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Fundamentals: Soundness

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Fundamentals: Soundness발음듣기

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(intro music) Hi, I'm Aaron Ancell.발음듣기

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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.발음듣기

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Let's start by looking back at validity.발음듣기

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You should already know what a valid argument is.발음듣기

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If you don't, I encourage you to watch the video on validity before watching the rest of this video.발음듣기

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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.발음듣기

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For example, the following is a valid argument.발음듣기

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Premise (1): All cats are purple.발음듣기

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

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Conclusion: Therefore, all cats are people.발음듣기

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This argument is valid, because it is impossible for the premises to be true while the conclusion is false.발음듣기

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If all cats were purple, and all purple things were people, then all cats would be people.발음듣기

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Of course, not all cats are purple, and not all purple things are people.발음듣기

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So even though this argument is valid, it's not really informative.발음듣기

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It does not establish the truth of its conclusion, since the premises are obviously false.발음듣기

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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.발음듣기

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This is where the notion of soundness comes in.발음듣기

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Soundness is a technical notion in philosophy.발음듣기

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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."발음듣기

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In philosophy, soundness, like validity, applies only to deductive arguments.발음듣기

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In order to be sound, an argument must meet two requirements.발음듣기

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First, the argument must be valid. All invalid arguments are unsound.발음듣기

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

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Any argument that has even a single false premise is unsound.발음듣기

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To be sound, an argument must meet both requirements.발음듣기

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

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Is this argument sound? Let's check.발음듣기

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

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But it definitely does not meet the second requirement, since not all of its premises are true.발음듣기

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In fact, both the premises are false.발음듣기

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But not every unsound argument has false premises. Consider another example.발음듣기

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Premise (1): All dead parrots are dead.발음듣기

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Premise (2): Parrots are not frogs.발음듣기

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Conclusion: Therefore, frogs exist. Both premises of this argument are true, so this argument satisfies the second requirement for being a sound argument.발음듣기

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However, it doesn't satisfy the first requirement, because the argument is invalid.발음듣기

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The conclusion does not follow from the premises.발음듣기

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So this is an unsound argument, even though all the premises are true.발음듣기

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Note that the conclusion is also true.발음듣기

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But that doesn't matter. It's still an unsound argument.발음듣기

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Here's another example.발음듣기

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Premise (1): Ostriches cannot fly.발음듣기

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Premise (2): All insects wear top hats.발음듣기

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Conclusion: Therefore, ostriches are insects.발음듣기

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This argument fails to meet both requirements.발음듣기

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

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So this argument is definitely unsound.발음듣기

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Now, you might ask, "why should I care "whether an argument is sound?"발음듣기

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The reason is that if we know that an argument is sound, then we know that the conclusion of that argument must be true.발음듣기

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There is no way that an argument can meet both requirements for soundness and have a false conclusion.발음듣기

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To meet the first requirement, an argument must be valid.발음듣기

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And by definition, a valid argument is one where the conclusion cannot be false if the premises are true.발음듣기

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And to meet the second requirement, the premises of the argument must all be true.발음듣기

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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.발음듣기