Dave: Welcome back to Rationally Minded Podcast. Irrational or poor patterns of reasoning are called fallacies. Each week, we invite an EFL educator and expert critical thinker to discuss different kinds of fallacies that come up in our everyday lives. We also discuss how you can learn to recognize fallacies and respond to other people’s fallacious statements and arguments with common and useful English expressions. I’m David Gann and this is Rationally Minded Podcast.
Today we’re pleased to have with us, Vanessa Armand a lecturer at Tokyo International University. She’s been active in doing research in critical thinking skills for several years. Good afternoon, Vanessa.
Vanessa: Good afternoon.
Dave: In our previous episode we discussed basic non-sequiturs. So today Vanessa you’ve come to tell us today about a more advanced kind on non-sequitur. What is it?
Vanessa: I’m going to talk about. The first is called affirming the consequent and the second is called denying the antecedent. They’re really two sides of the same fallacious coin.
Dave: So how are they different from basic non-sequiturs?
Vanessa: Well, I think that basic non-sequiturs like you featured in your earlier episode are a kind of rhetorical trick, and are often purposely dishonest. As your guest said, it’s a way of avoiding answering the question. But the non-sequiturs I’m discussing today are usually honest mistakes that any of us could make. And like arguments that appear in the form of syllogisms, these arguments also appear in the format of a first reason, a second reason and a conclusion.
Dave: Sure, and in our other podcast, Critically Minded, Nicholas Bufton and I discuss syllogisms. Could you give us an example of a flawed or incoherent syllogism that affirms the consequent? And first, what is a consequent? And what does “affirm” mean?
Vanessa: A consequent is the second half of a conditional statement.
Dave: The second half. Wait, before we go on maybe we should hear about the first half.
Vanessa: Sure. The first half is called the antecedent. A conditional statement is a statement that says when one thing is true, then another thing is also true. Or, if one thing happens, then another thing will also happen.
Dave: Like, for example, If I dance, then people will laugh at me.
Vanessa: Sure, if you say so. So what you’re saying then is that your dancing will be the cause of people laughing.
Dave: Exactly, it’s a real problem I have. I dance and then, as result, people laugh.
Vanessa: Well, I can’t help you with that, but that’s a good example. So the sentence, “If I dance, then people will laugh at me,” is a conditional statement. The condition of your dancing produces a result, people laughing. The clause, “If I dance” is the antecedent. And the clause, “people laugh,” is the consequent. People laugh as a result, or as the consequence, of your dancing.
Dave: Yeah, I don’t dance very often because of that.
Vanessa: I can understand why. Now, to affirm, or affirmation, means to say that something is true. So, the second premise in the argument, affirms, or, tells us that the consequent in the first premise is true.
Dave: Okay, well I wasn’t really making an argument there, but …
Vanessa: I see. Yeah, that’s a good point too. A conditional statement, by itself, isn’t an argument. It’s just a statement.
Dave: Right. To become an argument, the conditional statement must then be followed by at least one more statement, that is a premise, or a reason, and lastly, a conclusion.
Vanessa: Exactly. When the conditional statement is part of an argument, we treat it as a premise. Why don’t we look at an argument that includes a conditional statement:
Dave: Alright listeners. Let’s hear the first argument.
If there is helium in this balloon, it will rise in the air.
There is helium in this balloon.
Therefore, it will rise in the air.
Vanessa: Okay, so no problem there. That’s a good argument. But if we change the argument slightly, it can look almost the same, but become a non-sequitur. Listen again carefully:
If there is helium in this balloon, it will rise in the air.
It is rising in the air.
Therefore, there is helium in this balloon.
Dave: Think about that listeners? Can you tell me what’s wrong with that? Let’s listen to the two arguments again, one after the other. Here’s the first one.
If there is helium in this balloon, it will rise in the air.
There is helium in this balloon.
Therefore, it will rise in the air.
Dave: And the second one:
If there is helium in this balloon, it will rise in the air.
It is rising in the air.
Therefore, there is helium in this balloon.
Dave: Listeners, could you notice the difference?
Vanessa: First, look at the first correctly structured argument and look at its first statement. You’ll see it has two parts, one about helium in the balloon and the other about the balloon rising in the air. We call the first part the antecedent, and the second part, the consequent. Next, notice that the second premise refers to the antecedent, “If there is helium” and the conclusion refers to the consequent, “It will rise.”
Dave: But the second argument is quite different. Let’s listen to it again.
If there is helium in this balloon, it will rise in the air.
It is rising in the air.
Therefore, there is helium in this balloon.
Vanessa: So, what listeners should notice here is that although the first statement has not changed, the second premise, which has changed, now reads, “It is rising in the air,” and refers to and affirms the consequent.
Dave: And this was the opposite of what we saw in the first example. So, what’s the problem with that?
Vanessa: Well, the second statement only says that the consequent is true. It’s a mistake to believe that this means the antecedent is also true. On the surface, this looks like a real syllogism and an organized argument. But there isn’t really any real argumentation. The second premise simply repeats the consequent of the first premise and conclusion then says that the antecedent is therefore true. And that just doesn’t work. You can’t do that.
Dave: And think about it. Helium is not the only gas lighter than air. Other gases would also cause the balloon to rise. It might also be that there is just hot air in the balloon in a very cold room, or perhaps the balloon is outside and a wind current is pushing the balloon upwards into the air. We’ve all seen this.
Vanessa: And these other possibilities you’re mentioning show that affirming the consequent doesn’t work.
Dave: Alright, so much for affirming the consequent.
Vanessa: Yes, moving into the second kind of non-sequitur, we have denying the antecedent. To keep things simple, we’ll use the balloon example again.
If there is helium in this balloon, it will rise in the air.
There isn’t helium in the balloon.
Therefore, it will not rise in the air.
Vanessa: This is called denying the antecedent. Denying means to say something is not true and, remember, an antecedent is the part of the conditional statement that comes before or comes first. So, in a conditional statement, the antecedent is the “If x, then” or “When x happens, then,” part of the statement. The second premise in this argument, that the balloon doesn’t have helium in it, is the antecedent in the first premise. It says that the antecedent is not true—or that the conditions of the antecedent have not been met. Let’s hear it again.
If there is helium in this balloon, it will rise in the air.
There isn’t helium in the balloon.
Therefore, it will not rise in the air.
Dave: So, the second premise says that the condition described in the antecedent, the balloon containing helium, is not met. And the conclusion is then made that because the condition of the antecedent is not met, that the consequent is not true and the balloon will not rise.
Vanessa: But once again, you can’t do this. And you can understand why it doesn’t work, if you consider the possibilities, which we already discussed. Again, another gas like hydrogen would also cause the balloon the rise. And as we said before, it might also be that there is just hot air in the balloon in a very cold room, or perhaps the balloon is outside and a wind current is pushing it into the air. Because the conclusion does not follow from the reasons, this leaves the argument open to a thousand holes. And even if we don’t have the scientific knowledge to point out these flaws, we can still see the argument’s flaws, just by looking at the flawed structure.
Dave: Even if the argument were written in another language. Moreover, noticing the flawed structure can alert us to the fact that there are other possibilities that we haven’t considered.
Vanessa: Let’s look at different kinds of arguments that we are likely to see or hear in political discussions:
One sign of a good moral country’s strength is using diplomacy to settle disputes before going to war.
That country is not good and moral.
Therefore, that country will not use diplomacy first, before going to war.
Dave: And this is a fallacy of denying the antecedent because . . .
Vanessa: Well, because the second statement “That country is not good and moral” denies the antecedent “one sign of a good and moral country” in the first statement. It then tries to conclude that the country will be quick to go to war. But clearly there are other reasons, besides being good and moral, for a country to try diplomacy first. War is expensive and usually damaging to both sides in a conflict. Does that make sense?
Dave: Yeah, and I think we ought to look at the conditional statement in this argument again. Listen again:
One sign of a good and moral country’s strength is using diplomacy to settle disputes before going to war.
Dave: One sign of a good and moral country’s strength is using diplomacy to settle disputes before going to war.
Our listeners may have noticed that there is no If x, then y wording here.
Vanessa: Yes, that’s not a main point—
Dave: No, it isn’t a main point, but–
Vanessa: But it is something we should mention. Think of it this way then. When we say one thing is a sign of another thing, it’s really the same as saying, If one thing, then another thing. So, we could reword the statement as:
If a country is good and moral, then it uses diplomacy before war.
The cause and effect relationship is more clear with this kind of wording. But you’re quite right. We do have to be prepared for the variety of vocabulary and structures that are often used to express these common thoughts.
Dave: Yes, and that was one of those points, and I’m sorry to get hung up here on these language points, but they are important and before we move on, there’s one more important thing about the wording that we really must make clear to our listeners.
Vanessa: What’s that?
Dave: We’ve described the antecedent as what comes first and the consequent as what comes second. But I think our listeners may mistake the order that the parts are spoken for the logical order, and what we mean is the logical order of the argument and not the order in which the statement is said. Listen to a simple example. I could say, “There’s no food in my house, so I’m going to the supermarket,” . . . or . . . “I’m going to the supermarket, because there’s no food in my house.” In either case, going shopping is a result of there being no food.
Vanessa: Yes, I see what you’re getting at. It’s the order of the cause and effect that is important, not the order in which you say the words. And in the case of conditional statements, the same idea applies. What changed was the order or parts in first conditional statement. The meaning didn’t change. And the cause and effect relationship between the items in the first clause and the items in the second clause didn’t change. But, if you think that the antecedent is always spoken first and the consequent is always spoken last, then you’ll be mistaken nearly half the time.
Dave: Exactly. The spoken form may change but the cause and effect order of the logic never changes, and that’s what’s important. So, we can say:
One sign of a good and moral country’s strength . . . is trying to use diplomacy before military force.
Or
Trying to use diplomacy before military force is a sign of a good and moral country’s strength.
Vanessa: Likewise, we can say:
If a strong country is good and moral, then it will use diplomacy before war.
Or
A strong country will use diplomacy, if it is good and moral.
And you can follow any of these four expressions of the same idea, with the second premise, “That strong country is not good and moral,” and the conclusion, “Therefore, that country will not use diplomacy.” And if you test the argument four times, you’ll get the same four results. The logic is flawed and the argument does not work.
Dave: Right. Well . . . It’s time for . . . Name That Fallacy! In this part of the show we present you, our listeners, with dialogues, and challenge you to match each example dialogue to the correct fallacy. Lastly, we tell you how to respond to fallacies, using some easy English expressions. Are you ready Vanessa?
Vanessa: I think so!
Dave: Alright then. Here’s the first dialogue.
[A teacher is explaining the cold, hard, facts of life, to a failing student.]
Student: Mr. Thomas, on the first day of class, you said “If you plagiarize, you will fail the class.” I didn’t plagiarize, but I still failed the class! Why?
Teacher: Just because you didn’t plagiarize doesn’t mean you would automatically pass the class! You didn’t do most of the work for the class, so you failed. You assumed that if you didn’t plagiarize, you would definitely not fail. In other words, you thought you only had to not plagiarize in order to pass. Not plagiarizing was only one requirement for passing. I suppose you think you should get some kind of reward for not shoplifting and not sitting in the priority seats on the train too.
Dave: So what kind fallacy is this?
Vanessa: This one would be denying the antecedent.
Dave: That is right, denying the antecedent. And Vanessa, how could someone respond to someone who made this error?
Vanessa: Well, you could say, “You can’t assume that since the first thing didn’t happen that the second thing will also not happen.”
Dave: You can’t assume that “since the first thing didn’t happen that the second thing will also not happen.”
[A politician is criticizing this country’s educational system.]
Politician: … and this situation has become so bad that we can no longer afford these customized programs designed specifically for one area or another. We need to start demanding educational programs that deliver reliable measurable outcomes, outcomes that will show improvement across our glorious state! Am I right, people? Am I right? I know I’m right. It’s like developing a medicine to cure a debilitating disease or a vaccine to prevent that disease. You don’t throw millions of dollars at a medicine or vaccine that’ll only help the people living over there in Poplar Bluff or Antry. No, you don’t. And that’s because a treatment, if it is effective, will be effective in every city and every town and in every school district from Hannibal to Eureka Springs. If you ask me, this is the way we should be looking at our school system. People, I’m here to tell you that from north to south and east to west, education in this state is sick and we are badly in need of a cure.
Dave: Vanessa?
Vanessa: This seems to be a false analogy.
Dave: You got it. And what would you say to a person making a false analogy?
Vanessa: I’d say “First you’re comparing two things that are really nothing alike. You can’t compare the two things, because there are more differences than similarities.”
Dave: I’d have to agree. Well, you’re doing very good. Let’s go on now to the third and final dialog.
[At an Employee of the Month Party, the company owner Erika has announced she is paying for her employee’s meals]
Simons: I guess we had better figure out how to divide this bill. Let’s see, there are eleven of us.
Erika: Oh, don’t worry about that. I’ve already paid the bill.
Simons: Well, thank you Erika, that’s very generous of you. You’re the best boss ever!
Erika: And you’re a great employee, Craig. That’s why you’re employee of the month.
Simons: I’m just doing my job, like everyone here.
Travis: Say, Erika, a few weeks ago, after we got that big contract, you said you felt so lucky that you were planning to buy a suitcase of lottery tickets after work. And a few days ago you said that if you won the lottery that you would pay for our dinner and drinks this week. And you’ve just paid for our dinner and drinks. So I guess that can mean only one thing. You won the Lottery! Congratulations!
Erika: Well I do appreciate your congratulating me, but my recent remark about the lottery was just a turn of speech. I seriously hope you don’t think I’m stupid enough to waste my hard earned salary like that.
Travis: Oh, woah, no—I’m sorry I didn’t mean …
Erika: You didn’t mean what?
Joel: No Erika, you’ve got it all wrong. Travis didn’t mean anythi—
Simons: Travis’s a big boy, Joel. Let him speak for himself. He knows what he said.
Travis: You said you were planning to buy lottery tickets after work—
Erika: What are you saying now?
Simons: Insulting Erika like that? That’s no good. And with the poor reasoning skills you just demonstrated, it’s easy to understand why you have never been Employee of the Month.
Vanessa: Hmmm. Okay, what we have here is a case of affirming the consequent. The second premise, “You’ve just paid for our dinner,” refers to the consequent “You’ll know I’ll have won the lottery.” It may be true that winning the lottery could be a reason to pay for someone else’s meal, according to what we’re told Erika said last week. But that doesn’t mean that if she wins the lottery that she will definitely pay for everyone’s dinner and drinks. She could easily win the lottery, keep it a secret, and not pay the bill for everyone. And in fact, as she says, she doesn’t play the lottery. Nevertheless, she is paying for the dinner and drinks. So, clearly, affirming the consequent is not a very good way of reaching the truth of the matter. And the poor man who congratulated her has really put his foot in his mouth. I’m not sure I’d enjoy working for his boss though. She seems a little sharp-tongued.
Dave: So, what would you say here?
Vanessa: Let me see, um, just because the second thing happened doesn’t automatically mean that the first thing did.
Dave: “Just because the second thing happened doesn’t automatically mean that the first thing did”. Yes, I think that sounds like a very good response. Well, it’s been a bit of a long episode, so I think we’d better wrap it up here. Vanessa, thanks for helping us sort out these different points. And, listeners, there you have it. Affirming the Consequent and Denying the Antecedent. Thanks so much, Vanessa Armand, for speaking with us today.
Vanessa: You’re welcome, Dave. Thanks for having me on the podcast.
Dave: So, listeners, watch your step, and don’t FALL for any FALLacies. And until, next time this has been Rationally Minded.