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(intro music)
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Hi, I'm Aaron Ancell.
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I'm a graduate student at Duke University,
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and in this video I'm going
to tell you about soundness,
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an important notion
that philosophers use
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to evaluate arguments.
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Let's start by looking back at validity.
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You should already know
what a valid argument is.
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If you don't, I encourage you
to watch the video on validity
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before watching the rest of this video.
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As you learned in the video on validity,
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an argument is valid if it is impossible
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for all of the premises to be true
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while its conclusion is false.
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For example, the following
is a valid argument.
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Premise (1): All cats are purple.
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Premise (2): Everything
that is purple is a person.
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Conclusion: Therefore,
all cats are people.
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This argument is valid,
because it is impossible
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for the premises to be true
while the conclusion is false.
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If all cats were purple, and
all purple things were people,
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then all cats would be people.
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Of course, not all cats are purple,
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and not all purple things are people.
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So even though this argument is valid,
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it's not really informative.
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It does not establish the
truth of its conclusion,
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since the premises are obviously false.
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Since the goal of an
argument is usually to show
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that some conclusion is true,
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we usually want arguments
that are more than just valid.
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This is where the notion
of soundness comes in.
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Soundness is a technical
notion in philosophy.
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What philosophers mean by "sound"
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is a bit different than
what people ordinarily mean
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when they say things like
"that was sound advice,"
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or "she demonstrated sound judgement
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in making that decision."
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In philosophy, soundness, like validity,
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applies only to deductive arguments.
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In order to be sound, an argument
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must meet two requirements.
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First, the argument must be valid.
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All invalid arguments are unsound.
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Second, the premises of the
argument must all be true.
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Any argument that has even
a single false premise
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is unsound.
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To be sound, an argument
must meet both requirements.
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Let's go back to the example
with the purple cats.
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Is this argument sound? Let's check.
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The argument is valid, so it
meets the first requirement.
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But it definitely does not
meet the second requirement,
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since not all of its premises are true.
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In fact, both the premises are false.
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But not every unsound
argument has false premises.
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Consider another example.
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Premise (1): All dead parrots are dead.
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Premise (2): Parrots are not frogs.
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Conclusion: Therefore, frogs exist.
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Both premises of this argument are true,
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so this argument satisfies
the second requirement
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for being a sound argument.
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However, it doesn't satisfy
the first requirement,
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because the argument is invalid.
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The conclusion does not
follow from the premises.
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So this is an unsound argument,
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even though all the premises are true.
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Note that the conclusion is also true.
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But that doesn't matter.
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It's still an unsound argument.
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Here's another example.
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Premise (1): Ostriches cannot fly.
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Premise (2): All insects wear top hats.
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Conclusion: Therefore,
ostriches are insects.
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This argument fails to
meet both requirements.
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It isn't valid, and the
second premise is false.
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So this argument is definitely unsound.
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"Now," you might ask, "why should I care
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"whether an argument is sound?"
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The reason is that if we know
that an argument is sound,
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then we know that the
conclusion of that argument
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must be true.
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There is no way that an argument can meet
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both requirements for soundness
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and have a false conclusion.
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To meet the first requirement,
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an argument must be valid.
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And by definition, a valid argument
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is one where the
conclusion cannot be false
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if the premises are true.
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And to meet the second requirement,
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the premises of the
argument must all be true.
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Putting the requirements
for soundness together,
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we can say that a sound argument
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is one where the
conclusion cannot be false
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if the premises are true,
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and where the premises are all true.
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This shows that the conclusion of
a sound argument cannot be false.
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It has to be true.
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Sound arguments are very useful.
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They enable us to establish
that things are true.
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Let's finish off by looking at an example.
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Premise (1): Whales do not have fur.
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Premise (2): Whales are mammals.
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Conclusion: Therefore,
not all mammals have fur.
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This argument is valid.
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If the premises are true,
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then the conclusion must also be true.
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And the premises are true,
so this is a sound argument,
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and the conclusion must be true.
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Give it a try.
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See if you can write a
sound argument of your own.