What Is a Fallacy?
Critical thinking basics
A fallacy in Critical Thinking is an error in argumentation that makes an argument invalid. Fallacious arguments often look convincing, but in reality they don’t provide any evidence that their conclusion is correct.
This article is part of a series on Logic and Critical Thinking. Find all the articles in this series here.
In our modern, media-centric world, we are surrounded by arguments that aim to convince us to adopt their conclusions. Politicians, advocacy groups, social media friends, online discussions in forums, news outlets: they all argue for their positions with more or less good arguments. It is therefore essential that we are able to distinguish good from bad arguments, so that we can reject conclusions that are illogical or not based on sufficient evidence.
What is a fallacy?
A fallacy in Critical Thinking is an error in argumentation that makes an argument invalid. Fallacious arguments often look convincing, but in reality they don’t provide any evidence that their conclusion is correct.
An argument, in its most general form, consists of a number of statements (called the premises) that together support a conclusion. If the support that the premises provide is perfect, we have a “valid” argument.
In a valid argument, if the premises are true, the conclusion is certain to be true.
Not all arguments need to be valid arguments, though. Some arguments provide less support for their conclusions, so that, if the premises are true, there is some probability that the conclusion will be true. These are called inductive arguments and the support that they provide to their conclusion can be weak or strong.
A fallacy is at the other end of that spectrum. It is a wrong argument where the premises do not provide any support for the conclusion.
Valid, strong, weak and fallacious arguments
Here are some examples to make this more clear:
Valid argument: “If it is Tuesday, I will have my piano lesson. Today is Tuesday. Therefore, I will have my piano lesson.” This argument is valid because, if we assume that premises to be true, the conclusion must also be true. If I really have piano lessons every Tuesday and if it is indeed Tuesday, then there is no way how I could not have a piano lesson (otherwise one of the premises would have to be false).
Strong (inductive) argument: “I had piano lessons on 50 out of 52 Tuesdays last year. Today is Tuesday. So I will have a piano lesson today.” This argument does not make its conclusion certain, only very probable. So it is not valid. It it strong.
Weak (inductive) argument: “Once a month on Tuesdays I have a piano lesson. Today is Tuesday. Therefore, I will have a piano lesson today.” Here the premises provide some support for the conclusion, but the probability that the conclusion is true is not very high (around 20-25% percent, assuming that there are four or five Tuesdays in a month).
Fallacy: “I’m afraid of having a piano lesson on Tuesdays. Today is Tuesday. Given my bad luck, I’m sure that I will have a piano lesson today.” If we look at this from the outside, disregarding the speaker’s emotions, there is really no good reason to assume that there will be a piano lesson today. No evidence is provided that would make it more likely that the conclusion is true. The conclusion may still be true (assuming that the speaker has booked a piano lesson, there is some probability that it might happen to be today), but the particular premises don’t provide any additional support for the conclusion. Whether the conclusion is true or not does not depend on these premises at all.
This is important. Fallacies can have true conclusions. This does not mean that they are not fallacies.
For example:
“2+2=4. Germany is in Europe. Therefore, smoking is bad for one’s health.” Here, the premises are true and the conclusion is true, too. Still, this is a fallacy, because the premises do not provide any support to the conclusion. The conclusion just happens to be true, independently of these premises.
What are the different kinds of fallacies?
There are many different classifications of fallacies. On the Internet, one can find sites that list hundreds of fallacies and dozens of categories of fallacies that differ from site to site.
The easiest way to group fallacies is to begin with the definition of an argument (see above): An argument consists of a number of statements (called the premises) that together support a conclusion. Thus:
Argument = relevant reasons + logical connections between the reasons.
A fallacy breaks an argument because either:
- The relevant reasons are not good reasons, or there is not sufficient evidence, or the reasons are not relevant to the truth of the conclusion; or
- The logical connections between the reasons are wrong.
So we have essentially two kinds of fallacies. In both, the reasons do not support the conclusion; and this can be because:
- the evidence is missing, or
- the logical connection between reasons and conclusion is wrong.
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The ten most common fallacies
With hundreds of fallacies to choose from, it is always difficult to compile a list of ten fallacies that are the “most common” or “most important.” Still, here is our take on the ten most common fallacies.
Equivocation
Two words sound the same but mean different things.
“Peter is a good driver. If people are good, they can rise to the highest positions in society. Therefore, Peter can rise to the highest positions in society.” Here “good” is used in two different meanings and the conclusion is not really supported by the premises.
Slippery slope
Some process is assumed to become worse and worse over time.
“Today, a bus ticket costs two dollars. Next month, they’ll raise it to three. And before you know it, bus tickets will cost hundreds of dollars and nobody will be able to afford taking the bus!” This one is very common in politics, when politicians make predictions about the opponents’ performance in government.
Ad hominem
An argument is rejected because of an irrelevant property of the person who presents the argument.
“This woman is wearing a traditional Islamic dress, therefore she shouldn’t be allowed to teach children in our schools.” Recognise this one? Yes, it’s a fallacy. What fashion choices someone makes is irrelevant to their qualification or quality as a teacher. If I want to argue that this person is unsuitable as a teacher, I would have to support my conclusion with reasons that are related to her qualities as a teacher.
Appeal to fear
Instead of actual reasons that support the conclusion, we are presented with reasons to be afraid of something.
“If we don’t stop immigration, the immigrants will take up all the places in our schools and our own children will be left out.” Please note that this is an example for a fallacy, not a good argument.
Although what we fear might indeed happen under particular circumstances, here no reasons are given to support the conclusion. Fear of an outcome is not a valid reason to assume that the feared outcome will actually happen.
Begging the question
The premises include the assumption that the conclusion is true.
Example dialogue between two people on the street:
– “I am arresting you.”
– “How can you arrest me? Are you a police officer? You are not wearing a uniform. How do I know that you are a police officer?”
– “Of course I am. How could have I arrested you if I was not?”
Here the arresting person needs the conclusion to be true as part of the premises that, in turn, are supposed to provide evidence that the conclusion is true. So the argument is circular and the conclusion has no external support from any reasons.
Denying the antecedent and affirming the consequent
In an “if-then” sentence, the first part (after the “if”) is called the antecedent. The second part (after the “then”) is called the consequent. These two fallacies are caused by a wrong logical form of a conditional argument.
“If it rains, the street will be wet. It has not rained. Therefore, the street is not wet.” (Denying the antecedent). The conclusion may be wrong, because someone may have spilled a bucket of water onto the street. The fact that rain would wet the street does not exclude the possibility that other causes might also make the street wet.
“If it rains, the street will be wet. The street is wet. Therefore, it has rained.” (Denying the consequent). This is wrong for the same reason as the previous one, but its logical form is slightly different: look at the second sentence in both cases. It is “denying the antecedent” or “affirming the consequent”. These fallacies get their name from what the second premise is doing. Both are wrong argument forms.
By the way, the other two possible combinations, “affirming the antecedent” and “denying the consequent,” lead to valid arguments. Try them out with the example sentence above!
Hasty generalisation and biased sample
These two are called “statistical” fallacies.
In the hasty generalisation, we draw a conclusion from too few observations:
“I have a Chinese friend who speaks perfect French. Wow! The Chinese have such a gift for languages!” Again, it is not necessarily wrong that Chinese people might have a gift for languages; the problem is that this particular premise, the observation of one single case, does not provide enough evidence to support the conclusion. This is a hasty generalisation.
In the biased sample, we draw a conclusion from a wrongly selected sample of observations:
“I asked fifty people who were sitting at restaurant X whether they liked the food. They all said they did. Therefore, most people like restaurant X!” (Biased sample). Here, the speaker does have a bigger sample of data, but the way of selecting it is wrong. If you ask only people who are already sitting in that restaurant whether they like it, of course they will say that they do. After all, they went there because they liked it. In order to get good support for the conclusion, one would have to ask a random group of people if they like restaurant X, not those who are already customers!
False dilemma
A dilemma is a forced choice between two undesirable alternatives:
“Chocolate makes me happy but is unhealthy. I can either eat chocolate and do something unhealthy, or I won’t eat chocolate and I will be unhappy.” Dilemmas like this are common in everyday life.
A false dilemma is an argument that looks like a dilemma, but where the choice is not forced, or there are more available alternatives than just the two mentioned:
“Nuclear power does not produce CO2. Global warming is the greatest danger to the world right now. Global warming is caused by CO2. Therefore, we must use nuclear power in order to avoid global warming.” This is a common argument of the nuclear power industry.
There are multiple things wrong with this argument, but what interests us here is the dilemma presented: either we agree to nuclear power, or we have to accept global warming. A supposedly forced choice between two undesirable alternatives. But this dilemma is a false one, because we don’t have only these two choices. We can, for example, waste less energy, reducing our energy consumption, and making new energy sources unnecessary. Or we can find other sources of energy that also don’t produce CO2, like solar or wind energy. So, although this looks like a dilemma, it is a false dilemma: a fallacy that does not support its conclusion.
Confusing correlation and causation
It is concluded that one event must be causing the other just because they often appear together.
Example:
“Smaller shoe sizes are causing long hair. We measured ten thousand individuals’ shoe sizes and hair length. Statistically, those with smaller shoe sizes also tended to have longer hair.”
This example might be silly, but it shows clearly where the fallacy lies. The observation itself may actually be correct. It is perfectly plausible that people with smaller shoe sizes (many women) may have longer hair (also many women). But there is no reason to assume that the small shoes cause long hair. Rather, both phenomena, the smaller shoes and the longer hair, have another, common cause: the fact that some of the survey’s subjects are women.
This fallacy often appears in ads: “People who eat chia seeds live five years longer on average! So buy a pack of chia seeds today to lengthen your life!”
This is a fallacy for the same reason. There is probably a correlation between eating chia seeds and a long life, but it’s unlikely that eating chia seeds alone is the cause for longer life. Instead, the people who eat chia seeds also tend to generally eat healthier food, avoid fast food, do regular exercise, practice yoga and so on. A person who spends their time on the sofa devouring chocolate chip cookies is unlikely to prolong their life just by popping in a few chia seeds between the cookies. Correlation does not necessarily imply causation.
Burden of proof
It is assumed that a claim is true just because the other side cannot prove that it is wrong.
This is a very common fallacy used by conspiracy theorists. For example:
“The Earth must be flat because none of the people I asked could definitely prove that it is round in shape.” Or: “Vaccines must be made by evil government agents trying to control our minds, because no one can prove that they are not.”
Of course, not being able to prove the opposite doesn’t make a claim true. The so-called “burden of proof” means: which party has to prove their claim? Do the flat-Earthers have to prove that the Earth is flat, or do the round-Earthers have to prove that it is not? Since either proof is hard to supply convincingly by normal citizens (few have first-hand access to satellites or other astronomical equipment), it is crucial that we clarify whose job it is to provide the proof.
Generally, the side with the more surprising and least accepted claim is supposed to have the burden of proof. If almost all (including scientists and those whose job professionally it is to know such things) agree that the Earth is round, then the flat-Earthers have to prove that it’s not. Note that in another time, this might have been different: in the Middle Ages, the side that says that the Earth is round might have had the burden of proof (assuming most people and those in authority positions were convinced that it is flat).
When is a ‘fallacy’ not a fallacy?
One has to be careful with fallacies. Sometimes, something that looks like a fallacy might actually be a valid argument. For example:
“Last week you were smoking two cigarettes a day. This week it’s four. Next week you’ll be smoking eight and then the whole pack.”
This might not be a very strong argument, but it’s not a fallacy either. Due to the mechanisms of addiction to tobacco, it is plausible that someone might go from smoking two cigarettes a day to smoking much more in the future (as, indeed, most smokers do over time). Although it looks like a slippery slope, there is some support for the conclusion there. So it is probably a weak argument and not a fallacy.
This is true of most fallacies. Whether they are actually fallacies or good arguments often depends on their context.
“If you don’t vote for our party, you will end up poor in a country full of criminals.” This is a fallacy. But: “If you don’t take these pills that the doctor gave you, you will end up having terrible pain and will need to go to the hospital,” may not be. The threat here is real.
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Cover image by ActionVance on Unsplash.
