Critical Thinking Fallacy: Affirming The Consequent

In this video, Matthew C. Harris (Duke University) explains the fallacy of affirming the consequent, the formal fallacy that arises from inferring the converse of an argument. He also explains why you sometimes cannot conclude that you should bathe in a tub of peanut butter.

(intro music)

Hello, I'm Matthew Harris,

and I'm a philosophy grad
student at Duke University.

And today, I'll be discussing
the formal fallacy

of affirming the consequent,

and why you sometimes cannot conclude

that you should bathe
in a tub of peanut butter.

Affirming the consequent occurs

when someone tries to infer the truth

of the antecedent of a
conditional statement

from the truth of the
conditional and its consequent.

But let's see what this means in more detail.

There are two kinds of logical fallacies:

formal and informal.

Both kinds are defective
argumentative patterns.

First, we have informal fallacies,

which lack support for the conclusion

because of a flaw in its content.

We also have formal fallacies,

which all have in common
with affirming the consequent

that they have defects in
the forms of the argument

and that they are invalid.

Just to be clear, let's go
over a few more definitions.

We make conditional
statements all the time.

They're generally easy to spot

because they usually are of the form

"if P, then Q."

Here, "P" is the antecedent.

An easy way to spot antecedents

is to remember that they typically

come after the word "if,"
whether or not they're

at the beginning, middle
or end of sentences.

If you need help remembering that,

just remember that the antecedent comes

before the other logically,

and that it sounds a lot like "ancestor."

The consequent of the conditional

is the part that typically follows

after the word "then."

It should be easy to remember

because it sounds like "consequence"

and basically is just that.

So let's take the following
conditionals for examples.

Suppose someone tells you the following

true conditionals and statement:

"If the neighbors ate Susan's parrot,

"then Susan is angry,"

and "Susan is angry."

Just because it is true
that if the neighbors

had eaten the parrot, then
she would have been angry,

and it is also true that she is angry,

does not mean that she's angry

because they ate her parrot.

Perhaps she's mad because her parrot

isn't very interesting.

Or maybe she's angry that it doesn't know

how to use the toy car that she spent

all afternoon building for it.

Nevertheless, it does not
follow from the conjunction

of the true conditional
and the true consequent

that the antecedent is true.

Let's look at a few more examples:

"If Tom has a good reason to complain,

"then Tom will complain tomorrow."

Now, maybe you know Tom well,

so you know that this is true.

Maybe you even know that it's true

that he will complain tomorrow.

But it would not follow that Tom

has a good reason to complain.

Maybe he just doesn't know

any better way to get attention.

Now, let's take a look
at one more example.

Consider this conditional
and the assertion:

"If you are allergic to peanut butter,

"then it would be a bad idea

"to bathe in a tub of peanut butter,"

and "it is a bad idea to bathe

"in a tub of peanut butter;

"therefore, you are
allergic to peanut butter."

Just because it is true that it would be

a bad idea to bathe in
a tub of peanut butter

if you are allergic,

and it is also true that it is a bad idea

to bathe in a tub of
peanut butter in general,

does not mean that you are
allergic to peanut butter.

If you were to conclude this,

then you would be committing the fallacy

of affirming the consequent.

So that's the formal fallacy

of affirming the consequent,

and a few examples that you
could use in the future.