Dilemma (logic)
A dilemma in logic refers to a situation where an argument presents two or more undesirable choices or outcomes, leading to a logical impasse. It typically consists of a major premise with conjunctive propositions—offering conflicting scenarios—and a minor premise that is disjunctive. The challenge lies in the inability to derive a satisfactory conclusion from the premises, even when they have been accurately assessed. Dilemmas can be categorized into constructive and destructive types. Constructive dilemmas affirm the antecedents of the major premise, leading to a conclusion that presents one or more potential outcomes. In contrast, destructive dilemmas deny the major premise's consequent, resulting in a conclusion that negates the antecedent. Understanding these variations is crucial in the study of deductive reasoning, as they illustrate how logical structures can lead to difficult choices or contradictions within arguments.
Subject Terms
Dilemma (logic)
The word dilemma refers to a problem that can only be solved by making a choice between two or more equally undesirable solutions. In logic and philosophy, the term has a more precise definition. It refers to a type of argument in which deductive reasoning fails to produce an acceptable conclusion despite having properly evaluated the constituent propositions of the argument.
Terminology
In logic, a premise(or analytic proposition) is a declarative statement that can be evaluated for truth or falsity through a subsequent argument. Premises can be major (containing the predicate of the conclusion) or minor (containing the subject of the conclusion).
An argument(or syllogism)is an attempt to demonstrate, through valid deductive reasoning, the truth or falsity of the premise. A simple representation of how premises use arguments to reach conclusions can be given as follows: All A is C. All B is A. Therefore, all B is C.
In this example, the statement "all A is C" forms the major premise, while the related statement "all B is A" forms the minor premise. The implied argument is "since all B is A and all A is C, all B must be C." The statement "all B is C" is the argument's conclusion.
Furthermore, propositions can be conjunctiveor disjunctive.A conjunctive proposition is one that presents multiple alternatives that cannot all be true. In other words, it presents two or more incompatible scenarios, one (or more) of which can be logically eliminated through affirmation of another. A disjunctive proposition also presents two or more possibilities, which are linked with the operators "either" and "or." The major difference between a conjunctive and disjunctive proposition is that a conjunctive proposition does not necessarily have to contain any elements that are true, while at least one of the elements of a disjunctive proposition is always true.
A simple example of a conjunctive proposition (and its accompanying syllogism) can be given as follows: You cannot have been in New York and Los Angeles at the same time. You were in Los Angeles. Therefore, you were not in New York.
What makes this argument conjunctive is the fact that the subject ("you") may not have been in New York or in Los Angeles at all. However, if the subject was in Los Angeles, he or she cannot possibly have been in New York at the same time.
A disjunctive proposition differs in that it uses the operators "either" and "or" to establish the certain truth of one element of the proposition. It then uses the minor premise to affirm or refute the major premise. For example: Your name is either Elizabeth or Jennifer. Your name is not Jennifer. Therefore, your name is Elizabeth.
It is also important to understand the distinction between antecedentsand consequents, as they apply to premises taking the "if ... then" form. The antecedent is the "if" clause of such a proposition, and the consequent is its "then" clause. For example, consider the statement, "If it barks, then it is a dog." In this example, "if it barks" is the antecedent, and "then it is a dog" is the consequent.
Traditional Forms of the Dilemma
In broad terms, the dilemma can be summarized as an argument consisting of a major premise and a minor premise. The major premise is a conjunctive proposition consisting of two or more hypothetical scenarios, while the minor premise is a disjunctive proposition. A dilemma occurs when the elements of the minor premise either affirm the antecedent of the major premise or deny the consequent of the major premise. As a result, the conclusion of such an argument creates a situation that affirms the consequent of the major premise (which has already been denied because its antecedent was affirmed), or denies the antecedent of the major premise (which has already been affirmed because its consequent was denied). This leads to a kind of logical impasse, in which the thorough deductive evaluation of the major and minor premises failed to produce a clear conclusion.
Constructive dilemmas occur when the minor premise affirms all the antecedents of the major premise rather than systematically eliminating antecedents to create a clear conclusion. A constructive dilemma is said to be simple if the conclusion contains a consequent found in the major premise. Similarly, a constructive dilemma is complex if the consequent in the conclusion differs from the consequent of the major premise.
Simple constructive dilemmas take the following form: If A then C, and if B then C. Either A or B. Therefore, C.
Complex constructive dilemmas take the following form: If A then B, and if C then D. Either A or C. Therefore, B or D. For example, if you eat cheese you will get an upset stomach, and if you eat salad you will still be hungry. Either you eat cheese or you eat salad. Therefore, you will either get an upset stomach or you will still be hungry.
In contrast, destructive dilemmas are those in which the minor premise denies the consequent of the major premise. When the conclusion of such an argument shares an antecedent with the major premise, it is simple; when the antecedents of the conclusion and the major premise differ, it is complex.
A simple destructive dilemma takes the form, if A then B, and if A then C. Either not B or not C. Therefore, not A.
Complex destructive dilemmas take the form, if A then B, and if C then D. Either not B or not D. Therefore, not A or not C. For example, if David is hired then Jack will quit, and if Marsha is hired then Angie will quit. Either Jack will not quit or Angie will not quit. Therefore, David cannot be hired or Marsha cannot be hired.
In all cases, the conclusions of dilemma arguments produce undesirable results, assuming that the goal of the argument is to affirm at least one element of the major premise.
Bibliography
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Murray, Malcolm and Nebojsa Kujundzic. Critical Reflection: A Textbook for Critical Thinking. Montreal: McGill-Queen's Press, 2005. Print.
Parry, William T. and Edward A. Hacker. Aristotelian Logic. Albany: State University of New York Press, 1991. Print.
Smith, Robin. "Aristotle's Logic." Stanford Encyclopedia of Philosophy. Center for the Study of Language and Information, Stanford University. 18 Mar. 2000. Web. 17 July 2015. http://plato.stanford.edu/entries/aristotle-logic/