What is a fallacy?

Two definitions of “fallacy” and a case for the standard definition

The Bad Definition of Fallacy

Here is what I like to call the bad argument definition of fallacy:

A fallacy is an argument that is bad.

In Mastering Logical Fallacies, Withey (p.11) writes “[w]hen an argument goes wrong, its because its proponent has committed a fallacy.” On this definition, an argument isn’t “bad” simply because someone doesn’t like it. So, it must be bad because it fails to meet some objective standards. What are these objective standards? Three are usually listed:

1. Truth: The sentences (propositions) of the argument should be true.
2. Entailment: The conclusion should follow from the premises (valid/strong).
3. Relevance: The premises should be relevantly related to the conclusion.

In short, if an argument fails to meet one or more of these standards, then it is a “bad argument”; and, if an argument is bad, then it is a fallacy. For example, consider the following argument:

• P1: If I buy a lottery ticket, then I might win.
• C: Therefore, I should buy a ticket.

On the bad argument definition, this argument is a fallacy since the conclusion (“C”) does not follow from the premise (“P1”). The argument is invalid. Here is a more trivial example that violates a different objective standard:

• P1: Grass is grass.
• C: Therefore, snow is snow

This argument is a fallacy because the premise (P1) is not relevantly related to the conclusion.

The Standard Definition

A second definition of “fallacy” is what is known as the standard definition of fallacy (SDF). On this account, a fallacy is defined as follows:

A fallacy is an argument that seems good but is not.

This definition is identical to our “bad definition of fallacy” in every way except that it adds an appearance component to the definition. On the standard definition, not only does a fallacy need to be bad, but it has to look good to someone. It is similar to how a pear might look good but taste like sand.

For example, consider the following argument:

• P1: Roses are flowers.
• P2: Some flowers fade quickly.
• C: Therefore, roses fade quickly.

When I give variations of this argument to college students taking an introductory logic courses, anywhere from 50–90% of students think the argument is “good”. Even further, this same group will say that the conclusion follows with necessity from the premises (is deductively valid). But the argument is not good even if it appears good. While all of the propositions are true and relevantly related to the conclusion, the conclusion does not follow with necessity from the premises. The argument is invalid.

There are countless other examples of bad arguments that appear good. Let’s consider just one more. In Thinking, Fast and Slow (p.44), Daniel Kahneman asks his readers to quickly answer this question:

If a bat and a ball cost $1.10 and the bat costs one dollar more than the ball, then how much does the ball cost?

It must be 10 cents. Right? Kahneman notes that this is the answer given by 50% of students at Harvard, MIT, and Princeton and the answer given by 80% of students at other universities. But this answer is incorrect. It is 5 cents. If we reconstruct the reasoning of the students as an argument, this argument is fallacious since it is a bad argument that appears good.

Does it Matter?

I’ve presented two different definitions of “fallacy” (there are others). Which one should we use? I don’t have a strong preference for one over the other. But, if I were forced to choose between the two, I think there is a case to be made for using the standard definition over the bad argument definition.

First, what is the purpose of critical thinking and identifying fallacies? If classifying something as a “fallacy” is part of the broader human project of correcting irrational thinking, then using the bad argument definition is only weakly connected to this project. We call something a “fallacy” because we want to call out and correct bad reasoning. But, if any bad argument is fallacious, then we are calling out some forms of reasoning that no one would mistakenly take to be good.

Second, there is an appearance component to every named fallacy. For example, the strawman fallacy gives the appearance of defeating a theory by substituting a weaker form of an argument for that theory in place of the strongest argument for that theory. Arguments that commit the “fallacy of equivocation” give the appearance of being good arguments by trading on the ambiguity of words. And, arguments that commit the ad hominem fallacy give the appearance of being good arguments because people are prone to believe that the source of the argument is relevant to the quality of the argument when the argument’s quality is independent of the source. So, perhaps this appearance component is not only a key ingredient of every named fallacy but is also a key ingredient of what it means for an argument to be a fallacy.

Third, there is probably an instrumental case to be made for the standard definition. If I identify Tek as reasoning fallaciously, this identification requires me to consider what caused Tek to judge this bad argument as good (or at least what causes people in general to reason a certain way). Identifying the cause (e.g., whether they be cognitive biases, lack of education, or brainwashing) requires me to consider Tek’s situation in the world and Tek’s perspective on things. I’d like to think that this perspective-taking would not only make people more sympathetic to Tek but better able to help him not make the same mistakes in the future.

References and Further Reading

• Hamblin, Charles L. 1970. Fallacies. London, Methuen.
• Hansen, Has V. and R. C. Pinto., 1995. Fallacies: Classical and Contemporary Readings. University Park, Pennsylvania State University Press.
• Kahneman, Daniel. 2013. Thinking, Fast and Slow. 1st pbk. ed. New York: Farrar, Straus and Giroux.
• Withey, Michael. 2016. Mastering Logical Fallacies: The Definitive Guide to Flawless Rhetoric and Bulletproof Logic. Berkeley, CA: Zephyros Press.
• Articles on the definition of “fallacy” along with articles on specific fallacies can be found in the following academic journals: Argumentation, Argumentation and Advocacy, Informal Logic, and Philosophy and Rhetoric.
• Another example of a case where humans struggle to reason correctly is the THOG problem. See Wason, Peter C., and Philip G. Brooks. 1979. “THOG: The Anatomy of a Problem.” Psychological Research 41 (1): 79–90. https://doi.org/10.1007/BF00309425. For a video presentation of the THOG problem, see For the solution to the THOG Problem, see THOG problem: The Solution.