Affirming the consequent

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Affirming the consequent, sometimes called converse error, is a formal fallacy, committed by reasoning in the form:

An argument of this form is invalid, i.e., the conclusion can be false even when statements 1 and 2 are true. Since P was never asserted as the only sufficient condition for Q, other factors could account for Q (while P was false).

The name affirming the consequent derives from the premise Q, which affirms the "then" clause of the conditional premise.



One way to demonstrate the invalidity of this argument form is with a counterexample with true premises but an obviously false conclusion. For example:

Owning Fort Knox is not the only way to be rich. There are any number of other ways to be rich.

Arguments of the same form can sometimes seem superficially convincing, as in the following example:

But having the flu is not the only cause of a sore throat since many illnesses cause sore throat, such as the common cold or strep throat.

The following is a more subtle version of the fallacy embedded into conversation.

B attempts to falsify A's conditional statement ("if Republican then against gun control") by providing evidence he believes would contradict its implication. However, B's example of his uncle does not contradict A's statement, which says nothing about non-Republicans. What would be needed to disprove A's assertion are examples of Republicans who support gun control. If this refutation is then followed by A asserting that all true Republicans are against gun control, it would be a case of No True Scotsman fallacy.

Use of the fallacy in science

Although affirming the consequent is an invalid inference, it is defended in some contexts as a type of abductive reasoning, sometimes under the name "inference to the best explanation". That is, in some cases, reasoners argue that the antecedent is the best explanation, given the truth of the consequent. For example, someone considering the results of a scientific experiment may reason in the following way:

For example,

However, such reasoning is still affirming the consequent and logically invalid (e.g., Let P = geocentrism and Q = sunrise and sunset). The strength of such reasoning as an inductive inference depends on the likelihood of alternative hypotheses, which shows that such reasoning is based on additional premises, not merely on affirming the consequent.

See also

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