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Denying a Conjunct

Formal logical fallacy, in which the negation of one of two mutually exclusive statements is used to infer the other.

Example:

You can not vote for both, party A and party B.
You did not vote for party A,

Therefore, you must have voted for party B.

The premises do not imply that there were only two parties running, and that abstention or invalid votes are excluded. The conclusion is therefore not valid.

In this form, the denying a conjunct is closely related to “affirmative conclusion from a negative premise”, which is, however, specific to syllogisms.

Description

This fallacy arises from incorrect application of the Modus ponendo tollens, in particular when it is incorrectly mixed with the Modus tollendo ponens.

For comparison, the following table compares the two valid forms of inference with the fallacy:

Note: Both the contravalence A ⊻ B [A or B, but not both] and the negative conjunction ⌐(A ∧ B) [not both, A and B] are equivalent, i.e.: A ⊻ B⌐(A ∧ B).

See also

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