Affirming the consequent
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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".