the conclusion itself becomes a disjunction:

Either you have been beating your wife or you are continuing to beat her.

decision theory

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decision theory

statistics

Also known as: decision analysis, statistical decision theory

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Key People:: Daniel Ellsberg; Herbert A. Simon

Related Topics:: statistics; von Neumann–Morgenstern utility function; expected utility

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decision theory, in statistics, a set of quantitative methods for reaching optimal decisions. A solvable decision problem must be capable of being tightly formulated in terms of initial conditions and choices or courses of action, with their consequences. In general, such consequences are not known with certainty but are expressed as a set of probabilistic outcomes. Each outcome is assigned a “utility” value based on the preferences of the decision maker. An optimal decision, following the logic of the theory, is one that maximizes the expected utility. Thus, the ideal of decision theory is to make choices rational by reducing them to a kind of routine calculation.