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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[br]to tell you about soundness,

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an important notion[br]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[br]what a valid argument is.

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If you don't, I encourage you[br]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[br]is a valid argument.

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Premise (1): All cats are purple.

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

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Conclusion: Therefore,[br]all cats are people.

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This argument is valid,[br]because it is impossible

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for the premises to be true[br]while the conclusion is false.

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If all cats were purple, and[br]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[br]truth of its conclusion,

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since the premises are obviously false.

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Since the goal of an[br]argument is usually to show

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that some conclusion is true,

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we usually want arguments[br]that are more than just valid.

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This is where the notion[br]of soundness comes in.

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Soundness is a technical[br]notion in philosophy.

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What philosophers mean by "sound"

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is a bit different than[br]what people ordinarily mean

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when they say things like[br]"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[br]argument must all be true.

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Any argument that has even[br]a single false premise

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is unsound.

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To be sound, an argument[br]must meet both requirements.

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Let's go back to the example[br]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[br]meets the first requirement.

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But it definitely does not[br]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[br]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[br]the second requirement

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for being a sound argument.

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However, it doesn't satisfy[br]the first requirement,

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because the argument is invalid.

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The conclusion does not[br]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,[br]ostriches are insects.

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This argument fails to[br]meet both requirements.

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It isn't valid, and the[br]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[br]that an argument is sound,

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then we know that the[br]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[br]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[br]argument must all be true.

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Putting the requirements[br]for soundness together,

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we can say that a sound argument

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is one where the[br]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[br]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[br]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,[br]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,[br]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[br]sound argument of your own.