Affirming the consequent is a logical fallacy that occurs when someone mistakenly infers that the opposite of a true “if-then” statement is true.
It’s a formal fallacy, meaning that there is an error in the argument’s logical structure, rendering the conclusion invalid. Furthermore, it is also known as “converse error”, “asserting the consequent”, and “fallacy of the consequent”.
Affirming the consequent is a fallacious form of reasoning in which the converse of a true conditional statement (or “if-then” statement) is said to be true. In other words, it is assumed that if the proposition “if A, then B” is true, then “if B, then A” is true as well.
Thus, its logical form is:
- If X, then Y.
- Therefore, X.
One example would be:
- If it’s raining, then the streets are wet.
- The streets are wet.
- Therefore, it’s raining.
Here, even though the initial premise may be correct (if it’s raining, then the streets are wet), we cannot infer from it that the converse (if the streets are wet, then it’s raining) must be correct too; the fact that the streets are wet doesn’t necessarily mean that it is currently raining.
Why is Affirming the Consequent Invalid?
This error in reasoning is a type of formal fallacy (or deductive fallacy), which refers to a flaw in the structure of a deductive argument. A deductive argument is one that is intended to provide a necessarily valid conclusion if the premises are true: its validity is dependant on the structure of the argument.
Affirming the consequent is an invalid argument because its premises do not guarantee the truthfulness of the conclusion. As seen above, there is a flaw in the argument’s structure because it uses erroneous conditional logic, and it is this flaw that renders the conclusion invalid.
Here are a few more examples to further illustrate this.
- If he’s a pilot, then he has a job.
- He has a job.
- Therefore, he is a pilot.
- If an animal is a cat, then it has a tail.
- My pet lizard has a tail.
- Therefore, my pet lizard is a cat.
- If I have the flu, then I have a fever.
- I have a fever.
- Therefore, I have the flu.
- If the weather is good today, then I will go hiking.
- I will go hiking.
- Therefore, the weather is good today
Denying the antecedent is another formal fallacy and similar to the one previously explained, however, it essentially works the opposite way. It states that:
- If X, then Y.
- Not X.
- Therefore, not Y.
As in affirming the consequent, this form of argument is invalid since the premises do not warrant the truth of the conclusion; the fact that X is false doesn’t mean that Y must be false. This is easy to show with an example: “If he’s a human, then he has a brain. He isn’t a human (he’s a dog). Therefore, he doesn’t have a brain.”