I thought the same, but @Nemo2124 stated that '... all the men of Seville apart from himself.'
We have a good paradox or riddle here. The Barber of Seville can only be shaved by another barber from another city or village. The quid of this paradox is the location of the barber, because he is the Barber of Seville,' not a barber from anywhere else. So, the big paradox is he can only be shaved by another barber, but not from Seville.
Then, the Barber of Seville needed to go to another site to shave himself, because if there was another barber like him in Seville, he would not be the only barber in the city.
Reply to flannel jesus You don't have any clue about this linguistic paradox. Surprisingly! When you ranted on my posts about the staircase paradox.
You don't have any clue about this linguistic paradox.
This isn't a paradox. The sentence of the op is clearly, plainly, easily possible. Nothing remotely challenging about imagining a man shaving all men in his village except himself.
It will be very informative what you consider (and please explain) a paradox, because according to your posts, none of the previous threads are paradoxes.
The sentence of the op is clearly, plainly, easily possible. Nothing remotely challenging about imagining a man shaving all men in his village except himself.
That's where your mistake pops up. You only understand paradoxes as mathematical challenges against common sense. Again, this is a linguistic paradox, not something related to algebra.
We have a linguistic paradox here because of the following premises:
A) The Barber of Seville shaves all the men of Seville
B) Apart from himself.
And C) Who shaves the Barber of Seville then?
The paradox is that the Barber of Seville can shave everyone in Seville, but there is not another barber who can shave him.
If there are no more barbers in Seville apart from him... who shaves him, Sherlock?
Reply to javi2541997 someone from outside Seville, or someone who isn't a barber, or maybe there are more barbers in Seville but they aren't all called "the barber of Seville", and that title is reserved for him. All quite apparent solutions
Or maybe nobody shaves him, maybe he has a really long beard - or he doesn't grow a beard, because he's a trans man before the age of hrt
someone from outside Seville, or someone who isn't a barber,
You share my point then. It is a paradox because, although he is the one who shaves the people of Seville, there is not another who can shave him. So, he needs to leave the city to be shaved by a different barber of him.
Reply to flannel jesus Mate, this is not a simple story. If you are an expert at recognizing paradoxes, why do you not try to define them or at least explain how they work to me. I am still waiting for your answer.
I pour milk for everyone in my house except for me. Who pours milk for me?
The premise is badly written. The OP didnt say except but apart. This means if there is someone, apart from A, who can commit the action.
In the paradox of the OP, A is the barber, who shaves others in the same city. But, paradoxically, there cant be Y because there is not another barber apart from him. He can shave himself, but is there someone who can shave him?
The same happens in your irregular example. There could be a paradox if we say: you pour the milk for everyone in your house. You can pour the milk by yourself. But is there someone who could pour the milk apart from you?
Reply to flannel jesus See! It is a linguistic paradox. You are getting closer to the approach of this thread. :smile:
The text states that besides adds something to the clause. It means "plus". Except (of) means minus; it has a meaning of excluding something. Apart from is a combination of the two, meaning plus / minus depending on the context.
Apart from and except for are different things.
The first means plus. So, is there a barber in Seville apart from the one who shaves the people and himself? It is cumulative. There could be the possibility that others could shave the barber. But who If he is the only one in Seville?
The second means minus. Is there a barber except for the one who shaves others and himself? It is excluding. There cannot be a paradox because we already take for granted that the barber is the only one in Seville.
The first means plus. So, is there a barber in Seville apart from the one who shaves the people and himself? It is cumulative. There could be the possibility that others could shave the barber. But who If he is the only one in Seville?
The second means minus. Is there a barber except for the one who shaves others and himself? It is excluding. There cannot be a paradox because we already take for granted that the barber is the only one in Seville.
I'm not getting the impression from these words that you're entirely comfortable in English.
Reply to flannel jesus I know I am debating correctly when you dont know how to answer back to me rather than just attacking my English skills knowing that I am not a native speaker.
You give up on continuing debating on the paradox, right?
I didn't know that, and it's not meant to be an insult, but it is clear from all your language confusions in this thread. You're trying to correct me in ways you don't understand. If English really isn't your native language, then it would make sense for you to be a little more humble about your interpretations of these words, rather than latching on to some other persons confusions on stack exchange.
Reply to flannel jesus You are the one who is correcting me and highlighting my grammatical mistakes, mate
By the way, I tried to explain that except for and apart from are different. One is an adverb and the other is a preposition. When I translate into Spanish it makes a great difference if I use one or another in the sentence, but it seems in English it is not that important.
Lets leave it there. You just discovered I suck at a language I am not native to, and we derailed from the main point of the thread which is a paradox, not proofreading my sentences.
I experienced this before here in the forum. It is not the first time, and it will not be the last one
The Barber of Seville shaves those who don't shave themselves.
Who shaves the Barber then?
The barber of Seville sports a fine manicured beard, or else he shaves himself. Still no paradox.
To produce the paradox, the op needs rephrasing.
"The (male) Barber of Seville shaves all and only those men who do not shave themselves."
This Barber. who might be called @javi, or Jose, or Juan, some such throat clearing appellation, can only shave himself if he does not shave himself, and if he does shave himself, then he does not. Even the Spanish have some difficulty with learning to do this: British barbers regularly cut their clients throats instead and dispose of their bodies in meat pies, to avoid this sort of difficulty.
As mentioned, Russell's paradox is not "There is a b that shaves all who do not shave themselves except himself." Rather, Russell's paradox is "There is a b who shaves all and only those who do not shave themselves." Symbolized, Russell's paradox is:
Figaro shaved Bartolo, but not Rosina though she didn't shave herself, at least I don't think she did, but what do I know no matter, in a universe where Figaro is hairless, no such Figaro-shaving is applicable in the first place. Unless shaving a fake beard counts.
In this context, to claim that there is a paradox is to show how a contradiction is drawn. But there is no contradiction drawn from "The Barber of Seville shaves only the men of Seville who don't shave themselves". Three possibilities are each separately consistent with "The Barber of Seville shaves only the men of Seville who don't shave themselves": It is consistent that the barber is not shaven, and it is also consistent that the barber is shaved by someone who is not a man of Seville, and it is also consistent that the barber is shaved by someone who is a man of Seville.
(1) "The Barber of Seville shaves all the men of Seville apart from himself." [original post]
(2) "The Barber of Seville shaves only the men of Seville who don't shave themselves." [latest post]
Those are two different propositions.
Let 'Sx' stand for 'x is a man of Seville'.
Let 'Hxy' stand for 'x shaves y'.
(1) would be taken to mean "the barber is a man of Seville and if x is a man of Seville who is not the barber, then the barber shaves x", and probably tacit is "the barber does not shave himself".
Sb & Ax((Sx & ~x=b) -> Hbx) & ~Hbb
(2) would be taken to mean "the barber is a man of Seville and if the barber shaves x, then x is a man of Seville who does not shave himself."
Sb & (Hbx -> (Sx & ~Hxx))
But neither (1) nor (2) are paradoxical.
With (1) it is consistent that the barber is not shaven: ~Ex Hxb, and it is also consistent with (1) that the barber is shaved by someone who is not a man of Seville: Ex(~Sx & Hxb), and it is also consistent with (1) that the barber is shaved by someone who is a man of Seville: Ex(Sx & Hxb).
With (2) it is consistent that the barber is not shaven: ~Ex Hxb, and it is also consistent with (2) that the barber is shaved by someone who is not a man of Seville: Ex(~Sx & Hxb), and it is also consistent with (2) that the barber is shaved by someone who is a man of Seville: Ex(Sx & Hxb).
/
The actual contradictory formulation is (and we don't even need to mention maleness, a location such as Seville, or being a barber):
There is someone who shaves all and only those who do not shave themselves:
EbAx(Hbx <-> ~Hxx)
Put another way:
There is someone b such that for all x, if b shaves x then x does not shave x and if x does not shave x then b shaves x:
EbAx((Hbx -> ~Hxx) & (~Hxx -> Hbx))
TonesInDeepFreezeMay 25, 2024 at 19:57#9066320 likes
We could add that men of Seville are shaved only by men of Seville and that every man of Seville is shaved, and still we would not have a paradox in either case (1a) or (2a):
(1a) The barber is a man of Seville, and the barber shaves all the men of Seville who are not the barber, and the barber does not shave himself, and every man of Seville is shaved by a man of Seville.
It is consistent that the barber is shaved by a man of Seville:
Ey(Sy & Hyb)
(2a) The barber is a man of Seville, and the barber shaves only the men of Seville who do not shave themselves, and the barber does not shave himself, and every man of Seville is shaved by a man of Seville.
'the barber of Seville' is a definite description. There are different ways of handling definite descriptions, including, at least, both the Fregean and Russellian. To bring that complication into the example would require being exact in how we do it.
In any case, one can shave a person without being a barber. So, still, there is no paradox.
On the other hand, you could add a premise: There is one and only one man in Seville who does any shaving.
E!x(Sx & Ey Hxy)
But that premise is not in your statements.
Why don't you just look up the barber paradox to see that it involves:
one who shaves all and only those who do not shave themselves
You have to have both - all of those and only those.
If you say, "there is someone who shaves all and only those who do not shave themselves" then you do have a contradiction.
TonesInDeepFreezeMay 25, 2024 at 22:11#9066550 likes
To reiterate, the paradox doesn't even need any mention of maleness, barbers, towns or even humans. It is best seen in its starkest form:
Something shaves all and only those that do not shave themselves. Contradiction.
For set theory (replacing the 2-place relation 'shaves' with the 2-place relation 'is a member of'):
There is an x that such that for all y, y is a member of x if and only if y is not a member of y. Contradiction.
And most generally, in logic alone, for any 2-place relation R:
There is an x such that for all y, x bears the relation R to y if and only y does not bear the relation R to y. Contradiction.
In any case, one can shave a person without being a barber. So, still, there is no paradox.
Yes, but can you shave a barber without being to a certain extent a barber yourself? What I mean to say is this, that if a barber has someone else shave him, that person would require a degree of professionality, otherwise the role would cease to exist. This is also what the paradox is alluding to when you include the social setting of Seville. If you have a barber who has an amateur shave him, then he is diminishing his profession. I think there is a logical way to approach this paradox, but what is more interesting for me is to discover whether one can advance one's understanding of how society works.
TonesInDeepFreezeMay 25, 2024 at 23:15#9066630 likes
Such utterly incidental questions as to the meaning of 'barber' can't seriously be considered part of the subject of paradox.
Anyway, looking in several dictionaries, I find that merely shaving someone does not constitute being a barber.
Again, if you add the premise that there is only one man in Seville who does any shaving (viz. the barber), and that the barber does not shave himself, but that every man in Seville is shaved is by some man in Seville, then of course that is a contradiction. But so what?
On the other hand, if, as you now suggest, you're interested in looking at the subject of tonsorial practices in various societies, then you don't need Russell's paradox for that.
/
Yes, there is a logical way to look at the paradox. The most obvious is to observe the theorem of logic:
~ExAy(Rxy <-> ~Ryy)
which in set theory yields:
~ExAy(xey <-> ~yey)
"there is no set of all the sets that are not members of themselves"
The perspective I am advancing is the meaning of the paradox. This is interpretation. There are different approaches as has been shown here. So there's the logical aspect, the interpretive aspect and others perhaps. The Barber paradox is well-known and also alludes to Russell's paradox. I am not going to confine myself to purely logic here.
Take the Millet seed paradox. One seed falling on the ground makes no sound. Take a fistful, a thousand and they make a noise. How could something that makes no noise individually make noise collectively. Now you could approach this paradox from different angles (e.g. the collective over the individual). That's what I understand to be, in principle, interesting about them.
A paradox is like a puzzle without a definitive answer.
A function cannot be its own argument, because the functional sign already contains the prototype of its own argument and it cannot contain itself.
If, for example, we suppose that the function F(fx) could be its own argument, then there would be a proposition F(F(fx)), and in this the outer function F and the inner function F must have different meanings; for the inner has the form ?(fx), the outer the form ?(?(fx)). Common to both functions is only the letter F, which by itself signifies nothing.
This is at once clear, if instead of F(F(u)) we write (??) : F(?u) . ?u = Fu.
Of course there are many kinds of paradoxes ranging formal to informal. But you referred to Russell's barber paradox, which is an informal illustration standing for concerns in logic and mathematics, so I wrote in that context.
In any case, hopefully now you see that your presentations of Russell's barber paradox were incorrect and not paradoxes since they have easy non-perplexing answers.
Comments (44)
Rephrase: Joe, the Barber of Seville... etc.
I don't think this does it justice, so it remains a paradox.
That's all folks.
I thought the same, but @Nemo2124 stated that '... all the men of Seville apart from himself.'
We have a good paradox or riddle here. The Barber of Seville can only be shaved by another barber from another city or village. The quid of this paradox is the location of the barber, because he is the Barber of Seville,' not a barber from anywhere else. So, the big paradox is he can only be shaved by another barber, but not from Seville.
Then, the Barber of Seville needed to go to another site to shave himself, because if there was another barber like him in Seville, he would not be the only barber in the city.
You don't have any clue about this linguistic paradox. Surprisingly! When you ranted on my posts about the staircase paradox.
This isn't a paradox. The sentence of the op is clearly, plainly, easily possible. Nothing remotely challenging about imagining a man shaving all men in his village except himself.
Should have been:
The Barber of Seville shaves those who don't shave themselves.
Who shaves the Barber then?
It will be very informative what you consider (and please explain) a paradox, because according to your posts, none of the previous threads are paradoxes.
Quoting flannel jesus
That's where your mistake pops up. You only understand paradoxes as mathematical challenges against common sense. Again, this is a linguistic paradox, not something related to algebra.
We have a linguistic paradox here because of the following premises:
A) The Barber of Seville shaves all the men of Seville
B) Apart from himself.
And C) Who shaves the Barber of Seville then?
The paradox is that the Barber of Seville can shave everyone in Seville, but there is not another barber who can shave him.
If there are no more barbers in Seville apart from him... who shaves him, Sherlock?
Or maybe nobody shaves him, maybe he has a really long beard - or he doesn't grow a beard, because he's a trans man before the age of hrt
No. There aren't more barbers in Seville, this is the key of the paradox.
Quoting flannel jesus
You share my point then. It is a paradox because, although he is the one who shaves the people of Seville, there is not another who can shave him. So, he needs to leave the city to be shaved by a different barber of him.
Quoting flannel jesus
It is not about if someone shaves him or not, but if there is a possibility to be shaved in Seville by a different barber apart from him!
Quoting flannel jesus
You haven't explained what is a paradox yet! :blush:
A paradox certainly ISN'T a simple story, ended with a simple question that has a simple answer.
I pour milk for everyone in my house except for me. Who pours milk for me?
On the other hand
Quoting flannel jesus
The premise is badly written. The OP didnt say except but apart. This means if there is someone, apart from A, who can commit the action.
In the paradox of the OP, A is the barber, who shaves others in the same city. But, paradoxically, there cant be Y because there is not another barber apart from him. He can shave himself, but is there someone who can shave him?
The same happens in your irregular example. There could be a paradox if we say: you pour the milk for everyone in your house. You can pour the milk by yourself. But is there someone who could pour the milk apart from you?
Merriam: Other than, Besides, except for
You're stretching really far for all this my man.
https://english.stackexchange.com/questions/565669/difference-between-besides-apart-from-and-except-for-prepositions-vs-adv#:~:text=Except%20(of)%20means%20minus%3B,minus%20depending%20on%20the%20context.
Apart from and except for are different things.
The first means plus. So, is there a barber in Seville apart from the one who shaves the people and himself? It is cumulative. There could be the possibility that others could shave the barber. But who If he is the only one in Seville?
The second means minus. Is there a barber except for the one who shaves others and himself? It is excluding. There cannot be a paradox because we already take for granted that the barber is the only one in Seville.
I'm not getting the impression from these words that you're entirely comfortable in English.
You give up on continuing debating on the paradox, right?
I didn't know that, and it's not meant to be an insult, but it is clear from all your language confusions in this thread. You're trying to correct me in ways you don't understand. If English really isn't your native language, then it would make sense for you to be a little more humble about your interpretations of these words, rather than latching on to some other persons confusions on stack exchange.
I never debated a paradox here, there isn't one.
By the way, I tried to explain that except for and apart from are different. One is an adverb and the other is a preposition. When I translate into Spanish it makes a great difference if I use one or another in the sentence, but it seems in English it is not that important.
Lets leave it there. You just discovered I suck at a language I am not native to, and we derailed from the main point of the thread which is a paradox, not proofreading my sentences.
I experienced this before here in the forum. It is not the first time, and it will not be the last one
Really? So it wasn't you who started the conversation about my use of "except"? I think it was.
Quoting javi2541997
You started the semantic conversation, and now you're crying victim.
Let's leave it there. Sure. You're the victim, let's all shed a tear for javi.
Quoting jorndoe
The barber of Seville sports a fine manicured beard, or else he shaves himself. Still no paradox.
To produce the paradox, the op needs rephrasing.
"The (male) Barber of Seville shaves all and only those men who do not shave themselves."
This Barber. who might be called @javi, or Jose, or Juan, some such throat clearing appellation, can only shave himself if he does not shave himself, and if he does shave himself, then he does not. Even the Spanish have some difficulty with learning to do this: British barbers regularly cut their clients throats instead and dispose of their bodies in meat pies, to avoid this sort of difficulty.
The USians contract it out and sell the meat pies to various NGO's funded by grants who distribute it to those "in need"
Symbolize:
Sy <-> y lives in Seville
My <-> y is a man
Hxy <-> x shaves y
Premises:
Sb & Mb
Ay((Sy & My & ~y=b) -> Hby)
~Hbb
Consistent with those premises:
~Ey Hyb
Ey Hyb
There is no paradox in any of this.
As mentioned, Russell's paradox is not "There is a b that shaves all who do not shave themselves except himself." Rather, Russell's paradox is "There is a b who shaves all and only those who do not shave themselves." Symbolized, Russell's paradox is:
Ay(Hby <-> ~Hyy)
Quoting unenlightened
Canadians append a verbal "Sorry". :D
So, anyway, does the King of France shave himself or not? More importantly, have you stopped shaving your palms yet, well, have you?
But I think that the best answer will be that the Barber of Seville is female.
Now I am going to look at the answer
Does the Barber of Seville shave himself?
There's the paradox...
In this context, to claim that there is a paradox is to show how a contradiction is drawn. But there is no contradiction drawn from "The Barber of Seville shaves only the men of Seville who don't shave themselves". Three possibilities are each separately consistent with "The Barber of Seville shaves only the men of Seville who don't shave themselves": It is consistent that the barber is not shaven, and it is also consistent that the barber is shaved by someone who is not a man of Seville, and it is also consistent that the barber is shaved by someone who is a man of Seville.
(1) "The Barber of Seville shaves all the men of Seville apart from himself." [original post]
(2) "The Barber of Seville shaves only the men of Seville who don't shave themselves." [latest post]
Those are two different propositions.
Let 'Sx' stand for 'x is a man of Seville'.
Let 'Hxy' stand for 'x shaves y'.
(1) would be taken to mean "the barber is a man of Seville and if x is a man of Seville who is not the barber, then the barber shaves x", and probably tacit is "the barber does not shave himself".
Sb & Ax((Sx & ~x=b) -> Hbx) & ~Hbb
(2) would be taken to mean "the barber is a man of Seville and if the barber shaves x, then x is a man of Seville who does not shave himself."
Sb & (Hbx -> (Sx & ~Hxx))
But neither (1) nor (2) are paradoxical.
With (1) it is consistent that the barber is not shaven: ~Ex Hxb, and it is also consistent with (1) that the barber is shaved by someone who is not a man of Seville: Ex(~Sx & Hxb), and it is also consistent with (1) that the barber is shaved by someone who is a man of Seville: Ex(Sx & Hxb).
With (2) it is consistent that the barber is not shaven: ~Ex Hxb, and it is also consistent with (2) that the barber is shaved by someone who is not a man of Seville: Ex(~Sx & Hxb), and it is also consistent with (2) that the barber is shaved by someone who is a man of Seville: Ex(Sx & Hxb).
/
The actual contradictory formulation is (and we don't even need to mention maleness, a location such as Seville, or being a barber):
There is someone who shaves all and only those who do not shave themselves:
EbAx(Hbx <-> ~Hxx)
Put another way:
There is someone b such that for all x, if b shaves x then x does not shave x and if x does not shave x then b shaves x:
EbAx((Hbx -> ~Hxx) & (~Hxx -> Hbx))
(1a) The barber is a man of Seville, and the barber shaves all the men of Seville who are not the barber, and the barber does not shave himself, and every man of Seville is shaved by a man of Seville.
Sb &
Ax((Sx & ~x=b) -> Hbx) &
~Hbb &
Ax(Sx -> Ey(Sy & Hyx))
It is consistent that the barber is shaved by a man of Seville:
Ey(Sy & Hyb)
(2a) The barber is a man of Seville, and the barber shaves only the men of Seville who do not shave themselves, and the barber does not shave himself, and every man of Seville is shaved by a man of Seville.
Sb &
Hbx -> (Sx & ~Hxx) &
~Hbb &
Ax(Sx -> Ey(Sy & Hyx))
It is consistent that the barber is shaved by a man of Seville:
Ey(Sy & Hyb)
Consistency proof for both (1a) and (2a)
Let the universe be {barber, Charlie}
Let the men of Seville be {barber, Charlie}
Let the barber shave Charlie and Charlie shave the barber.
Symbolized:
U = {b c}
S = {b c}
H = {
Then that person becomes 'the' Barber of Seville, so that's not consistent.
'the barber of Seville' is a definite description. There are different ways of handling definite descriptions, including, at least, both the Fregean and Russellian. To bring that complication into the example would require being exact in how we do it.
In any case, one can shave a person without being a barber. So, still, there is no paradox.
On the other hand, you could add a premise: There is one and only one man in Seville who does any shaving.
E!x(Sx & Ey Hxy)
But that premise is not in your statements.
Why don't you just look up the barber paradox to see that it involves:
one who shaves all and only those who do not shave themselves
You have to have both - all of those and only those.
If you say, "there is someone who shaves all and only those who do not shave themselves" then you do have a contradiction.
Something shaves all and only those that do not shave themselves. Contradiction.
For set theory (replacing the 2-place relation 'shaves' with the 2-place relation 'is a member of'):
There is an x that such that for all y, y is a member of x if and only if y is not a member of y. Contradiction.
And most generally, in logic alone, for any 2-place relation R:
There is an x such that for all y, x bears the relation R to y if and only y does not bear the relation R to y. Contradiction.
In symbols:
ExAy(Rxy <-> ~Ryy). Contradiction.
Yes, but can you shave a barber without being to a certain extent a barber yourself? What I mean to say is this, that if a barber has someone else shave him, that person would require a degree of professionality, otherwise the role would cease to exist. This is also what the paradox is alluding to when you include the social setting of Seville. If you have a barber who has an amateur shave him, then he is diminishing his profession. I think there is a logical way to approach this paradox, but what is more interesting for me is to discover whether one can advance one's understanding of how society works.
Anyway, looking in several dictionaries, I find that merely shaving someone does not constitute being a barber.
Again, if you add the premise that there is only one man in Seville who does any shaving (viz. the barber), and that the barber does not shave himself, but that every man in Seville is shaved is by some man in Seville, then of course that is a contradiction. But so what?
On the other hand, if, as you now suggest, you're interested in looking at the subject of tonsorial practices in various societies, then you don't need Russell's paradox for that.
/
Yes, there is a logical way to look at the paradox. The most obvious is to observe the theorem of logic:
~ExAy(Rxy <-> ~Ryy)
which in set theory yields:
~ExAy(xey <-> ~yey)
"there is no set of all the sets that are not members of themselves"
which in set theory yields:
~ExAy yex
"there is no set of all sets"
Take the Millet seed paradox. One seed falling on the ground makes no sound. Take a fistful, a thousand and they make a noise. How could something that makes no noise individually make noise collectively. Now you could approach this paradox from different angles (e.g. the collective over the individual). That's what I understand to be, in principle, interesting about them.
A paradox is like a puzzle without a definitive answer.
I'll leave it at that.
"You shall be careful with self-reference."
Quoting Wittgenstein
I'm guessing these sorts of things show up elsewhere as well.
Of course there are many kinds of paradoxes ranging formal to informal. But you referred to Russell's barber paradox, which is an informal illustration standing for concerns in logic and mathematics, so I wrote in that context.
In any case, hopefully now you see that your presentations of Russell's barber paradox were incorrect and not paradoxes since they have easy non-perplexing answers.
No, it does appear as if my original expositions of the paradox were erroneous.
That said, it is difficult to find a definitive version on the web.
The Barber of Seville remains elusive.
Clear versions are available on the Internet. Moreover, I stated clear versions in this thread. Here again, in greatest generality:
Someone shaves all and only those who do not shave themselves.