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The Barber Paradox is given as: "In a village, there is a male barber who shaves only those who do not shave themselves. The question is: Does the barber shave himself?".

But, here is the problem: the barber himself is undeniably a man. Put simply, the same entity is referred to by two distinct identities: man and barber.

Can't we conclude, then, that the man, who happens also to be the barber, shaves himself? In other words, the barber does not shave himself, but the man, who happens to be a barber, shaves himself?

This interpretation resolves the paradox by recognising the dual identity of the man as both a barber and a man. What is wrong with this explanation?

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    It seems to violate the principle of the indiscernibility of identicals.
    – Bumble
    Jul 1, 2023 at 11:31

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Suppose we change the paradox to say that in the village there is a man who shaves all the men who do not shave themselves. How would you propose to apply your logic now?

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You are right to think that applying different descriptions to the same person might resolve the paradox. But not in this case.

If we define that role (in this context) as a person who shaves those who need it, we don't necessarily get the paradox. Which is why the statement of the paradox includes "male". Then you get the paradox.

Your solution doesn't work because a man who shaves those who need it is by definition a barber. It is true that in another village with a female barber, the paradox won't work. But that doesn't affect the paradox.

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Identity or "the entity" in this case is being mistaken for a pointer, name or reference. The pointers may have different labels but they point to the same entity. Resolving this entity is essential, and both "identities" resolve to the same entity. Dual identity is therefore an imaginary concept that does not really solve the paradox.

As you said, "the same entity is referred to by two distinct identities". Or in other words, you simply referred to "that entity" twice. Appending more pronouns or references does not mute identity, it simply comes up with another name for the same entity, which for logical consistency are necessarily equivalent.

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