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(intro music) Hello, I'm Paul Henne and I'm a philosophy graduate student at Duke University. And in this video I'm going to discuss validity, an important tool for evaluating deductive arguments. You've probably heard someone say "that's a valid point," or maybe in an argument you've heard a friend say something like "that's valid, but..." In these everyday uses of the term "valid" or "validity," people often mean to convey something like "that's a good point," or "that statement's true." But I won't be talking, in this video at least, about those usages. Instead, I'll be discussing the technical philosophical notion of validity, as in "a valid argument." You already know that an argument is a set of statements, and that one or more of these statements is offered in support of some other statements. The statements doing the supporting are called "premises," and the statements being supported are called "conclusions." Validity, in the sense that I'm talking about it, applies to deductive arguments. So an argument is valid or invalid. Validity, then, isn't a property of statements or anything of the like. So, what exactly is a valid argument then? Well, suppose that you make the following argument, and here I'll use "P"s to stand for "premises" and I'll use a "C" to stand for the conclusion. (P1): All humans are mortal. (P2): Iris Murdoch is a human. (C): Therefore, Iris Murdoch is mortal. Suppose that I say that your argument is valid. Do I mean to say that your argument is good? Do I mean to say that your conclusion, or that all of the premises and the conclusion, are true? While this might sound like what I'm saying, validity has nothing to do with the truth of the conclusion or with how good the argument is in general. So, let's define it. An argument is valid if and only if the truth of its premises guarantees the truth of its conclusion. That is, validity is a property of arguments, such that if the premises of the arguments are true, then the conclusion must be true. So it's impossible for a valid argument to have all true premises unless the conclusion is also true. When an argument is valid in this sense, we say that the premises entail the conclusion. So, let's back up for a second. An argument is composed of statements. Statements can be true or false, like the statement "this square is orange." Arguments cannot be true or false. They can, however, be valid or invalid, as well as other things. And, if an argument is valid, then if its premises are true, its conclusion is true. Notice that I have not said that a valid argument has true or false premises or a true and false conclusion. I have said something conditional. That is, if the argument is valid, then the truth of its conclusion follows from the truth of its premises. Conversely, if the truth of the premises entails the conclusion, then the argument is valid. Now, this all sounds very abstract, so let's return to some examples. Let's look at our previous example. I have said that the argument about the British philosopher, Iris Murdoch is valid. Am I right? Yes! If the premises of the argument are true, then the conclusion must be true, in this case. Remember, it doesn't matter if our premises are true or false. Consider, for example, an argument with all false premises in it. (P1): All humans are immortal. Premise (2): Iris Murdoch is a human. Conclusion: Therefore, Iris Murdoch is immortal. This argument is also valid, just like the first argument. The truth of the premises entails the truth of the conclusion, right? If it is the case that all humans are immortal, and it is the case that Iris Murdoch is one of these humans, then it's necessarily the case that Iris Murdoch is immortal. Let's try an example with premises of which we don't know the truth. (P1): All aliens speak English. (P2): Splock is an alien. Conclusion: Therefore, Splock speaks English. We don't know if there are aliens, let alone ones that can speak at all. We don't know if they speak English. It could be the case, or it couldn't be the case. But this argument, nonetheless, is valid. If premise one and two are true, then the conclusion must be true. We could even use undefined terms. (P1): All sliff are splat. (P2): Sniff is a sliff. Conclusion: Therefore, sniff is a splat. Again, although the truth of the premises is undefined, we have a valid argument. This is just one type of valid argument form, and you can learn about others in upcoming videos. Note now what it means for an argument to be invalid. The truth of the argument's premises does not entail the truth of the conclusion. For instance: (P1): All dogs have fur. (P2): Claire has a lot of fur. Conclusion: Therefore, Claire is a dog. Now, it could be the case that all of the premises in this argument are true, but the conclusion false. The truth of this conclusion, in other words, does not follow from the premises, right? Because cats also have a lot of fur. So this is an invalid argument. You may wonder why validity matters at all, if the truth of the premises doesn't matter. This is a good question to ask, and it deserves a long discussion. But the short answer is that validity is used to determine whether or not an argument obeys valid inference rules, the laws of deductive logic. That is, we are ensuring that inferences in the argument are good inferences to make. I'll leave you with one last example, and ask you to determine its validity or invalidity. (P1): All fruit is a chair. (P2): Square is a chair. Conclusion: Therefore, square is a fruit. What do you think? Subtitles by the Amara.org community