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Affirming a disjunct is a fallacy. The formal fallacy of affirming a disjunct also known as the fallacy of the alternative disjunct or a false exclusionary disjunct occurs when a deductive argument takes the following logical form: [1] A or B A Therefore, not B. Or in logical operators:
In linguistics, a disjunct is a type of adverbial adjunct that expresses information that is not considered essential to the sentence it appears in, but which is considered to be the speaker's or writer's attitude towards, or descriptive statement of, the propositional content of the sentence, "expressing, for example, the speaker's degree of truthfulness or his manner of speaking."
Affirming a disjunct; Argument from fallacy This page was last edited on 2 June 2023, at 23:46 (UTC). Text is available under the Creative Commons Attribution ...
Affirming a disjunct – concluding that one disjunct of a logical disjunction must be false because the other disjunct is true; A or B; A, therefore not B. [10] Affirming the consequent – the antecedent in an indicative conditional is claimed to be true because the consequent is true; if A, then B; B, therefore A. [10]
Equivalently, if P is true or Q is true and P is false, then Q is true. 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.
Then if is true, that rules out the first disjunct, so we have . In short, P → Q {\displaystyle P\to Q} . [ 3 ] However, if P {\displaystyle P} is false, then this entailment fails, because the first disjunct ¬ P {\displaystyle \neg P} is true, which puts no constraint on the second disjunct Q {\displaystyle Q} .
Logical fallacy: Since most of the green is touching red, and most of the red is touching blue, most of the green must be touching blue. This, however, is a false statement. In the strictest sense, a logical fallacy is the incorrect application of a valid logical principle or an application of a nonexistent principle: Most Rimnars are Jornars.
Although the type of a logical disjunction expression is Boolean in most languages (and thus can only have the value true or false), in some languages (such as Python and JavaScript), the logical disjunction operator returns one of its operands: the first operand if it evaluates to a true value, and the second operand otherwise.