(intro music)

Hi, I'm Aaron Ancell.

I'm a graduate student at Duke University,

and in this video I'm going
to tell you about soundness,

an important notion
that philosophers use

to evaluate arguments.

Let's start by looking back at validity.

You should already know
what a valid argument is.

If you don't, I encourage you
to watch the video on validity

before watching the rest of this video.

As you learned in the video on validity,

an argument is valid if it is impossible

for all of the premises to be true

while its conclusion is false.

For example, the following
is a valid argument.

Premise (1): All cats are purple.

Premise (2): Everything
that is purple is a person.

Conclusion: Therefore,
all cats are people.

This argument is valid,
because it is impossible

for the premises to be true
while the conclusion is false.

If all cats were purple, and
all purple things were people,

then all cats would be people.

Of course, not all cats are purple,

and not all purple things are people.

So even though this argument is valid,

it's not really informative.

It does not establish the
truth of its conclusion,

since the premises are obviously false.

Since the goal of an
argument is usually to show

that some conclusion is true,

we usually want arguments
that are more than just valid.

This is where the notion
of soundness comes in.

Soundness is a technical
notion in philosophy.

What philosophers mean by "sound"

is a bit different than
what people ordinarily mean

when they say things like
"that was sound advice,"

or "she demonstrated sound judgement

in making that decision."

In philosophy, soundness, like validity,

applies only to deductive arguments.

In order to be sound, an argument

must meet two requirements.

First, the argument must be valid.

All invalid arguments are unsound.

Second, the premises of the
argument must all be true.

Any argument that has even
a single false premise

is unsound.

To be sound, an argument
must meet both requirements.

Let's go back to the example
with the purple cats.

Is this argument sound? Let's check.

The argument is valid, so it
meets the first requirement.

But it definitely does not
meet the second requirement,

since not all of its premises are true.

In fact, both the premises are false.

But not every unsound
argument has false premises.

Consider another example.

Premise (1): All dead parrots are dead.

Premise (2): Parrots are not frogs.

Conclusion: Therefore, frogs exist.

Both premises of this argument are true,

so this argument satisfies
the second requirement

for being a sound argument.

However, it doesn't satisfy
the first requirement,

because the argument is invalid.

The conclusion does not
follow from the premises.

So this is an unsound argument,

even though all the premises are true.

Note that the conclusion is also true.

But that doesn't matter.

It's still an unsound argument.

Here's another example.

Premise (1): Ostriches cannot fly.

Premise (2): All insects wear top hats.

Conclusion: Therefore,
ostriches are insects.

This argument fails to
meet both requirements.

It isn't valid, and the
second premise is false.

So this argument is definitely unsound.

"Now," you might ask, "why should I care

"whether an argument is sound?"

The reason is that if we know
that an argument is sound,

then we know that the
conclusion of that argument

must be true.

There is no way that an argument can meet

both requirements for soundness

and have a false conclusion.

To meet the first requirement,

an argument must be valid.

And by definition, a valid argument

is one where the
conclusion cannot be false

if the premises are true.

And to meet the second requirement,

the premises of the
argument must all be true.

Putting the requirements
for soundness together,

we can say that a sound argument

is one where the
conclusion cannot be false

if the premises are true,

and where the premises are all true.

This shows that the conclusion of
a sound argument cannot be false.

It has to be true.

Sound arguments are very useful.

They enable us to establish
that things are true.

Let's finish off by looking at an example.

Premise (1): Whales do not have fur.

Premise (2): Whales are mammals.

Conclusion: Therefore,
not all mammals have fur.

This argument is valid.

If the premises are true,

then the conclusion must also be true.

And the premises are true,
so this is a sound argument,

and the conclusion must be true.

Give it a try.

See if you can write a
sound argument of your own.