Affirming the Consequent

Affirming the consequent is a formal logical fallacy which consists of a conditional premise, a second premise that asserts the consequent of the first conditional premise, and a conclusion which asserts therefore the antecedent of the conditional is true. The general form of the argument is:

P1. If P then Q.
P2. Q
C. Therefore P.

Since P was never asserted as the only sufficient condition for Q, other factors could account for Q. Therefore, in terms of deductive logic, the argument form is invalid.

For example:

P1. If Bill Gates owns Fort Knox, then he is rich.
P2. Bill Gates is rich.
C. Therefore, he owns Fort Knox.

Obviously the consequent that Gates is rich is the result of factors other than owning Fort Knox.

It is important to understand that though affirming the consequent is a fallacy in terms of deductive reasoning, it can be used as a perfectly acceptable form of inference when used inductively or abductively. This of course is due to deductive reasoning's requirement that with a valid argument, if the premises are true then the conclusion must be true. On the other hand, induction and abduction do not have this certainty requirement and instead make inferences based on probability and plausibility.

For example:
P1. If the baby is hungry she will cry
P2. The baby is crying
C. The baby is hungry

This is not deductively valid since there are other reasons the baby may be crying. Perhaps she needs a diaper change or maybe she hit her head. On the other hand, depending on the circumstances, this could be considered a strong abductive argument. If we add more information through additional premises the strength of the argument becomes less ambiguous.

P1. If the baby is hungry she will cry
P2. The baby is crying
P3. The baby eats about every three hours
P4. The baby last ate about three hours ago
P5. The baby does not have a dirty diaper
C. The baby is hungry



Wikipedia: Affirming the Consequent 09/10/15

Reasoning: K. P. Mohanan and Tara Mohanan