[Epistemic status: I don't expect this to break new ground not already in core reading (such as Eliezer Yudkowsky's A Human's Guide to Words or Scott Alexander's Categorisation and Concepts), but I am writing this as a pointer for future reference]

[Trigger warning: analogical discussion of rape, kinda treating Scotsmen as if they're not there]

In Traditional Rationality, the No True Scotsman fallacy is a logical fallacy in which a person saying all X are Y, faced with an alleged counterexample Z where Z is X but not Y, deny the alleged counterexample Z is X, thus saving their statement from falsification.

Scotsmen

The archetypal example of the No True Scotsman fallacy, which gives it its name, is this one:

Imagine Hamish McDonald, a Scotsman, sitting down with his Glasgow Morning Herald and seeing an article about how the "Brighton Sex Maniac Strikes Again". Hamish is shocked and declares that "No Scotsman would do such a thing". The next day he sits down to read his Glasgow Morning Herald again; and, this time, finds an article about an Aberdeen man whose brutal actions make the Brighton sex maniac seem almost gentlemanly. This fact shows that Hamish was wrong in his opinion, but is he going to admit this? Not likely. This time he says: "No true Scotsman would do such a thing".

Flew, Antony (1975), Thinking About Thinking: Do I Sincerely Want to Be Right?, London: Collins Fontana, p. 47, ISBN 978-0-00-633580-1

Reading this, one is tempted to conclude that any argument of this form is wrong and fallacious and should not be used. But consider the following dialogue:

ALICE: All Scotsmen are UK citizens

BOB: But Xi Jinping is a Scotsman, yet he isn't an UK citizen.

ALICE: He is not a true Scotsman.

BOB: You're using the No True Scotsman fallacy !

It's self-evident that Alice is right and Bob is wrong. One might be tempted to call No True No True Scotsman Fallacy, but it fits the definition of the No True Scotsman fallacy we gave earlier: Alice is saying that all Scotsmen are UK citizens and, when faced with the alleged counterexample that Xi Jinping is a Scotsman but not an UK citizen, deny that Xi Jinping is a Scotsman, thus saving her statement from falsification. Either we should abandon all statements of the form "All X are Y" when faced with one of the Bobs of this world, either we should stop calling No True Scotsman a fallacy, or somebody has to get more subtle. Let's try the third option.

A question we can ask in our effort to get more subtle about this subject is why do we care about the Aberdeen man being a true Scotsman. It would be easy to say we care because if the Aberdeen man is a true Scotsman, then this would disprove Hamish's statement that no Scotsman would do such a thing. But this raise a second question: why do we care about whether Hamish's statement is correct ? How should our behavior change if Hamish's statement is correct ?

• If Hamish's statement is correct, then we should allocate less funds to efforts to reduce rape in Scotland.
• If Hamish's statement is correct, then detectives should spend less time studying Scottish suspects of rape.
• If Hamish's statement is correct, then Scotsmen should be preferentially hired in jobs that involve risks of rape such as teacher or priest.

Now, as explained in The Truth about Scotsmen, or: Dissolving Fallacies by Tesseract, most of those are consequences of "Scotsmen are less likely to rape" rather than "no true Scotsman would ever rape", but you could imagine a sociologist making a study showing that Scotsmen aren't less likely to rape, and Hamish saying "but no true Scotsman would do anything like that", so the question still exist. As you can see, all those statements depend on the statement "people from Scotland are less likely to rape", not "people who follow the Scottish Way of Life as defined by Hamish MacDonald are less likely to rape". As such, the No True Scotsman fallacy is properly understood as a form of equivocation between two different meanings of "Scotsmen".

Compare the argument between Alice and Bob. Why do we care about whether all Scotsmen are UK citizens ? How should your behavior change if most Scotsmen are UK citizens ? Well, a lot of things. For example, if most Scotsmen are UK citizens, then your new Uber For Kilts start-up should primarily care about UK business law. Here it is clear that no equivocation is going on: we clearly mean the ethnic group living in Scotland that is obsessed with kilts. Indeed it is Bob which is equivocating between "Scotsman" as "member of the ethnic group living in Scotland that is obsessed with kilts" and whatever definition he is using when he say Xi Jinping is a Scotsman.

Politics

Considering it is unlikely that many of this blog's readers will one day enter a discussion on the merits of Scotsmen, let's consider a more common use of the No True Scotsman Fallacy Fallacy: politics.

ALICE: I support cuddling puppies.

BOB: Cuddling puppies ? Isn't that a Blue policy ? Don't you know that Stalitler The Blue was an horrible dictator who killed 230 million of people through her policy of giving psychotic monkeys control over the economy ?

ALICE: Oh, but my Blue-ism involves more cuddling puppies and less giving psychotic monkeys control over the economy.

BOB: Won't any of you learn from the mistakes of past Blue regimes and stop supporting Blue policies ? I think Stalitler The Blue's death count is enough evidence against Blue ideology already.

ALICE: But Blue-ism means supporting cuddling puppies, Stalitler wasn't a real Blue !

BOB: You're using the No True Scotsman fallacy !

If you have ever made the mistake of wandering around lay political debates (or debates around religion, for that matter), you might recognize a common argument in this little dialogue. If you haven't, it's probably because you were on Bob's side and it's harder to notice bad arguments when they're used against your opponents. We can also use our new framework for understanding the No True Scotsman fallacy. Alice isn't equivocating between two definitions of Blue. She is consistently using "Blue" to mean "supporting cuddling puppies". It is, in fact, Bob who is equivocating between "Blue" meaning "supporting giving psychotic monkeys control over the economy" and "Blue" meaning "supporting cuddling puppies".

Conclusion

• A No True Scotsman fallacy involves the one committing the fallacy equivocating between two definitions of a term. For example, one may equivocate between "Scotsman" meaning "a person following the Scottish Way of Life" and "a person from Scotland".
• However, many arguments called out as an instance of the No True Scotsman fallacy aren't actually fallacious, because they don't involve equivocation. In fact, the person calling out the argument is generally the one committing equivocation between two definitions of a term.
• When faced by someone calling out someone else as committing the No True Scotsman fallacy, especially if the person making the calling out is on your side of an issue, check who is equivocating.