2.3. The Principle of Induction

Example 2.3.11:

The barber of Seville is that inhabitant of Seville who shaves every man in Seville that does not shave himself
This is a paradox, because who will shave the barber of Seville himself ? This is actually and example of an invalid recursive definition: In the definition the barber appears twice: one as the defined entity "barber of Seville" and again as a member of all men living in Seville. Such a recursive definition is invalid, and in fact leads to a contradiction in this case.
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