Also referred to as an inverse error or inverse fallacy, denying the antecedent fallacy is understood as a logical error involving an if-then statement.
When a person assumes that the antecedent (the first part of an If statement, or conditional statement) being false means that the consequent (the second part of a “then” statement) is also necessarily false. See below:
- First premise: if x, then y.
- Second: not x.
- Conclusion: therefore, not y.
This logic does not invariably lead to the correct or sound conclusion. Said differently, denying the antecedent occurs when someone takes one cause as a condition for the occurrence of a separate event, while stating that the latter will not occur when the condition being observed is found to be untrue.
See the examples below.
Denying the Antecedent Examples
- If she’s human, then she has a brain. But if she is a dog (not a human), then it follows that she does not have a brain.
- If they leave two hours early for class, then they will get there on time. They did not leave two hours early. Therefore, they did not get there on time.
- If Sarah works harder than Billy, then she’ll get a job. Billy doesn’t work harder than Sarah. Therefore, Billy won’t get a job.
- If your pet is a cat, then it has a tail. Your pet is not a cat. Therefore, it does not have a tail.
- If you are a mechanic, you have a job. You are not a mechanic. Therefore, you do not have a job.
- While plucking petals off a daisy, if my last petal is “he loves me” then my partner loves me. The last petal picked is not “he loves me.” Therefore, he does not love me.
- If the train departs on Track A then it is southbound. The train did not depart on Track A. Therefore, it is not southbound.
- If this individual is smart, then they can achieve success in life. This individual is not smart. Therefore, they cannot achieve success.
- Any person who blinks is alive. Sleeping people do not blink. Therefore, sleeping people are not alive.
- If you give Janie a gun, she may kill someone. Janie does not have a gun. Therefore, she will not kill anyone.
5 Best Examples
1. If you are a mechanic
When looking at this example, at its core, it is simple to understand: you have a job if you are a mechanic. So, being a mechanic means you have a job.
Where we see an issue is in the last part of the statement: you are not a mechanic; therefore, you do not have a job.
Here, the argument is flipped, and the claim being made is that not being a mechanic equals not having a job. This, of course, is logically flawed as it overlooks every other job opportunity that one could have.
2. Plucking daisy petals
The old childhood game that involves pulling the petals off a daisy, and with each petal stating either “he loves me” or “he loves me not” altering between the two phrases with each petal until the last one remaining concludes how your partner may feel about you.
This can be seen as an example of denying the antecedent: believing that if the last petal plucked is the ‘he loves me petal’ then your partner loves you. If the last petal plucked is not ‘he loves me’, then your partner does not love you.
While this particular example is in reference to a game, it nevertheless portrays the rationale that exists when denying the antecedent fallacy by coming to a conclusion based on flawed and inaccurate logic.
3. The train on track A
Making the assumption that the train is not going southbound because it did not depart on track A ignores the possibility that the train may be heading southbound on a track other than track A.
In this scenario, as is the case with all forms of denying the antecedent fallacy, it assumes that the opposite of the first presented scenario is necessarily true.
This, however, is not always the case. It may be true that the train did not depart on track A, but that does not suggest or deny the direct track that the train is going on.
To better understand the direction, it would require further investigation of possibilities and directions for departures, and less assumptions.
4. Janie’s got a gun
Perhaps a more morbid example, suggesting that Janie will not harm anyone because she doesn’t have a gun is flawed in logic.
There are many ways to cause harm to others which don’t include this specific weapon. Suggesting that Janie not having a gun will result in no harm done does not necessarily follow.
It is possible, however, that an argument that denies the antecedent could potentially be valid, should the argument observe another valid form. That is, switching from an “if-then” premise to an “if and only if” claim, which are typically rare.
5. Blink once if you’re alive
Plenty of movies use a humorous denying the antecedent fallacy when a character checks if their friend has died or is just asleep: “blink once if you’re alive!”
Here’s why it’s a denying the antecedent fallacy:
- Any person who blinks is alive.
- Sleeping people do not blink.
- Therefore, sleeping people are not alive.
It’s clear to see how this is a fallacious form of reasoning in formal logic.
We know that people who sleep are not blinking since their eyes are closed. This does not mean they are not living.
They are breathing, and potentially moving, their heart is pumping, and blood is circulating, which are all anatomic conditions of living. They’re not blinking because they are asleep.
In this statement, denying the antecedent makes the mistake of assuming that if the antecedent is denied, then this means that the consequent (the conclusion) must also be denied.
Related: Circular Reasoning Fallacy
Even though two premises of an argument may be true (i.e., the premise of “if x, then y” and the premise of “not X”), it would be denying the antecedent fallacy to conclude that “not X” is equal to “not Y.”
This would be executing flawed conditional logic, meaning that the basis of the argument does not guarantee the accuracy and truthfulness of its conclusion. We can see how there is a flaw in the structure of said argument.
In order to reconcile this error in reasoning, it is important to think critically about the conditional statements that we are placing on ourselves and others. Are our conclusions logical or are they riddled with assumptions that have no basis? Being honest with oneself and acknowledging assumptions and biases will help to resolve falling victim to denying the antecedent fallacy.