Critical Thinking Fallacy: Denying The Antecedent

In this video, Matthew C. Harris (Duke University) explains the fallacy of denying the antecedent, the formal fallacy that arises from inferring the inverse of a conditional statement. He also explains why graduate students might also be humans.

(intro music)

Hello, I'm Matthew Harris.

I'm a philosophy graduate
student at Duke University,

and today I'll be discussing

the formal fallacy of
denying the antecedent.

Denying the antecedent
is a formal fallacy,

meaning that the argument has a flaw

contained in its logical form.

This is important because

whenever this pattern of argument occurs,

regardless of topic or content,

the argument will always be invalid.

So how can we tell when

the fallacy of denying
the antecedent occurs?

Well, it happens when we mistake

the direction of a conditional,

or confuse it for a biconditional.

And it starts with the denial of

the conditional statement's antecedent,

then concludes the
denial of its consequent.

The logical form of arguments that commit

the fallacy of denying the
antecedent look like this:

"If P, then Q.

"Not P. Therefore, not Q."

Now, let's take a look
at this conditional:

"If you are a ski instructor,
then you have a job."

The antecedent statement
of this conditional

is "you are a ski instructor,"

and the consequent is "you have a job."

But suppose someone made an argument

with this conditional
as its first premise.

Premise (1): If you are a ski
instructor, then you have a job.

Premise (2): But you are
not a ski instructor.

Conclusion: Therefore,
you do not have a job.

Here, the second premise is
a denial of the antecedent.

This premise does not tell us

that only ski instructors have jobs.

So, even if the conditional
statement is true

(that ski instructors have jobs),

it cannot be inferred that if
you are not a ski instructor,

then you are unemployed.

A conditional could validly

be used to argue for the
truth of this consequent

by affirming the antecedent.

We find this in the arguments

of a form called "modus ponens."

It is also valid to argue from
the denial of a consequent

to a denial of the antecedent.

But it is never, ever valid
to deny the antecedent

to reject its consequent.

Let's try another example:

"If you are a property
owner, then you are a human.

"But you are not a property owner.

"Therefore, you are not a human."

The antecedent, that you are

a property owner, is being denied.

Even though you need to be
a human to own property,

this has no bearing on humans

who do not own property at all.

For example, graduate students.

Let's consider one last example:

"If anyone is watching this video,

"then they are on the internet.

"Some people are not watching this video.

"Therefore, they are not on the internet."

Again, denying the antecedent

by pointing out that not everyone

is currently watching this video

does not validly demonstrate
the denial of the consequent,

that they're not on the internet at all.

These have been a few cases
that I hope will come in handy

in avoiding this formal
fallacy in your own arguments.

For more related to the fallacy
of denying the antecedent,

I recommend that you take a
look at the other related videos

on informal and formal fallacies,

the fallacy of affirming the
consequent, and conditionals.