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Denying_the_antecedent.
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Denying the antecedent
Denying the antecedent is a type of logical fallacy.
Suppose in an argument one were to deny the "if" part of a conditional (the antecedent) first, and conclude with the denial of "then" part (the consequent).
If P, then Q.
P is false.
Therefore, Q is false.
This argument form has the name denying the antecedent, because in arguing this way one does indeed deny the antecedent in the second premise. This is a logical fallacy. If we argue this way, we make a mistake. One can see this with an example:
If there is fire here, then there is oxygen here. (Since oxygen is required for fire.)
There is no fire here.
Therefore, there is no oxygen here.
See also: modus ponens, modus tollens, affirming the consequent.
The above article is adapted from from Wikipedia All Wikipedia article text is available under the terms of the GNU Free Documentation License
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