Affirming a disjunct

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:

A or B

Therefore, it is not the case that B

Or in logical operators:

p \vee q

p

{} \vdash {}

q

Where ${} \vdash {}$ denotes a logical assertion.

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.

Example

The following argument indicates the invalidity of affirming a disjunct:

Max is a cat or Max is a mammal.

Max is a cat.

Therefore, Max is not a mammal.

This inference is invalid. If Max is a cat then Max is also a mammal. (Remember "or" is defined in an inclusive sense not an exclusive sense.)

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.

External links

Fallacy files: affirming a disjunct

Formal fallacies

Masked man fallacy

In propositional logic	Affirming a disjunct Affirming the consequent Denying the antecedent Argument from fallacy False dilemma

In quantificational logic	Existential fallacy Illicit conversion Proof by example Quantifier shift

Syllogistic fallacy	Affirmative conclusion from a negative premise Exclusive premises Existential Necessity Four-term fallacy Illicit major Illicit minor Negative conclusion from affirmative premises Undistributed middle

Other types of formal fallacy List of fallacies

Affirming a disjunct

Explanation

Example

See also

External links