Affirming the Consequent

Affirming the consequent, sometimes called converse error or fallacy of the converse, is a logical fallacy of inferring the converse from the original statement.  For instance, consider the following argument:

Premise 1: If Fiona won the lottery last night, she’ll be driving a red Ferrari today.

Premise 2: Fiona is driving a red Ferrari today.

Conclusion: Therefore, Fiona won the lottery last night.

An argument of this form is invalid, that is, the conclusion can be false even when the premises are true.  Since Premise 1 was never asserted as the only sufficient condition for Premise 2, other factors could account for Premise 2, such as:

  • Fiona could have inherited a large amount of money; or
  • She might just be borrowing the car; or
  • Perhaps she even stole it.

The fallacious argument has the general form:

Premise 1: If P, then Q.

Premise 2: Q.

Conclusion: Therefore, P.

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

Premise 1: If I have the flu, then I have a sore throat.

Premise 2: I have a sore throat.

Conclusion: Therefore, I have the flu.

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.

In contrast, a logically valid form of a similar argument would be:

Premise 1: If P, then Q.

Premise 2: P.

Conclusion: Therefore, Q.

This valid form of argument is a classical logical form known as modus ponens, with a history going back to antiquity.

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1 Comment

Filed under Logical fallacies

One response to “Affirming the Consequent

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