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The name "disjunctive syllogism" derives from its being a syllogism, a three-step argument, and the use of a logical disjunction (any "or" statement.) For example, "P or Q" is a disjunction, where P and Q are called the statement's disjuncts. The rule makes it possible to eliminate a disjunction from a logical proof. It is the rule that
In Disjunctive Syllogism, the first premise establishes two options. The second takes one away, so the conclusion states that the remaining one must be true. [3] It is shown below in logical form. Either A or B Not A Therefore B. When A and B are replaced with real life examples it looks like below.
A second example provides a first proposition that appears realistic and shows how an obviously flawed conclusion still arises under this fallacy. [3] To be on the cover of Vogue Magazine, one must be a celebrity or very beautiful. This month's cover was a celebrity. Therefore, this celebrity is not very beautiful.
In the 19th century, modifications to syllogism were incorporated to deal with disjunctive ("A or B") and conditional ("if A then B") statements. Immanuel Kant famously claimed, in Logic (1800), that logic was the one completed science, and that Aristotelian logic more or less included everything about logic that there was to know.
Disjunctive syllogism ... Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples:
A false dilemma can also occur in the form of a disjunctive syllogism: [6] disjunctive syllogism: (), In this form, the first premise is responsible for the fallacious inference. Lewis's trilemma is a famous example of this type of argument involving three disjuncts: "Jesus was either a liar, a lunatic, or Lord". [3]
Modus ponens is a mixed hypothetical syllogism and is closely related to another valid form of argument, modus tollens. Both have apparently similar but invalid forms: affirming the consequent and denying the antecedent. Constructive dilemma is the disjunctive version of modus ponens. The history of modus ponens goes back to antiquity. [4]
The form of a modus tollens argument is a mixed hypothetical syllogism, with two premises and a conclusion: . If P, then Q. Not Q. Therefore, not P.. The first premise is a conditional ("if-then") claim, such as P implies Q.