Who was that masked man?

The Masked Man Fallacy

Alias: Illicit Substitution of Identicals

Type: Formal Fallacy

Forms
a = b
Ca (where C is an intensional context).
Therefore, Cb.
Ca (where C is an intensional context).
Not-Cb.
Therefore, it is not the case that a = b.
Examples
The masked man is Mr. Hyde.
The witness believes that the masked man committed the crime.
Therefore, the witness believes that Mr. Hyde committed the crime.
The witness believes that the masked man committed the crime.
The witness doesn't believe that Mr. Hyde committed the crime.
Therefore, Mr. Hyde is not the masked man.
Counter-Examples
The masked man is Mr. Hyde.
The witness claims that the masked man committed the crime.
Therefore, the witness claims that Mr. Hyde committed the crime.
The witness claims that the masked man committed the crime.
The witness denies that Mr. Hyde committed the crime.
Therefore, Mr. Hyde is not the masked man.

Exposition:

Substitution of Identicals, also known as "Leibniz' Law", is a validating form of argument so long as the context in which it occurs is what is called "extensional", or "referentially transparent". What is an "intensional" or "referentially opaque" context? Basically, it's one in which Leibniz' Law does not hold! This is not very helpful, but the distinction can be drawn by examples:

Given that Mark Twain wrote Huck Finn and that Sam Clemens was the same person as Mark Twain, then Sam Clemens wrote Huck Finn. The context "x wrote Huck Finn" is extensional, which means that we can validly substitute identicals within it. In contrast, if Joe said "Mark Twain wrote Huck Finn", it does not follow that he said "Sam Clemens wrote Huck Finn", for he may have said no such thing. A quoted context is an intensional―or, referentially opaque―context, as are such other contexts as:

  • Propositional attitudes: belief, desire, fear, etc. A "propositional attitude" is a context that expresses the "attitude" of a person towards a proposition. For instance, consider the proposition "Satan exists". "Larry believes that Satan exists", "Curly desires that Satan exists", and "Moe fears that Satan exists", report propositional attitudes, specifically, the attitudes of Larry, Curly, and Moe towards the proposition that Satan exists.
  • Modal contexts: necessity, possibility, etc. Propositions involving modalities, such as necessity and related notions, are intensional. For example, it's true that Sam Clemens was necessarily identical to Sam Clemens. However, it is false that Sam Clemens was necessarily identical to Mark Twain, even though Sam Clemens was, in fact, identical to Mark Twain. Clemens could have chosen a different pen name, or died young, or decided not to be a writer, etc. It's the context of necessity here which makes the proposition intensional.

The Fallacy of Illicit Substitution of Identicals—or, more colorfully, "The Masked Man Fallacy"—is an application of Leibniz' Law within an intensional context. The most familiar uses of Substitution of Identicals are mathematical, where the contexts are always extensional. This may mislead one into thinking that substitution is valid in all contexts, but we have seen that this is not the case.

Source:

Ted Honderich (editor), The Oxford Companion to Philosophy, 1995.


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