Critical Thinking Fundamentals: Validity

Paul Henne (Duke University) discusses the philosophical concept of validity. After reviewing the structure of an argument, he defines validity: an argument is valid if and only if its premises guarantee the conclusion. He reviews a few examples of validity and invalidity, and he leaves you with one example to figure out on your own.

(intro music)

Hello, I'm Paul Henne

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

And in this video I'm
going to discuss validity,

an important tool for
evaluating deductive arguments.

You've probably heard someone say

"that's a valid point," or

maybe in an argument you've heard a friend

say something like
"that's valid, but..."

In these everyday uses of the term

"valid" or "validity,"

people often mean to
convey something like

"that's a good point," or

"that statement's true."

But I won't be talking,

in this video at least,

about those usages.

Instead, I'll be discussing the technical

philosophical notion of validity,

as in "a valid argument."

You already know that an
argument is a set of statements,

and that one or more of these statements

is offered in support

of some other statements.

The statements doing the supporting

are called "premises,"

and the statements being supported

are called "conclusions."

Validity, in the sense
that I'm talking about it,

applies to deductive arguments.

So an argument is valid or invalid.

Validity, then, isn't a
property of statements

or anything of the like.

So, what exactly is a valid argument then?

Well, suppose that you make
the following argument,

and here I'll use "P"s
to stand for "premises"

and I'll use a "C" to
stand for the conclusion.

(P1): All humans are mortal.

(P2): Iris Murdoch is a human.

(C): Therefore, Iris Murdoch is mortal.

Suppose that I say that
your argument is valid.

Do I mean to say that
your argument is good?

Do I mean to say that your conclusion,

or that all of the premises
and the conclusion, are true?

While this might sound
like what I'm saying,

validity has nothing to do

with the truth of the conclusion

or with how good the
argument is in general.

So, let's define it.

An argument is valid if and only if

the truth of its premises

guarantees the truth of its conclusion.

That is, validity is a
property of arguments,

such that if the premises
of the arguments are true,

then the conclusion must be true.

So it's impossible for a valid argument

to have all true premises

unless the conclusion is also true.

When an argument is valid in this sense,

we say that the premises
entail the conclusion.

So, let's back up for a second.

An argument is composed of statements.

Statements can be true or false,

like the statement "this
square is orange."

Arguments cannot be true or false.

They can, however, be valid or invalid,

as well as other things.

And, if an argument is valid,

then if its premises are true,

its conclusion is true.

Notice that I have not
said that a valid argument

has true or false premises

or a true and false conclusion.

I have said something conditional.

That is, if the argument is valid,

then the truth of its conclusion

follows from the truth of its premises.

Conversely, if the truth of the premises

entails the conclusion,

then the argument is valid.

Now, this all sounds very abstract,

so let's return to some examples.

Let's look at our previous example.

I have said that the argument

about the British philosopher,
Iris Murdoch is valid.

Am I right?

Yes!

If the premises of the argument are true,

then the conclusion must
be true, in this case.

Remember, it doesn't matter

if our premises are true or false.

Consider, for example, an argument

with all false premises in it.

(P1): All humans are immortal.

Premise (2): Iris Murdoch is a human.

Conclusion: Therefore,
Iris Murdoch is immortal.

This argument is also valid,

just like the first argument.

The truth of the premises entails

the truth of the conclusion, right?

If it is the case that
all humans are immortal,

and it is the case that Iris
Murdoch is one of these humans,

then it's necessarily the case

that Iris Murdoch is immortal.

Let's try an example with premises

of which we don't know the truth.

(P1): All aliens speak English.

(P2): Splock is an alien.

Conclusion: Therefore,
Splock speaks English.

We don't know if there are aliens,

let alone ones that can speak at all.

We don't know if they speak English.

It could be the case,

or it couldn't be the case.

But this argument, nonetheless, is valid.

If premise one and two are true,

then the conclusion must be true.

We could even use undefined terms.

(P1): All sliff are splat.

(P2): Sniff is a sliff.

Conclusion: Therefore, sniff is a splat.

Again, although the truth of
the premises is undefined,

we have a valid argument.

This is just one type
of valid argument form,

and you can learn about others

in upcoming videos.

Note now what it means

for an argument to be invalid.

The truth of the argument's premises

does not entail the
truth of the conclusion.

For instance:

(P1): All dogs have fur.

(P2): Claire has a lot of fur.

Conclusion: Therefore, Claire is a dog.

Now, it could be the case

that all of the premises in this argument

are true, but the conclusion false.

The truth of this conclusion,

in other words,

does not follow from the premises, right?

Because cats also have a lot of fur.

So this is an invalid argument.

You may wonder why
validity matters at all,

if the truth of the
premises doesn't matter.

This is a good question to ask,

and it deserves a long discussion.

But the short answer is
that validity is used

to determine whether or
not an argument obeys

valid inference rules, the
laws of deductive logic.

That is, we are ensuring that
inferences in the argument

are good inferences to make.

I'll leave you with one last example,

and ask you to determine

its validity or invalidity.

(P1): All fruit is a chair.

(P2): Square is a chair.

Conclusion: Therefore, square is a fruit.

What do you think?