Affirming the consequent

Helping orphans the way you would do it

Affirming the consequent is a logical fallacy in the form of a hypothetical proposition. A hypothetical proposition is comprised of an antecedent and a consequent, respectively. A hypothetical proposition states that the truth-hood of the antecedent entails the truth-hood of the consequent. This does not work bi-directionally.

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

If P, then Q.

Therefore, P.

It 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 truth-hood of the antecedent. One way to demostrate the invalidity is to use an analogous counter-example. Here is an obviously wrong arguement:

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 wrong. The next argument may be more decieving:

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

Anna is mortal (Q).

Therefore Anna is human (P).

But in fact Anna is 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".