1. 3. Logical Fallacies

As you recall, logic is interested in the evaluation of arguments. Usually, in order to do this rigorously, we translate natural language sentences into formal notation, and then use formal tools to evaluate the argument. However, this might seem a bit removed from everyday life. In this section, we’ll discuss a phenomenon that is all too readily apparent in everyday forms of persuasion – logical fallacies. Fallacies are bad patterns of reasoning, and we’ll learn to identify various kinds of logical fallacies. By understanding these forms of bad reasoning, and what’s wrong with them, it will make it easier to deal with such arguments when you encounter them in the study of logic, or in ordinary discourse.

So, we’ll be going through a number of these examples and explaining when they apply. The names of the fallacies do suggest what is wrong with the arguments that they apply to, but you’ll still have to do a fair amount of memorization to be able to identify which fallacies apply to which situations.

(1) Appeal to Authority

First, let’s look at an obvious example of a fallacy, just to get started. Imagine a child is trying to prove to his friend that he is the smartest kid in the class. His argument is: “I’m the smartest kid in the class. My dad says so.” Is this is a good argument? Unless his dad is Albert Einstein, it’s probably not a good argument. Just because your dad says something, doesn’t necessarily make it true. So, this is an example of poor reasoning – the premise doesn’t really provide good support for the conclusion. Let’s look at another common example:

(20) Milk is bad for you. I heard someone say that on the internet.

Again, this is not a very good argument. The person is appealing to some random person that they heard on the internet, and this doesn’t provide very strong support for the conclusion. Notice, however, that there is something similar about both of these rather weak arguments. They both involve trying to appeal to some alleged authority as a way of justifying their claims. And, in both cases, the resulting argument is rather weak. So, we will call this an example of a fallacy – specifically, the fallacy known as “appeal to authority.” Oftentimes, we will be able to identify these kinds of patterns of bad reasoning – reasoning that is repeatedly misapplied in a number of different circumstances. So, as logicians, as critics of arguments, we want to be able to give names to these patterns of bad reasoning.

Appeal to authority is an argument that says that the conclusion must be true because somebody else says that it is true. “Milk is bad for you. I heard someone say that on the internet.” This is a fallacy because the mere fact that someone says something on the internet obviously does not make it true.

Now, occasionally, it can be a good thing to appeal to an authority. If the authority is an expert, like a medical doctor, then it might be sensible to listen to their opinion. But when the supposed authority being appealed to is not really knowledgeable about the subject matter, then it becomes a fallacy, which we call appeal to authority, or appeal to ignorant authority.

(2) Appeal to Force

In Appeal to Force, the arguer attempts to win the argument by attacking or threatening their opponent. For example:

(21) I should be the leader of this group. If anyone disagrees with me, I’ll break their legs!

Now, although this might be a pretty good way to win an argument, it obviously is not a rational argument. There is no reasoning involved as to why the conclusion is true, there’s just a threat about what will happen if the arguer doesn’t get his way. So, this is clearly bad reasoning from a logical point of view.

(3) Appeal to Pity

An argument that appeals to pity attempts to convince the opponent by making them feel sympathy or pity for the arguer’s position. For instance:

(22) John is going to be selected by the committee! He has to be -- just think how sad it’d be if he didn’t get the position!

The opponent might be persuaded to agree with the arguer out of sympathy, but that’s not really a rational basis for the conclusion. Again, an argument is supposed to provide reasons as to why the conclusion is true, not just why someone should go along with the conclusion, e.g., out of pity, or fear. So, in general, trying to win an argument by appealing to the other person’s emotions is not going to result in a good rational argument (even if it might be effective in practice).

(4) Subjectivism

A subjectivist argument is one which says that the conclusion is true simply because I think it’s true. It’s entirely subjective. Whatever I say, must be the case. So, for example:

(23) I should be the leader of this group. I just know I should and I’m always right about these feelings.

This is clearly a fallacy because you can’t know something like that to be true just because you feel that it’s true. A good argument should provide objective, logical reasons. If the goal of an argument is to persuade some other party who doesn’t already accept the conclusion, then the mere fact that the arguer believes the conclusion to be true probably won’t sway that person. So, this is another kind of fallacy.

(5) Straw Man

A straw man is an argument, or a counter-argument, which attempts to attack someone else’s views or position, but in doing so distorts and weakens the other person’s position, so that instead of responding to the real person, you are responding to a “straw man” – a weak imitation of the real view that you are attacking. So, with the straw man, someone makes an argument with a conclusion like “Global warming exists,” for example, Then, a straw man is a counter-argument which attempts to respond to the argument, but actually attacks a distorted or weakened version of the arguer’s position. So, in this example, the counter-argument states (correctly), “It doesn’t get hotter every single day of the year!” But the person who’s defending global warming obviously isn’t saying that that’s the case – that’s not what global warming implies. So the counter-argument is misrepresenting the position that they are attacking. Rather than attacking their real opponent, they are attacking a “straw man” (like, a weak imitation), in order to make their job easier. This is clearly cheating – if you want to have a rational argument with someone, it’s important to give a fair and accurate characterization of their side of the argument. Otherwise, you’re just not responding to that person’s real views at all!

(6) Slippery Slope

Another really common fallacy that you will see often in everyday life is the slippery slope. A slippery slope argument basically says that if one thing happens, that will send us falling down the slippery slope, and a whole bunch of other things are likely to follow. This is known as a fallacy, because usually the things that are supposed to follow are not actually that likely to happen, even given the initial event. So, for example:

(24) If they let men into the restaurant without a tie on, then pretty soon people will want to eat here in the nude.

The arguer is trying to say that they shouldn’t allow men to eat at the restaurant if they’re not wearing a tie, because if that happens, then the next step is that people will want to eat in the nude. But is that really the case? It sounds like a big leap. So, it’s a fallacy because the supposed “slippery slope” doesn’t really exist. Slippery slope arguments try to force you to choose between two extremes – it tends to ignore the possibility of a middle ground, since it tries to argue that once you are on that middle ground, you will quickly end up at the other extreme.

This type of reasoning is often applied when considering permissions and bans: “If you permit A, then people will want to do B, C, D, etc.” Or: “If they ban A, then pretty soon they’ll ban B, C, D, etc.” For a concrete example, consider the debate about gun control in the United States. Opponents of gun control argue that if the government enacts a ban on assault rifles, then pretty soon the Second Amendment will be entirely eliminated. Head of the National Rifle Association, Wayne LaPierre, goes so far as to argue that those who support gun control want to “eradicate all individual freedoms.” Notice that this argument assumes that moderate gun control is impossible – once you allow any limitations on individual freedoms (such as the freedom to buy military-grade weaponry), then all individual freedoms will disappear. So, this is a clear example of a slippery slope argument – it assumes that there is no possible middle ground.

Now, in some cases, a slippery slope type argument isn’t necessarily a fallacy. For instance:

(25) If Johnny gets the flu, then the rest of the class will get the flu as well.

This is still probably not a great argument, but at least there is some causal reason to believe that the flu could spread from Johnny to the rest of his classmates. So, we tend to call an argument a slippery slope when it really leaps to a conclusion that isn’t justified by the initial premises.

(7) False Alternative (False Dilemma)

When an argument exhibits a false alternative, or false dilemma, the arguer presents their opponent with a choice between two things, and suggests that only one of them is the truth. The problem, however, is that the choices, or alternatives, that are being offered, are not the only possibilities – so it’s forcing you to choose between A and B, when there is also the possibility of C, D, E, etc. So, consider:

(26) Either we stop at the next restaurant we see, or I’m going to die of hunger.

The obvious conclusion is that they should stop at the next restaurant, since it would be bad for the person to die of hunger. But this is a false alternative, because it’s not the case that the person is going to die of hunger if they don’t eat right away. So a false alternative presents a pair of options when there are really other possibilities to consider.

(8) Ad Hominem

“Ad hominem” means, roughly, “against the person.” An ad hominem fallacy is an argument that doesn’t try to win by offering good reasons or evidence, but rather directly attacks the personal character of the other person. For example:

(27) I didn’t cheat on the exam! You’re stupid and ugly!

You might notice this kind of fallacy coming up a lot with political advertisements, since these often appeal to some character flaw in their opponent. But, it’s usually a fallacy, since a logical argument ought to deal with reasons and justifications, and not try to undermine the other person’s character. Ultimately, when we consider an argument, we should consider it on its own merits – that is, we should consider the reasons and justifications that are offered for the conclusion, and try to respond to those reasons directly. In the end, it shouldn’t matter who is making the argument – even people with character flaws can produce valid forms of reasoning. So, attacking the arguer rather than the argument is not a rational form of argumentation.

(9) Tu Quoque

Tu quoque is a Latin phrase which means, roughly, “You too!” or, “So do you!” Essentially, it involves trying to win an argument or avoid some conclusion by accusing the other person of hypocrisy. For instance:

(28) You’re accusing me of cheating on the exam? I saw you copying the answers from Dave!

Notice that this is a fallacy because even if the other person did copy the answers from Dave, that doesn’t make it any more or less likely that the speaker cheated on the exam as well. Tu quoque is actually a kind of ad hominem argument – it is attacking the other person’s character, but specifically by calling them a hypocrite. But, just like with ad hominem arguments in general, even hypocrites can produce arguments that are, in themselves, persuasive. For example, suppose someone is arguing that smoking cigarettes is bad and dangerous, but they are addicted to smoking as well. That might make them somewhat of a hypocrite, but it doesn’t mean that they are making a weak argument. So if you want to engage in a logical debate, then you must address the argument itself, and not the arguer.

(10) Hasty Generalization

Hopefully, this fallacy should be pretty intuitive to grasp – we’ve probably all been guilty of this kind of reasoning at some point in the past. A hasty generalization is simply when you form a general conclusion about some group or class, but you do so on the basis of just a few examples. So, for instance:

(29) Alice is an adult and she’s tall. Bob is an adult and he’s also tall. So, I guess all adults are tall.

Obviously, one can’t form a conclusion about all adults on the basis of just two examples. That would be jumping to a conclusion. We looked at examples like this when discussing inductive strength and weakness. Recall that an inductively strong argument is one in which the premises make the conclusion very likely to be true. So, if the premises are true, then the conclusion is probably true as well. Whereas, a weak argument is one in which even if the premises are true, that still wouldn’t mean that the conclusion was all that likely. Clearly, this is an example of weak, rather than strong, inductive reasoning. Even if Alice and Bob are tall, that doesn’t make it very probable that all adults are tall, since there are billions of adults. So, this is a hasty generalization, or a kind of jumping to a conclusion. It’s clearly a fallacy because it’s a poor way to reason. A good inductive argument should appeal to a strong body of evidence to support the conclusion. If you form a hasty generalization, then you’re likely to be wrong much of the time. So, it’s definitely something to avoid.

(11) Weak Analogy

An argument exhibits a weak analogy when it tries to appeal to an analogy, or similarity, between two domains, say, X and Y, but in fact X and Y aren’t really that similar, or the analogy is a poor one. For example:

(30) You shouldn’t go to the concert. Going to a concert is like climbing a mountain – it’s dangerous and cold.

This strikes me as a pretty strange argument. Is going to a concert really like climbing a mountain? Maybe it’s true that some concerts are dangerous, but otherwise it doesn’t seem like a very intuitive or powerful metaphor for going to a concert. Now, analogical thinking, thinking in terms of analogies, is a very powerful and important cognitive tool. So it’s definitely appropriate to do so in certain circumstances. But the analogy must be a good one – one that really sheds light on the two things that are being compared. If you rely on a weak analogy, then it doesn’t make sense to draw any inferences about one thing on the basis of the other, since they’re not all that similar in the first place.

(12) Begging the Question

Begging the question frequently comes up in philosophical debates. It refers to an argument which contains a premise that already assumes that the conclusion is true, or, in other words, the conclusion is kind of just a restatement of the premises. For example, consider this argument:

(31) Carol is lying about her grade. I know she is because she’s not telling the truth.

Now, suppose you were trying to convince someone that Carol is lying about her grade. Normally, we assume that an argument is directed towards someone who doesn’t already agree with your conclusion. So, let’s suppose you’re trying to argue that Carol is lying about her grade, and you’re arguing with someone who thinks she’s not lying. Would they find this argument convincing at all? The problem is, if you don’t already believe that Carol is lying about her grade, then you’re not going to believe that she’s not telling the truth. The premise and the conclusion basically state the same thing! So, obviously that doesn’t make for a very persuasive argument. A good argument is supposed to persuade someone who doesn’t already accept the conclusion. And it’s supposed to do so by using premises that the other person will accept and agree with. But if an argument begs the question, then it won’t be very persuasive. If the premise and the conclusion are basically saying the same thing, then the other person won’t be inclined to accept the premises if they don’t accept the conclusion. So, basically, it’s not likely to convince anyone.

It’s worth mentioning that people sometimes use the phrase “begging the question” to really mean raising the question. So, for instance, someone might say: “We will soon be able to make trips to nearby planets. This begs the question – is space travel safe?” This doesn’t really beg the question, at least in the philosophical sense. Rather the sentence might raise the question of whether space travel is safe, but it doesn’t beg the question. In other words, it doesn’t assume, as a premise in an argument, that space travel is safe. So, it’s worth clarifying that begging and raising the question are two different things.

(13) Equivocation

OK, next let’s look at another kind of fallacy that is fairly widespread – equivocation. Equivocation is when an argument uses an ambiguous word in two different ways, but it ignores the ambiguity, and acts as though the word had one meaning. So, for instance:

(32) Justin Bieber is a star. Stars are giant astronomical objects. Therefore, Justin Bieber is a giant astronomical object.

Hopefully, the failure of reasoning in this argument should be clear to you. When the person says, “Justin Bieber is a star,” then clearly they mean that Bieber is a famous celebrity, which is true. But when they say, “Stars are giant astronomical objects,” then they’re using a different meaning of ‘star!' So it’s true that stars, in the astronomical sense, are giant astronomical objects. And it’s true, in the celebrity sense, that Justin Bieber is a star. But you can’t connect those two statements on the basis of the word ‘star,' since it has a different meaning in the two sentences! So, equivocation is when an argument ignores the fact that a certain word is ambiguous, and so draws faulty inferences on the basis of the assumption that it has a single meaning.

(14) Appeal to Majority

An argument involves appeal to majority when it tries to argue that something is true on the basis of the fact that most people believe is true. For instance, let’s go back to a time when people believed that the Earth was the center of the universe, and the Sun and stars revolved around the Earth. Then this guy Galileo gets up and says that the Earth actually revolves around the Sun, and someone responds by saying:

(33) The Sun revolves around the Earth. Come on, everyone knows that!

This is a fallacy because the fact that some belief is commonly held doesn’t necessarily make it true. People can be wrong about all sorts of things, and sometimes lots of people can be wrong at the same time. So, you can’t prove a point just by saying that other people agree with you. That’s not going to be very convincing to someone who disagrees with you. And it’s certainly not a valid form of reasoning, since human history contains all sorts of cases where basically everyone was wrong about a given question.

(15) Appeal to Ignorance

This fallacy is a little bit more subtle. An argument involves an appeal to ignorance when it tries to form a conclusion on the basis of a lack of proof against the alternatives. For instance, suppose we’re trying to debate who stole the cookies that were lying on the counter. Someone says:

(34) Alice stole the cookies. You’ve got no proof that anyone else did it!

This is a fallacy because the lack of evidence against your conclusion doesn’t necessarily make it true. Maybe there’s no proof at all about who stole the cookies – still, you can’t leap to the conclusion that it was Alice just because we can’t prove that it was Bob or Carol or Dave. The idea behind this fallacy is sometimes expressed in the phrase, “The absence of evidence is not evidence of absence.” In other words, just because you can’t find evidence of something doesn’t necessarily mean that it’s not the case. So, in the example we just looked at, the person is assuming that because there is no evidence that anyone else took the cookies, then it wasn’t anyone else, so it must be Alice. This is a very weak form of reasoning though. You can’t reliably infer that something is the case just because we haven’t been able to prove the opposite.

(16) Division

Now, we’ll look at two related fallacies – division and composition. Both of these fallacies have to do with ignoring the differences between a whole and its parts. Let’s start with division.

With division, a person infers that something is true about a thing’s parts just because it is true about the thing as a whole. For example:

(35) Central Park is beautiful. Therefore, every single blade of grass in Central Park is beautiful.

Now, Central Park is beautiful, but that doesn’t mean that every single part of Central Park, including every blade of grass, is also beautiful. You might think Central Park as a whole is beautiful, but not think that individual blades of grass are beautiful at all, even though blades of grass are part of what make up Central Park. So, in this case, it’s a fallacy because you are taking something that is true about a thing as a whole, and you’re assuming that it must also be true of all of its parts. But that’s just not the case.

(17) Composition

Composition is basically the opposite of division. With division, we infer from the whole to the parts. Whereas, with composition, we infer from the parts to the whole – we infer that something must be true about a thing as a whole on the basis of the fact that it’s true about its parts. For example:

(36) The table is composed of atoms, and the atoms are moving really fast. Therefore, the table is moving really fast.

Once again, this is a poor form of reasoning. In general, what these examples show is that there’s a difference between what’s true about a thing and what’s true about its parts. It’s true that material objects are made of atoms that are moving very fast at a sub-atomic level. But just because it’s true that the atoms are moving, we wouldn’t say that the table is moving when it’s just sitting there. So, once again, we see that what’s true about the parts, isn’t always true about the whole, and vice versa. When you make a fallacy by incorrectly inferring from something that’s true about the parts (e.g. the parts are moving) to a conclusion about the whole (e.g., the whole is moving), then that’s an example of the fallacy of composition.

(18) Non Sequitur (Missing the Point)

In ordinary discourse, a non sequitur is a statement that comes out of the blue – it seems disconnected from the rest of the conversation. Similarly, in logic, a non sequitur is when a person draws a conclusion that isn’t properly connected with the premises. So, for example:

(37) All dogs are furry, and Fido is a dog. Therefore, it’s probably going to rain tomorrow.

Huh?

Where does the conclusion that it’s probably going to rain tomorrow come from? It doesn’t appear to be connected at all with the statements that came before it. It just comes out of the blue. So, clearly, this is a bad form of argument. An argument is supposed to exhibit a logical connection between the premises and the conclusion. Not all examples of non sequitur are this blatant, but it’s obviously not a strong or valid way to reason.

(19) Affirming the Consequent

We often use conditional statements when we reason. Conditional statements are hypotheticals or “if...then…” statements. In other words, they are sentences that describe what will be the case, if something else is the case. Here’s an example:

(38) If it’s sunny tomorrow, we’ll go to the beach.

Now, you might be tempted to say that, if we know that (38) is true, we can conclude that the following is also true:

(39) If we go to the beach tomorrow, it’ll be sunny

But to do so would be to affirm the consequent. Affirming the consequent is a pretty common fallacy, one you should watch out for as the course continues. To see why it’s a fallacy, note that (38) (“if it’s sunny, we’ll go to the beach”) only tells us what we do if it’s sunny. It doesn’t say what we’re going to do if it’s cloudy or rainy. This means that it is consistent with (38) being true that we’ll also go to the beach when it’s cloudy or rainy! After all, it’s not inconsistent for someone to say, “if it’s sunny, we’ll go to the beach, but we’ll also go if it’s rainy, so long as it’s warm.” As such, we cannot conclude, from the fact that (38) is true, that (39) is true too.

(20) Denying the antecedent

This fallacy is closely related to the fallacy of affirming the consequent. Consider the following, again:

(38) If it’s sunny, we’ll go to the beach.

Sometimes, people are tempted to think that if they know (38) is true, then they can conclude that the following is true:

(40) If it’s not sunny, we won’t go to the beach.

But be careful -- that’s a fallacy! Just because we know that if it’s sunny, we’ll go to the beach, doesn’t mean we also know what we’ll do if it isn’t sunny. (38) is a statement about what we’ll do if it’s sunny, but (40) is a statement about what we’ll do if it isn’t sunny. The two sentences are saying different things, and the truth of (40) isn’t entailed by the truth of (38). After all, it’s possible that 38 is true, and we’ll go to the beach whether it’s sunny or not!

Summary

In this chapter, we have examined a variety of logical fallacies that arise both in philosophical debate, and in everyday conversation. Having these concepts in your toolkit can make it easier to identify when someone is using one of these fallacies in their argument. It also helps clarify the distinction between good rational arguments and bad ones. Below is a list of the fallacies that we covered in this chapter. Although other fallacies exist, this is a fairly representative sample.

1. Appeal to force
2. Appeal to pity
3. Tu quoque
4. Straw man
5. Appeal to authority
6. Slippery slope
7. Weak analogy
8. Hasty generalization
9. Appeal to ignorance
10. Begging the question
11. False alternative
12. Equivocation
13. Composition
14. Division
15. Subjectivism
16. Ad hominem
17. Missing the point (non sequitur)
18. Appeal to majority
19. Affirming the consequent
20. Denying the antecedent

KEY CONCEPTS

• Logical fallacy