Inverse Error (Denying the Antecedent)
The inverse error is a deductive fallacy that occurs when one denies the antecedent of a conditional statement and concludes the negation of the consequent. It is deductively invalid but can be inductively plausible.
THE IDEA
INVERSE ERROR 2
If President Obama is Muslim, then he’s not a Christian.
President Obama is not Muslim.
Therefore, President Obama is a Christian.
The inference would be valid with an additional premise restricting the alternatives to Muslim or Christian. We don’t believe that, of course, but we may have gotten into a mood of thinking these are the only alternatives for Obama; for example, if the only alternatives for Obama’s religion ever discussed were Muslim and Christian.
An interesting and important thing to know about the converse and inverse errors is that they are deductively invalid inferences. (That is, the conclusions don’t follow logically from the stated premises.) They may however be pretty good inductive conclusions. (That is, if the premises are true, the conclusion is more likely to be true.) It’s more likely that I have the flu if I have a sore throat than it is if I don’t have a sore throat. If it’s not raining, it’s less likely that the streets are wet than if it is raining. The plausibility of the inductive conclusion in these cases contributes to making the invalid deductive conclusion plausible as well.
When to use it
In political debates, where opponents deny a premise and conclude the opposite without logical necessity.
In everyday arguments, such as 'If I study, I will pass. I didn't study, so I will not pass.' This conclusion is not logically guaranteed, as other factors could lead to a pass.
In scientific reasoning, when interpreting conditional statements in experiments, it is important to recognize that denying the antecedent does not disprove the consequent.
FROM THEORY TO EVERYDAY LIFE
In practice
President Obama's Religion
If President Obama is Muslim, then he’s not a Christian. President Obama is not Muslim. Therefore, President Obama is a Christian. This is an inverse error because it denies the antecedent (not Muslim) and concludes the negation of the consequent (Christian). Adding a premise that restricts the alternatives to Muslim or Christian would make the inference valid, but that restriction is not generally true.
Flu and Sore Throat
Assume for the illustration: if I have the flu, I have a sore throat. It does not follow that, without flu, I cannot have a sore throat; another cause may produce it. Any probabilistic inference would need information about those causes as well.
Rain and Wet Streets
If it rains, the streets will be wet. It did not rain. Therefore, the streets are not wet. This is deductively invalid but inductively plausible because rain is a common cause of wet streets.
A MOMENT TO REFLECT
Put it to work.
Can you think of a real-world situation where someone commits the inverse error? What makes it persuasive?
Why does the inverse error feel logically sound even though it is not?
How can you avoid falling for the inverse error in your own reasoning?
CONTINUE THE CONVERSATION
Source texts
- Mindware Tools for Smart Thinking (Richard E. Nisbett)