This is a substantial revision, in the light of recent events, of an entry from about six years ago. This post examines the fallacy that Antony Flew brought to our attention and suggests that 'No True Muslim' is an equally good name for it.
In logic, a fallacy is not a false belief but a pattern of reasoning that is both typical and in some way specious. Specious reasoning, by the very etymology of the term, appears correct but is not. Thus a fallacy is not just any old mistake in reasoning, but a typical or recurrent mistake that has some tendency to seduce or mislead our thinking. A taxonomy of fallacies is useful insofar as it helps prevent one from seducing oneself or being seduced by others.
Fallacies are either formal or informal. An example of a formal fallacy is Affirming the Consequent. An example of an informal fallacy is Petitio Principii. Note than an argument that is formally valid can yet be informally fallacious. Arguments that beg the question are examples.
Among the so-called informal fallacies is Antony Flew's No True Scotsman. Suppose A says, "No Scotsman puts sugar in his porridge." B replies, "But my uncle Angus puts sugar in his porridge." A responds, "Your Uncle Angus is no true Scotsman!"
Second Example. Call it 'No True Muslim.' A says, "Islam is a religion of peace; Muslims do not do things like murder cartoonists and journalists with whose ideas they disagree." B replies, "On 7 January 2015, two Muslim gunmen forced their way into the offices of Charlie Hebdo in Paris, France and killed Stéphane Charbonnier, the editor of the satirical weekly, and several others." A responds, "Those gunmen were not true Muslims."
Third Example. A: "Nowadays all chess players use algebraic notation." B: "Not so, Ed Yetman does not use algebraic notation. He uses descriptive notation exclusively." A: "Ed Yetman? You call him a chess player?!"
Fourth Example. A: "When a complete neuroscience is achieved, we will know everything about mind, brain, and consciousness." B: "I can't agree, even a completed neuroscience will not explain how consciousness arises from brain activity." A: "A neuroscience that can't explain consciousness would not be a completed neuroscience."
Clearly, something has gone wrong in these examples. Person A is making an illicit dialectical move of some kind. The general form of the mistake seems to be as follows. Person A makes a universal assertion, one featuring a quantifier such as 'all,' 'no,' 'everything' whether explicit or tacit. Person B then adduces a counterexample to the universal claim. Person A illicitly dismisses the counterexample by modifying his original assertion with the use of 'true' or 'real' some equivalent designed to exclude the counterexample. Thus Uncle Angus is excluded as a counterexample by dismissing him as not a true Scotman, and the Muslim gunmen are excluded by dismissing them as not true Muslims.
The fallacy is informal since the fallaciousness depends on the content or subject matter. So we need to ask: When is it not a fallacy? By my count, there are at least four classes of cases in which the No True Scotsman move is not fallacious.
1. When the original assertion is either a logical truth or an analytic truth. If I point out that all bachelors are male, and you reply that your sister Mary is a bachelor, then I am justified in dismissing your 'counterexample' by saying that Mary is not a true bachelor, or a bachelor in the strict sense of the term.
2. When the original assertion is synthetic but necessary. If Saul Kripke is right, 'Water is H2O' is synthetic but necessary. If I say that water is H2O, and you object that heavy water is not H2O but D2O, then I am entitled to respond that heavy water is not water.
3. When the original assertion involves stipulation. Suppose Smith defines a naturalist as one who denies the existence of God, and I respond that McTaggart is an atheist who is not a naturalist. Have I shown that Smith is wrong? Not all. Smith may respond that McTaggart is not a naturalist as he defines the term. Wholly or partially stipulative definitions cannot be said to be either true or false although they can be more or less useful for classificatory purposes. Second example. Suppose Jack claims that libertarians favor open borders and Jill responds by adducing the case of libertarian John Jay Ray who does not favor open borders. Jack is within his epistemic rights in saying that Ray is not a full-fledged libertarian.
4. When the original assertion specifies the content of a belief-system or worldview. Suppose I point out that Communists are anti-religion, believing as they do that it is the opiate of the masses, an impediment to social progress, the sigh of the oppressed, flowers on the chains that enslave, etc. You say you know people who are Communists but are not against religion. I am entitled to the retort that such 'Communists' are not Communists at all; they are not true or real or genuine Communists, that they are CINOs, Commies in Name Only, etc. I have not committed the fallacy under discussion.
Back to the Muslims. A Muslim is so-called because of his adherence to the religion, Islam. There are certain core beliefs that are definitive of Islam, and thus essential to it, and that a Muslim must accept if he is to count as a Muslim. To take a blindingly evident example, no Muslim can be an atheist. Also: no Muslim can be a trinitarian, or a pantheist, or a polytheist, or believe in the Incarnation. And of course there are more specific doctrines about the Koran, about the prophet Muhammad, etc., that are essential to the faith of Muslims.
Now suppose I point out that Muslims deny that Jesus is the son of God. You reply that your Muslim friend Ali accepts that Jesus is the son of God. Then I commit no fallacy if I retort that Ali is no true Muslim.