Fundamentals: Validity

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Fundamentals: Validity발음듣기

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(intro music) Hello, I'm Paul Henne and I'm a philosophy graduate student at Duke University.발음듣기

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And in this video I'm going to discuss validity, an important tool for evaluating deductive arguments.발음듣기

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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..."발음듣기

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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."발음듣기

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But I won't be talking, in this video at least, about those usages.발음듣기

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Instead, I'll be discussing the technical philosophical notion of validity, as in "a valid argument."발음듣기

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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.발음듣기

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The statements doing the supporting are called "premises," and the statements being supported are called "conclusions."발음듣기

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Validity, in the sense that I'm talking about it, applies to deductive arguments.발음듣기

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So an argument is valid or invalid.발음듣기

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Validity, then, isn't a property of statements or anything of the like.발음듣기

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So, what exactly is a valid argument then?발음듣기

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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.발음듣기

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(P1): All humans are mortal.발음듣기

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(P2): Iris Murdoch is a human.발음듣기

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(C): Therefore, Iris Murdoch is mortal.발음듣기

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Suppose that I say that your argument is valid.발음듣기

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Do I mean to say that your argument is good?발음듣기

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Do I mean to say that your conclusion, or that all of the premises and the conclusion, are true?발음듣기

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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.발음듣기

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An argument is valid if and only if the truth of its premises guarantees the truth of its conclusion.발음듣기

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That is, validity is a property of arguments, such that if the premises of the arguments are true, then the conclusion must be true.발음듣기

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So it's impossible for a valid argument to have all true premises unless the conclusion is also true.발음듣기

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When an argument is valid in this sense, we say that the premises entail the conclusion.발음듣기

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So, let's back up for a second.발음듣기

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An argument is composed of statements.발음듣기

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Statements can be true or false, like the statement "this square is orange."발음듣기

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Arguments cannot be true or false.발음듣기

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They can, however, be valid or invalid, as well as other things.발음듣기

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And, if an argument is valid, then if its premises are true, its conclusion is true.발음듣기

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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.발음듣기

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That is, if the argument is valid, then the truth of its conclusion follows from the truth of its premises.발음듣기

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Conversely, if the truth of the premises entails the conclusion, then the argument is valid.발음듣기

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Now, this all sounds very abstract, so let's return to some examples.발음듣기

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Let's look at our previous example.발음듣기

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I have said that the argument about the British philosopher, Iris Murdoch is valid. Am I right? Yes!발음듣기

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If the premises of the argument are true, then the conclusion must be true, in this case.발음듣기

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Remember, it doesn't matter if our premises are true or false.발음듣기

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Consider, for example, an argument with all false premises in it.발음듣기

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(P1): All humans are immortal.발음듣기

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Premise (2): Iris Murdoch is a human.발음듣기

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Conclusion: Therefore, Iris Murdoch is immortal.발음듣기

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This argument is also valid, just like the first argument.발음듣기

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The truth of the premises entails the truth of the conclusion, right?발음듣기

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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.발음듣기

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Let's try an example with premises of which we don't know the truth.발음듣기

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(P1): All aliens speak English.발음듣기

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(P2): Splock is an alien.발음듣기

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Conclusion: Therefore, Splock speaks English.발음듣기

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We don't know if there are aliens, let alone ones that can speak at all.발음듣기

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We don't know if they speak English.발음듣기

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It could be the case, or it couldn't be the case.발음듣기

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But this argument, nonetheless, is valid.발음듣기

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If premise one and two are true, then the conclusion must be true.발음듣기

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We could even use undefined terms.발음듣기

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(P1): All sliff are splat.발음듣기

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(P2): Sniff is a sliff.발음듣기

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Conclusion: Therefore, sniff is a splat.발음듣기

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Again, although the truth of the premises is undefined, we have a valid argument.발음듣기

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This is just one type of valid argument form, and you can learn about others in upcoming videos.발음듣기

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Note now what it means for an argument to be invalid.발음듣기

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The truth of the argument's premises does not entail the truth of the conclusion.발음듣기

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For instance:(P1): All dogs have fur.발음듣기

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(P2): Claire has a lot of fur.발음듣기

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Conclusion: Therefore, Claire is a dog.발음듣기

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Now, it could be the case that all of the premises in this argument are true, but the conclusion false.발음듣기

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The truth of this conclusion, in other words, does not follow from the premises, right?발음듣기

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Because cats also have a lot of fur.발음듣기

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So this is an invalid argument.발음듣기

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You may wonder why validity matters at all, if the truth of the premises doesn't matter.발음듣기

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This is a good question to ask, and it deserves a long discussion.발음듣기

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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.발음듣기

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That is, we are ensuring that inferences in the argument are good inferences to make.발음듣기

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I'll leave you with one last example, and ask you to determine its validity or invalidity.발음듣기

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(P1): All fruit is a chair.발음듣기

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(P2): Square is a chair.발음듣기

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Conclusion: Therefore, square is a fruit. What do you think?발음듣기

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