If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Fundamentals: Soundness

Aaron Ancell discusses the philosophical concept of soundness. After reviewing validity, he defines soundness: an argument is sound when it is valid and has all true premises. He reviews a few examples of sound and unsound arguments, and he encourages you to develop sound arguments on your own.

Speaker: Aaron Ancell, Duke University.

Video transcript

(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. Subtitles by the Amara.org community