Logical Fallacy: Denying the Antecedent

Logical Fallacy: Denying the Antecedent

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We can look at life as a series of judgments and conclusions. What is that person’s intent? What should I have for lunch? And many other decisions. When we improve our reasoning, we improve our capacity to gather and verify facts as well as update our beliefs. Doing so helps us make sense of the world. Denying the antecedent is a common reasoning error that we all make. What is it? And why does it matter?

First, I’m going to discuss why understanding logical fallacies are important. Then, I’m going to present a quick refresher on formal arguments. Finally, I explain the denying the antecedent fallacy.

So, What’s the Point?

We make hundreds, if not more, decisions every day. Most of them are low-stakes so it’s not a high-priority to reach the optimal conclusion. But sometimes we need an optimal solution. In such cases, it’s worth the extra time and energy to make sure our reasoning is sound.

Remember from my previous article that a logical fallacy is an error in reason. Often, that error can lead to a weak or invalid conclusion. So, when we want an optimal solution, the ability to identify logical fallacies is a benefit.

A problem comes up because fallacies aren’t always easy to spot. So, we can end up making decisions based on unsound reasoning.

Despite our capacity for reason, we all make errors. It could be our friends and family, politicians, or the media. Sometimes those errors are innocent mistakes.

But sometimes fallacies are intentional. For example, advertisers design commercials to elicit an emotional response. They do so in the hopes that your emotions will override reason and get you to take the desired action. This is an appeal to emotion. A powerful fallacy used by politicians and the media every day.

Today, we’re bombarded by more information than ever. Sales pitches and pundit opinions are all around us.

Knowing how to spot fallacies gives us the tools we need to make sense of this noise. And it improves our decision-making. And better decisions give you more control over your life.

Let’s Take a Quick Stroll Down Memory Lane

First, a little review. In a formal argument, if all the premises are true then the conclusion must be true.

For example:

  1. All P are Q.
  2. X is P.
  3. Therefore, X is Q.

To make the argument easier to understand, let’s use words instead of letters:

  1. All humans are mortal.
  2. Socrates is human.
  3. Therefore, Socrates is mortal.

Since premises 1 and 2 are both true, then the conclusion must be true. We call this deductive reasoning.

Remember, the conclusion could be true even though we used flawed logic to reach the conclusion.

That’s the end of our quick review. Go back and re-read my first article on logical fallacies for more information.

Denying the Antecedent

Denying the antecedent (inverse error or inverse fallacy) is a common formal fallacy. In this fallacy, we infer the inverse from a statement. We confuse the directionality of a statement.

Doing so leads us to believe that if a statement is true, then the negation of that statement must also be true.

Denying the antecedent takes the form:

  1. If P, then Q.
  2. Not P.
  3. Therefore not Q.

Example:

  1. If it’s raining outside, then [Shirley the Dog] is wet.
  2. It’s not raining outside.
  3. Therefore [Shirley the Dog] is not wet.

Explanation:

This is an obvious fallacy. Because it’s not raining outside doesn’t mean Shirley the Dog isn’t wet. She could be swimming in a lake, getting a bath, or she’s still wet from a recent rain.

Denying the antecedent isn’t always easy to spot. The words we use in an argument can sometimes hide the structure of the argument. So, replacing words with letters and rearranging the statement can help simplify it.

Why it’s important?

Here’s a common argument. Please note that I’m presenting the argument this way to make it easier to analyze. People making this argument don’t always state it in this explicit manner. That’s one reason logical fallacies are hard to spot.

  1. If you’re against Politician X, you’re a good person.
  2. You support Politician X.
  3. Therefore, you’re a bad person.

There could be hundreds of reasons to support or not support a politician.

Let’s say Politician X is weak on civil rights but strong on prison reform.

The person making this argument ranks civil rights as the most important consideration. So, he’s basing his argument on Politician X’s poor track record on civil rights. What he’s saying is, if you support Politician X, you don’t support civil rights. And since you don’t support civil rights, you’re a bad person.

But civil rights are only one of many policy questions. Someone else may rank prison reform higher than civil rights. So that person supports Politician X despite his poor stance on civil rights.

Neither person is good or bad based on their feelings about Politician X.

It’s nothing more than a difference of opinion about the importance of two policy issues.

Conclusion

If our reason is sometimes flawed, then we must expect flaws in others’ reason as well. Understanding logical fallacies help us identify reasoning errors. When we spot reasoning errors, we improve our conclusions.

Denying the antecedent is a common error. By understanding it, we improve the quality of our conclusions. The stronger our conclusions, the better our decisions based on those conclusions. If we want a life free from the impact of poor decisions, it’s important to be able to identify faulty reasoning. Not only from others but from ourselves.

Do you have an example of denying the antecedent? Let me know in the comments below.

Bibliography and Additional Reading

Books

Online

  • “Formal Fallacy.” Wikipedia. Wikimedia Foundation, March 14, 2020. https://en.wikipedia.org/wiki/Formal_fallacy.
  • “Denying the Antecedent.” Wikipedia. Wikimedia Foundation, September 6, 2019. https://en.wikipedia.org/wiki/Denying_the_antecedent.
  • Curtis, Gary. “Denying the Antecedent.” Logical Fallacy: Denying the Antecedent. Accessed March 17, 2020. https://www.fallacyfiles.org/denyante.html.
  • “Denying the Antecedent.” RationalWiki. Accessed March 17, 2020. https://rationalwiki.org/wiki/Denying_the_antecedent.

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