1.2: Thinking Critically

There are lots of ways that an argument can go wrong. Some of the mistakes that can logically tank an argument are repeated often enough that we give them names. Unfortunately, many of these bad arguments strike us intuitively as good arguments despite their irrationality and we often find ourselves (even those of us who know better) employing them in conversation as if they were good ways of thinking (which they are not). We call these reasoning errors fallacies and they come in quite a variety. In this section, we will introduce some of these fallacies and teach you how to spot them.

Equivocation

Arguments have to be set out in terms of language – you can’t do logic through interpretive dance. But words can be ambiguous, that is, they can have more than one meaning. This can lead to logical problems.

Definition: Equivocation

The reasoning error wherein an operative word is used in two different ways in an argument.

Consider the following argument. “Tables are furniture. There are tables in my statistics book. Therefore, there is furniture in my statistics book.” Is it a good argument? Of course not. But at first glance, it seems valid and well-grounded. If the premises are true, they seem to lead to the conclusion. And those premises are both true. So, what’s the problem? The word “table” is ambiguous. It means both a flat raised surface for placing things on and a rectangular array of numbers. The word “table” is used in two completely different ways and we changed which way we were using it in the middle of the argument. The word “table” in the first premise does not mean the same thing as the word “table” in the second premise. But for the argument to work structurally, they have to mean the same thing. Therefore, we equivocated on the word “table,” and the argument is unsound.

Ad Hominem

Arguments are made by people. Arguments can be valid or invalid, well-grounded or not well-grounded. People can be kind or mean, smart or dumb, powerful or powerless, rich or poor, cool or nerdy, objective or self-interested, well-dressed or analytic philosophers. The logical status of the argument depends solely upon the internal structure of the argument and whether the premises are true or not. The kindness, intelligence, power, wealth, coolness, objectivity, or ability to match pants and shirts have absolutely nothing to do with the structure of an argument or the truth of its premises. Arguments stand or fall on their own merits, not on whose mouth they come out of. To argue against the arguer and not the argument is what we call ad hominem.

Definition: Ad hominem

The reasoning error wherein one tries to undermine an argument by attacking the person who made the argument and not the validity or well-groundedness of the argument itself.

The phrase “ad hominem” is Latin for “to the man.” The idea being that you are not addressing your concerns with the idea, with the argument, but directly to the person. You could take a perfectly good argument and put it in the mouth of Abraham Lincoln and Adolf Hitler, Mother Teresa and Jeff Bezos, Bill Nye and Kanye West. No matter who says it, if it is a good argument it is a good argument. To focus on the arguer and not the argument is to miss the logical point and to commit a fallacious ad hominem attack.

Anytime you hear (1) name calling, (2) labelling, or (3) an appeal to the arguer’s self-interest, you are probably looking at an ad hominem attack. “Don’t listen to that moron” – ad hominem. “That’s exactly what you would think, you’re a conservative/ liberal/male/female/Christian/Muslim/Jew/atheist…” – ad hominem. “The only reason you are arguing that is that if it were true, you would benefit” – ad hominem. Ad hominem attacks can be very effective. If you can tear down the person making the argument, people think that what they have to say cannot be that valuable. But the fact that it works does not make it good reasoning.

Circular Argument

A good argument has to be valid, but not every valid argument is a good one. Consider the following argument: It is Monday, therefore it is Monday. It is certainly valid. If we assume the truth of the premise, we are led to the truth of the conclusion. But does it give us reason to believe the conclusion? No. The reason we need an argument is to provide support for an uncertain conclusion. If the premise and the conclusion say the same thing, and one is uncertain, then so is the other. This means that while the argument is valid, it is not well-grounded. You cannot support a claim simply by repeating it. No matter how many times you say it, it doesn’t make it more true. We call this a circular argument.

Definition: Circular argument

The reasoning error in which the premise contains the same information as the conclusion.

The most obvious case of the circular argument is the one above, where the premise and the conclusion are the same sentence. The trickier version is where you have two different sentences that express the same proposition in different words. Consider the argument: It is morally wrong to kill animals because you shouldn’t take the life of anything that can feel pain. The only things that can feel pain are things with a central nervous system. The only things with a central nervous system are animals. So, while the two parts of the argument seem different, they turn out to be just different ways of saying the same thing. It is a circular argument.

It could be rescued from circularity by adding content to the premise about why feeling pain gives rise to interests that are morally relevant. But doing so would be to add premises. It would add information that would make the conclusion and the premise say different things. That is what a good argument does. But in its naïve current form, it is a complex form of circular argument.

Slippery Slope Fallacy

A common reasoning error is what is called the slippery slope or domino fallacy. It involves chains of cause and effect relations. The reason this error is often called the domino fallacy is that it resembles the tipping of dominoes. Set them up on edge and knock down the first and it will tip the second which hits the third and in a row they all go down. It is a metaphor for a causal (not casual) chain, that is a chain of events which cascade from some initial happening.

There are, of course, such chains. If you forget your homework one day, it could be the difference between an A and a B. Not getting that A might be the thing that keeps you out of medical school. Getting rejected from mad school causes you to despair. The despair leads you to drink. You become an alcoholic. You drink away all of your money except for a single dollar bill. With that dollar bill, you buy a lottery ticket. It turns out to be the winner and you become a multi-millionaire all because you forgot your homework that day.

It could happen. Probably won’t. But, it could. But, it probably won’t. If you want to assert the existence of a whole chain of events like this, you have to justify each and every link in the causal chain. The slippery slope fallacy is where you simply assert that once you take the first step, you will necessarily slide all the way down the hill.

Definition: Slippery Slope Fallacy

The reasoning error wherein one asserts a chain of causally interconnected events without providing cause and effect arguments for each link in the chain.

Again, these sorts of chains of events do happen, but if you want to claim that any given situation is like this, you must provide full evidence for each and every step.

Faulty Analogy

Arguing by analogy is a perfectly fine way of arguing. If two things are like each other in relevant ways, then you can infer something about the other from the first. We reason like this in science all the time. We think of current through a wire as if it was water moving through a hose. The equations governing them are similar enough that the analogy works.

But for such an argument to work, the two things need to be alike in the relevant ways. If they are not properly analogous, then any inference you try to draw from one to the other will not be legitimate. To do so, is to commit the fallacy of faulty analogy.

Definition: Faulty Analogy

The reasoning error wherein an argument by analogy is based on two things that are not analogous.

A while back, when anti-smoking campaigns were aimed at children, they had posters in classrooms that read “kissing a smoker is like licking an ashtray.” About a decade later, the messages were about drug use and featured a television commercial of a young lady putting an egg on a counter saying, “This is your brain.” She then hit the egg with a pan, splattering it everywhere, saying, “This is your brain on drugs. Any questions?” Now, it is true that cigarettes and heroin are bad for you. (Do not smoke. Do not shoot up heroin.) But in both cases, the arguments by analogy fail because they are bad analogies. Smoking does yellow teeth and give bad breath. But kissing a smoker is not like sticking your tongue in an ashtray. Drugs do cause neurological damage, but their use does not smash the brain beyond recognition. If you want to argue by analogy, use good analogies.

Taking a Quotation Out of Context

In academic work, we often use quotations from other authors as premises in the arguments we make. It is important to refer to the work of others in order to make our points. There have been lots of smart people who have thought about the sorts of questions we are still thinking about and we need to work from their insights in order to make progress. Isaac Newton, perhaps the most important thinker in human history wrote that the reason he was able to see so far was that he thought of himself as standing on the shoulders of giants.

However, there are two ways that using someone else’s good ideas can go horribly logically wrong. The first is that we can misrepresent the meaning of their words by taking a quotation out of context. What words mean is often a matter of who is saying them, why they are saying them, to whom they are saying them, and how they are saying them. The same sentence can mean completely different things, if any of these contextual factors are changed.

Suppose Jack asks his roommate Rob whether he is going to ask out Rhonda, whom Jack knows has a thing for Rob, and Rob replies, “Yeah, sure, I’ll ask out Rhonda, when my dog writes a dissertation on Hegel.” Jack then says to Rhonda, “I ask Jack and 22 he literally said the words ‘I’ll ask out Rhonda.’ He said it. I swear.” Did he say it? Well…yes and no. Those words did leave his lips, but that was not what he was saying. Rob took the quotation out of context.

Definition: Quotation taken out of context

The reasoning error wherein someone uses as support the words of another person, but changes the meaning of those words by changing the context in which they are reported.

Quotations are important in scholarship, just make sure the words as you write them mean what the author meant.

Faulty Authority

The second way a quotation can go wrong is if the person quoted does not offer the support you need in making your argument. We quote experts because their words can be taken as likely true. But it is important when citing the work or ideas of an authority, that the person is a legitimate authority. If not, it is an example of the fallacy “faulty authority.”

Definition: aulty authority

The reasoning error in which someone uses a quotation from an authority as a premise for an argument, but the purported authority is not a legitimate authority.

Legitimate authorities have three properties. The first, and this may seem trivial, is that they actually have to exist. A real authority needs to be both real and an authority. This is the problem when people say things like, “You know, I read somewhere that…” Where? If you want me to believe this on the basis of someone’s authority, you need to tell me who the authority is. By simply saying that you read it somewhere or heard it somewhere, you are asserting that I should agree with this because the place you read or heard it is authoritative, but to justify that I need to know who the purported authority is.

The second condition for being an authority is that the person is actually an expert in this field. Your uncle Murray the dry cleaner may be an authority in stain 23 removal, but not whether homeopathic remedies are effective treatments for bacterial infections.

The final condition is that the person cited as an authority has to be objective, that is, not have a direct interest in your believing one way or another. If you go to your doctor and he prescribes an expensive medication to treat some symptoms you are having and you later learn he is receiving kick-backs from the drug company that makes it, you have every right to wonder if there was a better or less expensive alternative that was ignored because of the doctor’s personal financial interests. The doctor exists and is an expert in the relevant field, but to be fully satisfied that this is a legitimate authority, their claim has to not have effects on them personally.

Fallacy of the Mean

Contrasting arguments are the hallmark of philosophy. Smart people disagree over hard questions with smart arguments on different sides. This often flusters students. If both sides gave strong arguments, who’s to say? Students throw up their arms and declare the matter “subjective,” it must just be whatever you think it is. NO! It just means you have to think harder.

The other move students tend to take when coming across strong and opposing arguments is to try to split the difference, find a way that makes them both true, assume the truth is in between the two positions. There are certainly times when this is the case. Sometimes it is best to compromise, to split the difference. But sometimes it is not. The middle path is itself a position that requires independent argumentation. To simply assert that a view is correct because it is the mean between two extremes is to commit the fallacy of the mean.

Definition: Fallacy of the Mean

the reasoning error wherein one contends that a moderate viewpoint must be correct because it is the moderate view.

The idea of a big logical group hug is warm and fuzzy, but that is not the way the world always is. Sometimes the truth does lay in the extreme. Does it? Doesn’t it? Everything needs an argument…and not just any argument, but the strongest argument. Which argument is the strongest? THAT is what philosophy is all about.

Exercise \(\PageIndex{1}\)

Name the fallacy in the joke:

1. Why did the chicken cross the road? To get to the other side.

2. James Randolph Worthington III was waiting for the subway when a young man wearing ripped jeans and a t-shirt stands next to him on the platform. With an air of indignation, Worthington checks his watch and the young man asks, “Excuse me, sir, do you have the time?” Worthington ignores him. The young man says, “I saw you look at your watch. I don't have one. I asked politely for the time. Why can't you tell me?” Worthington turns and says, “Look, if I tell you the time, we'll have a conversation. We'll get to know each other and become friends. I'll invite you to my house for dinner. You'll meet my lovely daughter who is your age. You'll ask her out on a date and fall in love. You'll ask her to marry you, and she'll accept.” The younger man said, “…and what is wrong with that?” Worthington replied, “My daughter will not be married to a man who can't afford a watch!”

3. Son: Dad, global warming is real. The scientists all say so. Dad: You’re so stupid, you’d climb a glass wall to see what was on the other side.

4. A man walks in an optometrist and says, “Doc, I think I’m a moth.” The eye doctor, says, “What?” “I think I’m a moth.” The eye doctor says, “I’m an optometrist. You need a psychiatrist.” The man says, “I know.” “Then why did you come to see me?” The man says, “Your light was on.”

5. Frogs are green and bounce. Tennis balls are green and bounce. Your check is green. I don’t think I’ll accept it.

6. “Susan, I heard you got a cancer diagnosis. I’m so sorry.” “Well, Karen, it’s a little more complicated. I have this tumor. The first doctor said it was cancer and had to come out immediately. So, I went to get a second opinion. The next doctor said it was benign and should stay because the surgery itself is dangerous.” “So, what are you going to do? Which doctor should you listen to?” “They are both professionals, so I’m going to listen to both and have them only remove half of it.”

7. Today at the bank, on old lady asked me to check her balance. So, I pushed her over.

8. A man walks into a bar and orders a drink with a big smile on his face. The bartender asks, “Why so happy, Joe?” “Well,” the Joe says, “You know how I was worried that my wife was being unfaithful?” “Yeah, so?” the bartender asks. “Well, now I know she isn’t.” “How do, you know that, Joe?” “Well, last week, I was sick and had to stay home from work a couple days and every time she would see the mailman, she would run out waving her arms, yelling ‘My husband is home! My husband is home!’ How could someone so proud to have me around be unfaithful?”

Answer

1. Circular argument. “Crossing the road” and “getting to the other side of the road” are different ways of saying the same thing. What makes this a joke is that it asks for the goal that the chicken was trying to accomplish by crossing the road but answers with a restatement that the chicken crossed the road in different words.

2. Slippery Slope. Worthington sets out an entire chain of events that he contends will result from his giving the young man the time without justifying any of the steps.

3. Ad hominem. The father responds with an insult rather than addressing the argument made.

4. Faulty authority. The man went to see a doctor about his condition, but it was the wrong sort of doctor.

5. Faulty analogy (and equivocation). The speaker is drawing an analogy between frogs, tennis balls, and checks. This analogy clearly does not hold. (There is also an equivocation here as bouncing a tennis ball and bouncing a check are different meanings of “bounce” – either answer is acceptable since both fallacies are committed.)

6. Fallacy of the mean. Susan got medical advice to both have surgery to remove the tumor and not have surgery to remove the tumor. By seeking the middle ground, Susan does not get the best of both worlds, but will rather have both the danger of a possibly of a cancerous tumor and the danger of the surgery.

7. Equivocation. You are psychologically primed by setting the joke in a bank to interpret the word “checking one’s balance” as determining the amount of money ne has in a checking account. But the punch line changes the meaning of “checking one’s balance” to testing the ability to stay on one’s feet.

8. Taking a quotation out of context. Joe takes his wife’s words “My husband is home!” to be a statement of her adoration of him instead of a warning to the mailman that their usual activities would have to be postponed.