The

formal fallacy In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (; Latin for " tdoes not follow") is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic sy ...

of affirming a disjunct also known as the

fallacy A fallacy is the use of invalid or otherwise faulty reasoning, or "wrong moves," in the construction of an argument which may appear stronger than it really is if the fallacy is not spotted. The term in the Western intellectual tradition was int ...

of the alternative disjunct or a false exclusionary disjunct occurs when a

deductive Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if it is impossible for the premises to be true and the conclusion to be fals ...

argument takes the following

logical form In logic, logical form of a statement is a precisely-specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambig ...

: :A or B :A :Therefore, not B Or in logical operators: :

p \vee q

p

\vdash

q

Where

\vdash

denotes a

logical assertion In mathematical logic, a judgment (or judgement) or assertion is a statement or enunciation in a metalanguage. For example, typical judgments in first-order logic would be ''that a string is a well-formed formula'', or ''that a proposition is tru ...

Explanation

The fallacy lies in concluding that one disjunct must be false because the other disjunct is true; in fact they may both be true because "or" is defined inclusively rather than exclusively. It is a fallacy of

equivocation In logic, equivocation ("calling two different things by the same name") is an informal fallacy resulting from the use of a particular word/expression in multiple senses within an argument. It is a type of ambiguity that stems from a phrase havi ...

between the operations OR and

XOR Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false). It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , , ...

. Affirming the disjunct should not be confused with the valid argument known as the disjunctive syllogism.

Examples

The following argument indicates the unsoundness of affirming a disjunct: :Max is a mammal or Max is a cat. :Max is a mammal. :Therefore, Max is not a cat. This

inference Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that ...

is unsound because all cats, by definition, are mammals. A second example provides a first proposition that appears realistic and shows how an obviously flawed conclusion still arises under this fallacy. :To be on the cover of

Vogue Magazine ''Vogue'' is an American monthly fashion and lifestyle magazine that covers many topics, including haute couture fashion, beauty, culture, living, and runway. Based at One World Trade Center in the Financial District of Lower Manhattan, ''Vog ...

, one must be a celebrity or very beautiful. :This month's cover was a celebrity. :Therefore, this celebrity is not very beautiful.

External links

Fallacy files: affirming a disjunctAffirming a disjunct – logicallyfallacious.com
Propositional fallacies Syllogistic fallacies Logic articles needing expert attention

References

{{reflist

Explanation

Examples

See also

External links

References