(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.