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Encyclopedia > Affirming the consequent

Affirming the consequent is a logical fallacy in the form of a hypothetical proposition. The fallacy of affirming the consequent occurs when a hypothetical proposition comprising an antecedent and a consequent asserts that the truthhood of the consequent implies the truthhood of the antecedent. This does not work bidirectionally.

In standard symbolic notation, the following hypothetical syllogism exemplifies the fallacy of affirming the consequent.

If P, then Q.
Q.
Therefore, P.

This logical error is called the fallacy of affirming the consequent because it is mistakenly concluded from the second premise that the affirmation of the consequent entails the truthhood of the antecedent. One way to demonstrate the invalidity is to use an analogous counterexample. Here is an argument that is obviously incorrect:

If Stephen King wrote the bible (P), then Stephen King is a good writer (Q).
Stephen King is a good writer (Q).
Therefore, Stephen King wrote the bible (P).

The previous argument was obviously incorrect, but the next argument may be more deceiving:

If someone is human (P), then they are mortal (Q).
Anna is mortal (Q).
Therefore Anna is human (P).

But in fact Anna can be a cat; very much a mortal, but not a human one.

However, be aware that affirming the consequent is valid if the first premise asserts "if and only if" rather than "if".

Results from FactBites:

 Logical Fallacy: Affirming the Consequent (266 words) Affirming the Consequent is a non-validating form of argument in propositional logic; for instance, let "p" be false and "q" be true, then there is no inconsistency in supposing that the first, conditional premiss is true, which makes the premisses true and the conclusion false. So, in general, in an instance of the form Affirming the Consequent, if it is reasonable to consider the converse of the conditional premiss to be a suppressed premiss, then the argument is not fallacious, but a valid enthymeme. Thus, the Counter-Example is a fallacious instance of Affirming the Consequent.
 Affirming the consequent - Wikipedia, the free encyclopedia (229 words) Affirming the consequent is a logical fallacy in the form of a hypothetical proposition. The fallacy of affirming the consequent occurs when a hypothetical proposition comprising an antecedent and a consequent asserts that the truthhood of the consequent implies the truthhood of the antecedent. If P, then Q. Therefore, P. This logical error is called the fallacy of affirming the consequent because it is mistakenly concluded from the second premise that the affirmation of the consequent entails the truthhood of the antecedent.
More results at FactBites »

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