The "No True Scotsman" Fallacy



In a 2020 interview with popular rapper, Charlamagne, Joe Biden, who was then running for president against Donald Trump, made a claim that shocked and offended many people. Interrupting Charlamagne at one point in the interview, he said this:

"If you have a problem figuring out whether you're for me or Trump, then you ain't black."

This impassioned appeal for the black vote, to say the least, was unpersuasive. Whatever you think defines what it means to be black, it is doubtful that voting for a particular presidential candidate could disqualify someone from being part of that group. Group loyalties and identities have become a major point of contention and debate in the United States, and Biden's claim is indicative of this facet of American culture.


Though this example is silly, it is a good illustration of the "No True Scotsman" fallacy. The "No True Scotsman" fallacy is yet another informal fallacy that requires discernment in order to identify. As with the "Tu Quoque" fallacy, some forms of argumentation can look like the "No True Scotsman" fallacy, even if they are do not commit such a fallacy.


In order to understand the "No True Scotsman" fallacy, one must understand what a generalization is. A generalization is a kind of claim that attributes to all or most of a single group some attribute or quality. Another way to put it is that a generalization predicates of all or most members of a class some property. There are varieties of generalizations, and the way that they are shown to be true vary depending on the type of generalization. Here are some examples of generalizations:

  1. All ravens are black.

  2. Most Americans believe in God.

  3. Many people like cake.

  4. Some people live in Croatia.

There are two important observations that need to be noted about these generalizations. First, what it takes to prove the truth of each statement depends on how many members of the class to which the property in question is being applied. In the case of statement (1), this statement is quite difficult to prove, since it would be difficult to find all the ravens in the world and check to see whether they are black. Perhaps there are non-black ravens living in a part of the world that we haven't explored. Statement (2) is easier to prove than (1), but it is nonetheless somewhat difficult. One would need a sufficiently large and representative sample of Americans in order to establish, via a survey, that most Americans believe in God. Though there could be dispute about this, "most" can be understood as meaning "more than 50%," such that if more than 50% of Americans believe in God, then most Americans believe in God.


Statement (3) is, in one sense, even easier to prove than (1) and (2), but it is subject to a problem of ambiguity. It is not entirely clear how the word "many" is to be understood. Should it be understood in terms of absolute amount of people or as a percentage? If we survey 100 people as to whether they like cake, and 5 people indicate that they like cake, we probably wouldn't say that many of those people like cake. If 45 people indicate that they like cake, then "many" seems like an accurate descriptor for the number of those people who like cake (even though "most" would be inaccurate). So, though (3) is easier to prove, there is a problem of ambiguity. Statement (4) is the easiest of these statements to prove. "Some" is typically understood to mean "at least one." So, if at least one person lives in Croatia, then some people live in Croatia. Similarly, statements (1), (2), and (3) logically entail these three statements:

  • Some ravens are black.

  • Some Americans believe in God.

  • Some people like cake.

From this, we can infer the following rule for generalizations: for any statement made about members of a certain class, that statement is more difficult to prove in correlation with the increasing scope of the statement. (Here, "scope" refers to the portion of the members of the class covered by the statement. "All" statements are more difficult to prove than "most" statements, and so on.


This leads directly to our second observation: what it takes to disprove the truth of each statement depends on the scope of each statement. In general, generalizations are disproved with counterexamples. A counterexample is a claim that, if true, conflicts with or contradicts outright a rule, theory, or generalization. When applied to generalizations, typically, counterexamples involve finding an example of a member of a class that lacks the property attributed to the members of the class in the initial generalization.


Consider (1). Statement (1) claims of all members of a certain class - ravens - that they are black. Since the scope of this statement covers every member of the class, it is disproven just in case there is at least one non-black raven. If we can even one non-black raven, then it is not true that all ravens are black. Statement (2), however, is not disproved if there is at least one American who doesn't believe in God. Rather, it is disproven if there are enough counterexamples that it turns out not to be the case that most Americans believe in God. Perhaps most Americans don't believe in God. Thus, just one counterexample is not enough to disprove (2). It is much more difficult to disprove (3) than it is to disprove (1) or (2) because "many" statements are ambiguous. Let's say that we conduct a survey in which a representative sample of people are asked whether they like cake and that the number of people who claim to like cake is so minute that it wouldn't be right to say that many people like cake. As it turns out, the vast majority of people don't like cake. Thus, for (3) to be disproven, there would need to be enough counterexamples to establish that the vast majority of the members of that class do not have the property attributed to many of them in the generalization. Finally, disproving (4) is the most difficult task of the four statements, since if even one person lives in Croatia, then some people live in Croatia. Thus, the only way to disprove (4) is to prove that "no one lives in Croatia."


From this, we can infer another rule for generalizations: for any statement made about members of a certain class, disproving that statement is more difficult in correlation with the decreasing scope of the statement. "Some" statements are more difficult to disprove than "many" statements, and so on. Notice that this rule is a corollary of our first rule.


Why is all of this important to understanding the "No True Scotsman" fallacy? In order to identify the "No True Scotsman" fallacy, one must be able to identify a generalization as well as what it would take to disprove that generalization. In philosophy, a distinction is made between two types of statements: analytic and synthetic statements. Analytic statements are true by definition. They can be seen as true by simply understanding the definitions of the terms involved in the statement. Here is an example of an analytic statement:

  • All unmarried men are bachelors.

This statement is obviously true because bachelors are, by definition, unmarried men. Thus, this generalization is true, and there is no possible counterexample to it. But it adds nothing to our understanding of unmarried men or bachelors, so it counts as a kind of cheap victory in philosophy and is not very interesting.


Synthetic statements, though difficult to define, can be understood as statements that add something of intellectual substance to the subject. Proving a synthetic statement requires more work than simply understanding the definitions of the terms in the statement. Another way of defining a synthetic statement is that it is any statement that is not analytic. Thus, if it cannot be proven true by definition, then it is synthetic. Here is an example of a synthetic statement:

  • All dogs have four legs.

As an "all" statement, this would be difficult to prove. Proving it would involve more work than in the analytic statement, since it would require scientific observation. This statement also turns out to be false, since there are many examples of dogs without four legs. Many dogs, for various reasons, lose a leg, and losing a leg doesn't mean that the dog isn't a dog.


To further complicate things, some statements predicate to a subject something that is part of the subject's essence. Whatever makes up a thing's essence is what that thing is and that, if lacked, the thing would cease to be what it is. Here is an example of a statement like this:

  • All squares have four sides.

Let's say that someone were to attempt to come up with a counterexample to this statement:

  • Shape X is a square and doesn't have four sides.

The supposed counterexample is that of a square that doesn't have four sides, but immediately, we can see that this is nonsense. Having four sides is part of what it means to be a square. Whatever shape X is, it is not a square. Thus, a good rejoinder to this supposed counterexample would be this: "Shape X is not a square." (If you're wondering whether the statement, "All squares have four sides," is analytic or synthetic, that is an excellent question. But answering it would take us too far afield.)


This brings us to the key to understanding the "No True Scotsman" fallacy. The "No True Scotsman" fallacy is a kind of response to a counterexample to a generalization that denies that the counterexample is a member of the class covered by the generalization. That's an abstract way to put it, but let's go back to Biden's comment in 2020 to illustrate this. Biden's claim was that if one did not vote for him, then one is not black. This fallacious argument can be laid out as a response to an objection to a generalization:


Generalization: All black people vote Democrat (or for Biden).

Counterexample: Some black people don't vote Democrat (or for Biden).

Response: Those people aren't black.


The generalization, in this case, is synthetic and clearly false. Though most black people tend to vote Democrat, not all do. But Biden's claim is a kind of response to the fact that some black people don't vote Democrat that denies their membership in the black community. Such an appeal to group membership and identity can be rhetorically powerful, but not when a white politician makes that appeal. In fact, black people criticized Biden harshly for the comment, claiming rightly that he was being presumptuous in assuming that black people would vote Democrat. In other words, they saw the hidden generalization that Biden was trying fallaciously to save from the counterexample.


The "No True Scotsman" fallacy is committed whenever someone treats as essential to being in the class something that is, in fact, not essential. Being black has nothing to do with how someone votes, but Biden treated it as a qualifying property for whether one is black. Also, note that the "No True Scotsman" fallacy is a desperate move. It is a desperate response to an objection that tries to save the truth of one's generalization.


I did so much work to cover the logic of generalizations because denying that the counterexample is about a member of the class covered under the generalization is not necessarily fallacious. This can be seen in the example counterexample above involving Shape X. Note, however, in that case that Shape X cannot be a square because having four sides is part of the essence of being a square. In this case, denying that Shape X is a square is exactly the right response. This is why understanding the concept of essence is important to identifying the "No True Scotsman" fallacy.


Christians can be guilty of the "No True Scotsman" fallacy as well. Consider, for instance, a hypothetical discussion between Jones and Bob:


Jones: Why are you not Reformed? All true Christians are Reformed.

Bob: I know plenty of Christians who love Jesus and are not Reformed.

Jones: Well, I guess that they aren't true Christians.


This example is simplistic, but it is a clear example of the "No True Scotsman" fallacy that I hear in discussions with Christians quite often. Christians interpret Scripture in different ways and hold to different systems of theology. Some are Calvinists or Reformed; others are non-Calvinists. Some believe in a literal Genesis creation narrative; others believe that the creation narrative is metaphorical, mythical, or some mixture of literal and non-literal. Some are pre-, post-, or amillennialists. These are important theological issues, but they are issues that are discussed among Christians. They are not issues that define who is or is not a Christian.


Defining what one must believe in order to be a Christian is not always easy, but some common defining markers have been affirmed:

  • Trinity

  • Incarnation

  • Salvation by grace through faith in Christ alone

  • The resurrection of Christ

  • Christ's second coming

  • Etc.

These are the kinds of things affirmed in the historic ecumenical creeds such as the Apostles' Creed, Nicene Creed, and Athanasian Creed, as well as others. From this, evangelicals have distinguished between primary and secondary issues in Christian theology. Primary issues concern what defines being a Christian from not being a Christian and include the doctrines listed above. If one rejects the doctrine of the Trinity, one may claim to be a Christian, but one is not truly a Christian. Secondary issues concern important theological issues that are discussed between Christians. These include whether one is or is not Reformed, which is why Jones commits the "No True Scotsman" fallacy with his claim that non-Reformed Christians are not "true Christians."


The upshot here is that appeals to group membership and identity may be rhetorically powerful, but it is often logically fallacious. It is too often used as a kind of manipulation tactic to prevent substantive intellectual discussion by simply denying that one is part of the "inner group" or "club." When Christians use it against one another, it can be tremendously damaging. Brothers and sisters, let's strive to be more intellectually virtuous in our use of argumentation, only separating over primary issues when needed.


That's it for this post! These posts are intended to very short and easy to read. I want them to a helpful resource for reference and an introductory resource for people who haven't been exposed to these concepts. I hope that the content will be edifying to you. If you have questions or would like to reach out to me to discuss these things, feel free to comment here or to send me an email or message on Facebook. If this blog has been helpful and interesting for you, feel free to subscribe to be notified of any new posts. Finally, if this post would benefit anyone else, please feel free to share it on social media. Thanks for reading!


Sources


For the sake of full disclosure, this is the main resource that I will be using for this series. This is an excellent textbook and worth checking into if you want more information on the subject:


Hurley, Patrick J. A Concise Introduction to Logic. Twelfth Edition. Stamford, CT: Cengage Learning, 2015.


I've also begun using this great resource for Christians on critical thinking:


Dickinson, Travis. Logic and the Way of Jesus: Thinking Critically and Christianly. Nashville, TN: B&H Academic, 2022.

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