Denying the antecedent, also known as inverse error and fallacy of the inverse, is a logical fallacy whereby someone fallaciously makes an inverse deduction in a conditional statement. It takes one cause as a condition for something else to occur and then states that the latter won’t occur when the condition is observed to be untrue.
It’s a type of formal fallacy, and closely related to affirming the consequent. They both are among the most common formal fallacies.
Definition
Denying the antecedent occurs when the consequent of an “if-then” statement is inferred not to be true based on the fact that its antecedent is also said to be not true.
In an “if-then” statement, the “if” part is the antecedent while the “then” part is called the consequent.
Its logical form goes as follows:
- Premise 1: If X, then Y.
- Premise 2: Not X.
- Conclusion: Therefore, not Y.
An example of denying the antecedent would be:
- Premise 1: If he’s a human, then he has a brain.
- Premise 2: He isn’t a human (he’s a dog).
- Conclusion: Therefore, he doesn’t have a brain.
Here, even though the two premises of the argument are true, its conclusion is still incorrect. Thus, the argument is invalid because it follows flawed conditional logic; the premises of the argument do not guarantee the truthfulness of the conclusion.
As such, it’s a formal fallacy because the error arises from a flaw in the structure of the argument, rather than from the strength of the evidence supporting the conclusion.
Examples
- If you work harder than me, then you’ll be able to get a job.
- You don’t work harder than me.
- Therefore, you won’t be able to get a job.
- If my pet is a dog, then he has a tail.
- My pet is not a dog.
- Therefore, he doesn’t have a tail.
- If someone has billions of dollars, they are rich.
- He doesn’t have billions of dollards.
- Therefore, he isn’t rich.
- If I’m smart, then I can achieve success in life.
- I’m not smart.
- Therefore, I cannot achieve success.
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