• 3-minute read
• 5th April 2021

Fallacy Watch: Denying the Antecedent

A fallacy is a bad or faulty argument. One such fallacy, associated with academic writing, is denying the antecedent. But what does this involve? And how can you avoid it? In this post, we explain the basics for students and other academic writers.

What Is Denying the Antecedent?

‘Denying the antecedent’ is a logical fallacy based on drawing an untrue conclusion from an ‘if–then’ argument. We can represent it like this:

If X is true, then Y is also true.

X is not true, so Y is not true either.

The idea here is that, if ‘X’ causes or leads to ‘Y’, the latter being untrue rules out the former as well. This makes it like the reverse of affirming the consequent. However, both fallacies involve an unjustified jump from a premise to a conclusion.

To see how this fallacy works in practice, we’ll move on to an example.

Example of Denying the Antecedent

To see the issue here, we’ll use an example that should be obviously false:

If you are a proofreader, you have a job.

Thus, if you are not a proofreader, you do not have a job.

The first claim here (if X, then Y) is clear enough:

If you are a proofreader, you have a job.

This is simple to understand: proofreading is a job, so being a proofreader means you have a job. The problem comes in the second part:

Thus, if you are not a proofreader, you do not have a job.

Here, we flip the argument, which means we end up claiming that not being a proofreader equates to not having a job. But this overlooks every other job that someone could have (i.e. every other condition that would make ‘Y’ true).

Not all cases of denying the antecedent will be this clearly wrong. But they all make the same invalid move, ignoring the relationship between the ‘X’ and ‘Y’ conditions to imply that negating ‘X’ also implies negating ‘Y’. As in the example above, though, this does not necessarily work from a logical point of view!

How to Avoid the Fallacy

An argument that denies the antecedent may look a lot like a valid argument. In addition, not every argument that takes the form above will be wrong. For instance:

If I am an unmarried man, I am a bachelor.

I am not an unmarried man, so I am not a bachelor.

Here, the second claim follows from the first. But this is because ‘bachelor’ and ‘unmarried man’ mean the same thing: you are a bachelor if and only if you are an unmarried man. As a result, negating either means negating both.

But this only works when you have an ‘if and only if’ relationship between two conditions. As with the ‘proofreader’ example, it does not work if there are other possible explanations for ‘Y’ – the second part of the argument – being true.

There is no simple trick to avoiding this fallacy. The key instead is to approach arguments critically. If you back up ideas with evidence and consider other possible explanations any claim, you should avoid the pitfall of denying the antecedent.