What Is a Fallacy?

What is a fallacy?

Suppose I ask you to multiply two large numbers–say 12,653 and 65,321. How would you get the correct answer? You’d probably use a calculator or the good old multiplication algorithm you learned as a kid. One thing is clear: if you don’t use the correct method, then you’re not guaranteed to get the correct answer. 

Suppose now that I ask you to defend some claim that you believe–that I ask you to give me reasons, in other words, to believe that the claim is true. What’s true in the multiplication case is also true here: if your reasoning doesn’t follow a correct method, then you’re not guaranteed to get a correct conclusion. 

Reasoning, or argumentation, is the process of supporting a statement by appeal to other statements. The statement you’re trying to support is called the conclusion, and the statements that are supposed to support it are called premises. Reasoning can be correct or incorrect in just the way that mathematical calculation can. When reasoning is performed incorrectly, we say that it commits a fallacy.

A fallacy is an error in reasoning. 

The telltale sign of a fallacy is this: even if your premises are true, they still tell you nothing about whether or not your conclusion is true. Let’s look at an example. Here are two arguments: 

Fallacious Argument A

(1) If it’s 2021, then it’s the 21st Century

(2) It’s the 21st Century

Therefore, it’s 2021

Premise (true statement)

Premise (true statement)

Conclusion (true statement)

Fallacious Argument B

(1) If it’s 2016, then it’s the 21st Century

(2) It’s the 21st Century

Therefore, it’s 2016

Premise (true statement)

Premise (true statement)

Conclusion (false statement)

Argument A and Argument B have the same form. We can represent that form as follows:

Affirming the Consequent (Fallacy)

If P, then Q

Q

Therefore, P

Here ‘P’ and ‘Q’ are variables. In Argument A, the variable P has the value ‘it’s 2021’ and the variable Q has the value ‘it’s the 21st Century’. In Argument B, the variable P has the value ‘it’s 2016’ and the variable Q has the value ‘it’s the 21st Century’. 

When we plug in these values for the variables, we end up with true premises in both of the arguments: it’s true that if it’s 2021, then it’s the 21st century; it’s true that if it’s 2016, then it’s the 21st century, and it’s true that it’s the 21st century. 

Both arguments, then, have true premises. If we reason correctly from true premises, then we should arrive at a true conclusion every time. By analogy, if we correctly execute a multiplication algorithm then we should arrive at the correct product every time. 

But notice what happens when we reason by affirming the consequent: sometimes true premises yield a true conclusion, and sometimes they don’t. This shows us that reasoning in this way is unreliable. Even if you have true premises, those premises still tell you nothing about whether or not the conclusion is true. 

That’s why we call this form of reasoning a fallacy. It’s an example of incorrect reasoning: even if the premises are true, they still don’t give you any reason to accept the conclusion.

You can contrast affirming the consequent with a correct form of reasoning called modus ponens. Here’s an example:

Valid Argument (Modus Ponens)

(1) If it’s 2021, then it’s the 21st Century

(2) It’s 2021

Therefore, it’s the 21st Century

Premise

Premise

Conclusion

What makes this argument valid is that if its premises are true, then its conclusion is guaranteed to be true. What secures this guarantee is the argument’s form which we can represent as follows:

Modus Ponens (Valid)

If P, then Q

P

Therefore, Q

Premise

Premise

Conclusion

If we fill in values for P and Q that make the premises of the argument true, then it is impossible for the conclusion to be false. That’s what makes an argument valid.

By contrast, we’ve seen that with a fallacy, even if the premises are true, it’s still possible for the conclusion to be false. That’s what makes fallacies unreliable forms of reasoning.

Here are some common fallacies: 

  • Appeal to Authority Fallacy: Appeal to authority arguments look to support a claim by appeal to the person who’s making the claim. For example, if I say that there is an afterlife because Aristotle believes in it, this is a fallacy called the appeal to authority.
  • Appeal to Popularity Fallacy: Appeal to popularity happens when someone makes a claim based on popular opinion or on a common belief among a specific group of people. For example, if I say that there is an afterlife because most people believe in it, this is a fallacy called the appeal to popularity. This is a fallacy because you believe something to be true since it is a popular opinion not because there is a reason to believe that. 
  • Ad Hominem Fallacy (also known as a personal attack): Ad hominem means “to the person” in Latin. Ad hominem arguments look to falsify an opponent’s argument by attacking the arguer. For example, “Since Hitler is evil, everything he said is false.” A claim’s truth or falsity doesn’t depend on who’s making it. Hitler is a bad person, but that doesn’t mean that everything he says is false. (Conversely, just because people are good, that doesn’t mean everything they say is true. Even good people can be wrong.) Dismissing a claim simply because a bad person says it is an example of Ad hominem. 
  • Hasty Generalization Fallacy: A generalization is stronger or weaker depending on the size of the initial sample. Hasty generalizations are weak generalizations. A generalization is hasty when we endorse a general claim without having observed a sample large enough to be confident that the claim is true. For example, if someone says, “All the parrots I’ve ever seen are yellow, so all parrots must be yellow,” then they are making a hasty generalization based on seeing a small sample.
  • Straw Man Fallacy: The straw man is a logical fallacy that replaces something (a person, a viewpoint, an argument) with a distorted version that blows the opponent’s position out of proportion to make it easier to attack. For example, “Wife: “I’d rather go to a beach than New York City.” Husband: “Why do you hate New York City?” The wife never said that she hates New York City. The husband misrepresents what she says to make her preferences seem more extreme than they are. 

Here are the names of some other common fallacies: Post hoc ergo propter hoc, Red herring fallacy, Slippery slope fallacy, Begging the question (circular reasoning), Ad populum (Bandwagon fallacy), The correlation/causation fallacy, Tu quoque. 

Formal Fallacies Versus Informal Fallacies

Some people distinguish formal fallacies from informal ones. To understand the difference you first have to know that there are two kinds of arguments that actually support their conclusions: valid and inductive. In a valid argument, true premises guarantee a true conclusion. In an inductive argument, true premises don’t guarantee a true conclusion, but they give us good reason to think that the conclusion is true. Here are two examples to illustrate the difference:

Valid

All Athenian men are bald 

Socrates is an Athenian man

Therefore, Socrates is bald

Inductive

90% of Athenian men are bald 

Socrates is an Athenian man

Therefore, Socrates is (probably) bald

If the premises of the valid argument are true, then the conclusion is guaranteed to be true–it’s impossible for it to be false. On the other hand, if the premises of the inductive argument are true, the conclusion isn’t guaranteed to be true, but it’s probably true.

When people try to advance a valid argument but commit an error, we call it a formal fallacy. On the other hand, when people try to advance an inductive argument but commit an error, we call it an informal fallacy. That’s the difference between formal and informal fallacies.

Free Thinkers and Fallacies

Regardless of what kind of fallacies we’re talking about, free thinkers are committed to avoiding them. They’re committed to developing critical thinking skills–including the ability to identify and avoid errors in reasoning. They are careful to make sure their arguments are either valid or inductive, and if they don’t know how to argue for a particular claim, they’ll wait and give it more thought. Free thinkers will default to withholding judgment until they get better reasoning to accept or reject a claim.

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