The logical fallacy of affirming a disjunct occurs in a disjunctive syllogism when an argument takes the form: A logical fallacy is an error in logical argument which is independent of the truth of the premises. ... A disjunctive syllogism is one valid, simple argument form: A or B If not A Then B In logical operator notation: ¬ where represents the logical assertion. ...
The fallacy lies in concluding that B must be false because A is true; in fact they may both be true. The second, or "minor premise" must be negative in order for this kind of argument to be valid. The middle term is the term that occurs in both premises (but not in the conclusion) of a categorical syllogism. ... In a categorical syllogism, the minor premise is the premise whose terms are the syllogisms minor term and middle term. ... In logic, an argument is said to be valid if the truth of the conclusion follows from the truth of the premises. ...
NOTE: if the or is really a xor then this is not a fallacy. OR Logic Gate Logical disjunction (usual symbol or) is a logical operator that results in true if either of the operands is true. ... Exclusive disjunction (usual symbol xor) is a logical operator that results in true if one of the operands (not both) is true. ...
Example:
Tomorrow it will either rain or the sun will shine.
The weather forecast said it would rain tomorrow.
Therefore, the sun will not shine tomorrow.
This inference is obviously false, because the sun can be shining while it is raining (they are not exclusive events).
Either the Glasgow Celtics or Glagow Rangers will win in their game today.
Rangers didn't win.
Therefore, Celtics won
This premise is false on football, where the game can also end in draw (inclusive OR). but not in games where the game cannot end in draw (exclusive XOR).
See also:syllogistic fallacy. Syllogistic fallacies are logical fallacies that occur in syllogisms. ...
Affirming a Disjunct is a non-validating form of argument when "or" is inclusive (see below), as it is standardly interpreted in propositional logic.
As with other propositional fallacies, an argument which affirms a disjunct is most likely to seem valid when we take into consideration some further information not explicitly mentioned in the argument.
The exclusive disjunction of propositions A and B is usually called A xor B, where "xor" stands for "exclusive or" and is pronounced "eks-or" or "zor".
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