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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 between the operations OR and XOR.
Affirming the disjunct should not be confused with the valid argument known as the disjunctive syllogism.
Fallacy files: affirming a disjunct
* {{Formal fallacy Propositional fallacies Syllogistic fallacies
The formal fallacy
In logic and philosophical logic, philosophy, a formal fallacy is a pattern of reasoning rendered validity (logic), invalid by a flaw in its logical structure. propositional calculus, Propositional logic, for example, is concerned with the meaning ...
of affirming a disjunct also known as the fallacy of the alternative disjunct or a false exclusionary disjunct occurs when a deductive
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false. For example, th ...
argument takes the following logical form
In logic, the 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, unamb ...
:
:A or B
:A
:Therefore, not B
Or in logical operators:
:
:
: ¬
Where 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 between the operations OR and XOR.
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. Thisinference
Inferences are steps in logical 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 distinct ...
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, one must be a celebrity or very beautiful.
:This month's cover was a celebrity.
:Therefore, this celebrity is not very beautiful.
See also
*Exclusive disjunction
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or Logical_equality#Inequality, logical inequality is a Logical connective, logical operator whose negation is the logical biconditional. With two inputs, X ...
* Logical disjunction
In logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is ...
* Syllogistic fallacy
A syllogism (, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
In its earliest form (define ...
References
External links
Fallacy files: affirming a disjunct
* {{Formal fallacy Propositional fallacies Syllogistic fallacies