06 Aug 11
1 edit
Originally posted by LemonJelloYes, it is a paradox.
ATY already gave the right response. Given your supposition, the barber shaves himself and it is wrong to say that it is reasonable to describe this barber by the rule you provide.
What you present is not a paradox. The "rule" you provide, though, would be where a paradox lies.
If the barber shaves himself, then he must not be shaved by the barber; only, when he does shave himself, he is being shaved by the barber. So the barber cannot shave himself.
And the barber hasn't the option to not shave at all because every man in the town keeps himself clean shaven.
And the barber hasn't the option to have someone else shave him, because anyone who doesn't shave himself must be shaved by the barber.
http://en.wikipedia.org/wiki/Barber_paradox
Edit: the barber's paradox is just a version of Russell's paradox, which arises in "naive set theory" when one attempt to define the set of all sets that are not elements of themselves:
http://en.wikipedia.org/wiki/Russell%27s_paradox
06 Aug 11
6 edits
Originally posted by SoothfastActually I think you may be correct that the OP still presents a "paradox". The wikipedia article actually presents it better because it makes it at least more explicit that each does one (only) of the two options (either shave himself or go to the barber). If you fail to specify this constraint, it does not work. I find the OP ambiguous on this.
Yes, it is a paradox.
If the barber shaves himself, then he must not be shaved by the barber; only, when he does shave himself, he is being shaved by the barber. So the barber cannot shave himself.
And the barber hasn't the option to not shave at all because every man in the town keeps himself clean shaven.
And the barber hasn't the op that are not elements of themselves:
http://en.wikipedia.org/wiki/Russell%27s_paradox
Of course, I realize there is a "paradox" captured within the concept of some male barber who lives is some town wherein he shaves all and only those men in that town who do not shave themselves. I think the concept is logically impossible. That was not the issue. The issue about the presentation is whether or not the initial statement actually translates faithfully to the supposed restatement (here, whether or not the "rule" is a faithful restatement of the preceding supposition). Here I definitely still think the OP is ambiguous on this and I would not let it pass strictly on face value. But it could still pass, I suppose.
06 Aug 11
Originally posted by LemonJelloThere is a bit of ambiguity in how the OP presented the situation. I almost said as much, but decided to let the Wikipedia article speak for itself.
Actually I think you may be correct that the OP still presents a "paradox". The wikipedia article actually presents it better because it makes it at least more explicit that each does one (only) of the two options (either shave himself or go to the barber). If you fail to specify this constraint, it does not work. I find the OP ambiguous on this.
Of ...[text shortened]... s and I would not let it pass strictly on face value. But it could still pass, I suppose.
10 Aug 11
Originally posted by SoothfastWell according to the OP the barber is specified with "He" so it is male, so being female is not in the specification. That still allows for the barber to be either too young to need shaving or to be older and he just has a beard and so doesn't need shaving. Either way, that satisfies the puzzle.
There is a bit of ambiguity in how the OP presented the situation. I almost said as much, but decided to let the Wikipedia article speak for itself.
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12 Aug 11
Originally posted by sonhouseNo, and no. In the original version of the riddle, the barber (who is male) shaves all men who do not shave themselves, and no man who does shave himself. No mention of whether they need it or not; if a man in the village does not shave himself, the barber does, beard or no beard. Being a bearded tit myself, I can assure you that a presentable beard does need shaving at the edges every now and then.
Well according to the OP the barber is specified with "He" so it is male, so being female is not in the specification. That still allows for the barber to be either too young to need shaving or to be older and he just has a beard and so doesn't need shaving. Either way, that satisfies the puzzle.
Richard
