This seventh episode of Critically Minded, is about validity and soundness. Nick and Dave discuss how to evaluate arguments in terms of these two terms.
SCRIPT:Dave: Welcome back to Critically Minded in the Language Lab podcast. We’re your hosts David–
Nick: And Nick.
Dave: We’re back again after last week’s episode on hypothetical premises and arguments.
Nick: We’ll talk more about premises in future episodes but in this episode we’re taking a BIG step forward.
Dave: Yes, we sure are. You listeners may have noticed that we haven’t introduced any new vocabulary for several weeks—
Nick: We did introduce the word “hypothetical” last week.
Dave: Okay, one word. Just one.
Nick: And I’m sure that has made our listeners very happy.
Dave: Yes, well that may be. But today we are going to learn some new words.
Nick: Let’s have them.
Dave: All right listeners, please repeat after me: sound, unsound, valid, invalid, logical, illogical.
Nick: That’s not so bad. Really, just three new words. Let’s look at the word “sound” first. In the context of logic, an argument is sound if the premises are true and the premises lead to a valid conclusion. The argument must be both true and logical. We’ll look at several examples. Let’s look at the word “valid” now. In everyday speech the word valid means one of the following: sound, reasonable, justifiable, logical or credible. We hear people say, “He has a valid point.” Or “He has a valid opinion.” However, in philosophy and formal logic, the word valid means that it follows a set pattern.
Dave: An argument can be valid even if the premises and the conclusion are false.
Nick: That’s right. In terms of validity an argument is its own little world. Let’s have a look at an example: All animals can fly. Humans are animals. I am a human. Therefore I can fly.
Dave: The skydiver who made this argument would have a very short sky diving career, but his reasoning, according to formal logic, would be valid.
Nick: Unfortunately for him, his argument is not sound. It’s unsound.
Dave: Imagine how surprised he’d be when he found out.
Nick: Why is the argument valid? It’s valid because IF . . . IF all animals could fly, then certainly humans, being a member of the animal kingdom, could also fly. And therefore I, being human, could fly. So, even though the second and third premises, both minor premises are true, the first premise, that is the major premise is false.
Dave: Let’s try changing the argument a bit so that the premises are all true but the reasoning is invalid. How about: SOME animals can fly. Humans are animals. I am a human. Therefore I can safely skydive with no parachute.
Nick: The result is the same. A dead skydiver. Although the premises are true, there are now two groups in the argument: the group of some animals that can fly and the group of humans. These two groups do not intersect. They have no members in common, unless you count superman and he is not a real person, so the argument is invalid.
Dave: The word “invalid” can also be pronounced “invalid,” meaning a person who is too ill or has been too badly injured to work.
Nick: Just as this argument doesn’t work.
Dave: If you trust your life, health and safety to invalid arguments, so that you jump out of airplanes with no parachute you’ll probably become an invalid—or dead.
Nick: If you survive, you’ll probably never work again. So we’ve looked at two arguments, the first valid, the second invalid and both unsound.
Dave: In both the first and the second example the argument is said to be unsound, in the first case because of a false major premise and in the second case because of invalid reasoning.
Nick: Shall we have a look at another invalid argument?
Dave: Sure . . . how about this one: All guitars are musical instruments. All pianos are musical instruments. Thus, all guitars are pianos.
Nick: Well that’s not right.
Dave: No, it isn’t. The two premises are true, but the person making this argument has made a mistake in reasoning.
Nick: I’d say so.
Dave: Yup, and as any traveling musician will tell you, carrying a guitar is much easier than carrying a piano!
Nick: We’ll have an episode later about what exactly is the logical error, but for now it’s enough for our listeners to simply recognize that this argument though based on true premises is invalid.
Dave: If this argument were a person it’d be an invalid. Nick, I think we can mention that again this argument contains one group, musical instruments, but makes an error when it assumes that all members of a group are identical and equal to each other in every way.
Nick: Yup. That’s called the fallacy of generalization and it is such a common fallacy—or mistake—and such an important mistake that in a few weeks we’re going talk A LOT, just about that.
Dave: You know there’s one other kind of unsound argument that we haven’t looked at yet.
Nick: What’s that David?
Dave: Well, we just looked at an argument about musical instruments where the first and second premises are true but the conclusion is false. But you know it is also possible to have an argument that has false premises and yet still arrives at a true conclusion. For example listen to this one: All white houses are large. The Whitehouse is white. Therefore, the Whitehouse is large.
Nick: That’s a pretty bad argument, David.
Dave: Can you tell our listeners why it’s a bad argument.
Nick: Premise one is clearly false. We have all seen white houses that were not large and most of us have probably seen some very small white houses. It is true that the Whitehouse in Washington D.C. is both large and white. But it’s not large because it’s white. There’s no connection at all between its color and size.
Dave: So again, as with the first arguments about flying animals and humans, we had another argument with two separate groups, white houses and large houses and a fallacy of generalization that led this time to a true conclusion.
Nick: The dangerous thing about a fallacy of generalization is that it can lead to a true conclusion. You might think that since the pattern of reasoning seemed to work for one argument that it will work for other arguments as well. You could trust it for an argument that involved a high risk or even dangerous situation and then find out too late that you had been done in by your own unsound argument.
Dave: You’d be kicking yourself, wouldn’t you?
Nick: Not if you were dead.
Dave: Well, we’ll talk a lot about that in a few weeks but for now, don’t you think that that should be enough for this time? Shall we go on to the quiz?
Nick: Our quiz question last week was: Other than the word “If,” what other word might a hypothetical premise begin with? (a) Because; (b) Supposing; (c) Then. And the answer was?
Dave: “Supposing.” A premise would never begin with the word “then.” Then can appear in the middle of a hypothetical premise. The word “because” may come at the beginning of a premise, but not a hypothetical premise. The word “supposing” is often used in the same or a similar sense as the word “If.” For example, “Nick, supposing you win the lottery. Would you then give me half of the money?”
Nick: No. Actually David you could say, supposing, if, or when, but I ain’t gonna give you half the money. If I win the lottery I won’t even be here for next week’s podcast.
Dave: Well fine, then. Here’s the quiz for next week: Nick is a host of Critically Minded. My name is Nick. Therefore I am a host of Critically Minded.
Nick: That sounds like identity theft.
Dave: It sounds unsound. The question is, why is that argument unsound?
Nick: Think about it and so until next time–
Dave: You have been listening to–
Nick: Critically Minded (Critical Thinking for 2nd Language Learners).