Umm recursiveness?

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Simfish
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Main Question or Discussion Point

"Let the barber of Seville shave every man of Seville who does not shave himself.
Who shall shave the barber?"

So my book says that this is self-contradictory. but how?

From my reading of it, it's just that the barber of Seville shaves every man in Seville who doesn't shave themselves. Well the barber doesn't have to shave himself (or he could shave himself). So then someone else can shave the barber along with every man of Seville (and those who do not shave themselves can be shaved twice...)
 

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"Let the barber of Seville shave every man of Seville who does not shave himself.
Who shall shave the barber?"

So my book says that this is self-contradictory. but how?

From my reading of it, it's just that the barber of Seville shaves every man in Seville who doesn't shave themselves. Well the barber doesn't have to shave himself (or he could shave himself). So then someone else can shave the barber along with every man of Seville (and those who do not shave themselves can be shaved twice...)
If the barber is shaving others then others is not "himself". He cannot shave himself because he shaves those who don't shave themselves. Since he must shave those that don't shave themselves he must shave himself.

To your answer:
Note that it says "the barber" not "a barber" as was often the case in days past. If someone else shaves the barber he didn't shave himself therefore it violated the rule that the barber shave those that don't shave themselves. The act of shaving himself is a violation of the rule that he shaves those that don't shave themselves.

The self-contradiction is only a problem when formulated under strict rule sets, which is what mathematics is.
 
HallsofIvy
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Of course, there is no contradiction- the barber of Seville is a woman!

Also a more precise wording would be "The barber of Seville shaves every man in Seville who does not shave himself and does not shave any man who does shave himself. If we assume that the barber is a man in Seville then
1) He cannot shave himself because he "does not shave any man who does shave himself".
however,
2)he also cannot NOT shave himself because he "shaves every man in Seville who does not shave himself".
 
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