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(intro music)

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Hello, I'm Matthew Harris,

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

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And today, I'll be discussing
the formal fallacy

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of affirming the consequent,

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and why you sometimes cannot conclude

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that you should bathe
in a tub of peanut butter.

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Affirming the consequent occurs

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when someone tries to infer the truth

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of the antecedent of a
conditional statement

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from the truth of the
conditional and its consequent.

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

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There are two kinds of logical fallacies:

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formal and informal.

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Both kinds are defective
argumentative patterns.

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First, we have informal fallacies,

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which lack support for the conclusion

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because of a flaw in its content.

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We also have formal fallacies,

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which all have in common
with affirming the consequent

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that they have defects in
the forms of the argument

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and that they are invalid.

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

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We make conditional
statements all the time.

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They're generally easy to spot

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because they usually are of the form

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"if P, then Q."

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Here, "P" is the antecedent.

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An easy way to spot antecedents

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is to remember that they typically

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

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at the beginning, middle
or end of sentences.

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If you need help remembering that,

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just remember that the antecedent comes

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before the other logically,

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and that it sounds a lot like "ancestor."

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The consequent of the conditional

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is the part that typically follows

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after the word "then."

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It should be easy to remember

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because it sounds like "consequence"

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and basically is just that.

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So let's take the following
conditionals for examples.

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Suppose someone tells you the following

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true conditionals and statement:

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"If the neighbors ate Susan's parrot,

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"then Susan is angry,"

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and "Susan is angry."

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Just because it is true
that if the neighbors

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

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and it is also true that she is angry,

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does not mean that she's angry

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because they ate her parrot.

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Perhaps she's mad because her parrot

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isn't very interesting.

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

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how to use the toy car that she spent

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all afternoon building for it.

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Nevertheless, it does not
follow from the conjunction

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of the true conditional
and the true consequent

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that the antecedent is true.

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Let's look at a few more examples:

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"If Tom has a good reason to complain,

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"then Tom will complain tomorrow."

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Now, maybe you know Tom well,

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so you know that this is true.

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Maybe you even know that it's true

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that he will complain tomorrow.

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But it would not follow that Tom

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has a good reason to complain.

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Maybe he just doesn't know

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any better way to get attention.

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

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Consider this conditional
and the assertion:

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"If you are allergic to peanut butter,

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"then it would be a bad idea

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"to bathe in a tub of peanut butter,"

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and "it is a bad idea to bathe

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"in a tub of peanut butter;

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"therefore, you are
allergic to peanut butter."

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Just because it is true that it would be

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a bad idea to bathe in
a tub of peanut butter

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if you are allergic,

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and it is also true that it is a bad idea

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to bathe in a tub of
peanut butter in general,

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does not mean that you are
allergic to peanut butter.

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If you were to conclude this,

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then you would be committing the fallacy

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of affirming the consequent.

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So that's the formal fallacy

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of affirming the consequent,

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