Dear Krassimir,
Thank you!!
Yours is the most creative resolution of the Barber Paradox that I have 
encountered.
Perhaps we can apply it also to the Russell Paradox.
I do not know. Let us think about it.
Another paradox that is resolved in the human realm is the card that reads

################################################################
“No one holding this card can verify the truth of this statement inscribed upon 
it.”
################################################################

For a human holding the card can say “Suppose I were not holding the card. Then 
indeed the statement can be seen to be true
since if my friend Max were holding the card, then the statement would lead Max 
into a contradiction if he were to attempt to verify it.
Thus I have verified the statement on the card by imagining that I do not hold 
the card."

I submit that this solution (modal logical as it is) is a close relative of 
your mirror solution to the Barber.
For in your mirror solution the Barber must understand that he does not shave 
himself, but that he shaves his mirror image.
Similarly the card holder must imagine that he does not hold the card but that 
another holds the card.
Very best regards,
Lou Kauffman


> On Oct 21, 2017, at 12:35 PM, Krassimir Markov <mar...@foibg.com> wrote:
> 
> Dear FIS Colleagues,
> 
> It is time for my second post this week.
> 
> First of all I am glad to participate in such very interesting discussion!
> 
> Thank you for the nice posts.
> 
> More than 25 years ago, working on the new theory, I had to solve the
> problem with concept of entity which has information activity. There were
> many candidates for such concept: “robot”, “agent”, “intelligent agent”,
> “interpreter”, “subject”, “information subject”, “intelligent subject”,
> etc. Every such concept had its own history and many domains of meanings
> which caused many misunderstandings.
> In the same time, if one had a single meaning then it couldn’t be applied
> to all entities with information activity. For instance, concept “robot”
> is not good to be used for a human.
> 
> Because of this, we had proposed a new word: “INFOS”, which had no meaning
> in advance and may be defined freely without misunderstandings. I shall
> use it in my further posts.
> 
> I do not want to define it now. Step by step its meaning will arise from
> what I shall write. In many discussions till now, I had seen that this
> approach is the best way to introduce a new concept.
> 
> ***
> 
> I want specially to thank Bruno for his post from 18.10.2017 about
> “Self-reference”!
> 
> For me, it is very important it to be analyzed. I shall do this on the
> basis of an example.
> 
> Not all kinds of self-reference concern information activity and Infos.
> But, if at least one case exists, then we have to analyze it.
> 
> Such case, for instance, is the Barber paradox: A barber (who is a man)
> shaves all and only those men who do not shave themselves. Does he shave
> himself?
> 
> This paradox exists only in “3D” mathematical world based on triad
> (x, y, f)
> or, in other writings: (x, f, y), y=f(x), etc.
> (there are several nice publications of Mark Burgin about triads !).
> 
> I.e. paradox exists only if we ignore the fact that the Barber is a human.
> 
> The paradox could not exist in the “4D” world of informatics where we have
> quadruple (x, y, f, I) or, in other words, for Infos “I”, “y” is
> information about “x” because of evidence “f”.
> 
> What is happen when the Barber shaves someone?
> 
> At the first place, it is a direct collecting, by eyes, the data about the
> place where the razor has to be put to shave.
> 
> Have you ever seen a Blind barber?
> 
> NO! OK, this is a fundamental condition.
> 
> Not only Barber, but every human COULD NOT DIRECTLY COLLECT DATA about
> his/her face, head, or back.
> 
> In another case, for instance, we have to have eye on the end of the nose
> which has to be as long as the elephant trunk!
> 
> This means: the barber cannot shave himself because he could not see where
> to put the razor!
> 
> But every man can shave his beard! How he can do it?
> Of course, everyone will say, by using a mirror!
> 
> But this is NOT DIRECT REFLECTION (data collecting).
> It is TRANSITIVE SELF-REFLECTION via mirror!
> 
> Who does the barber shave: himself or the man in the mirror?
> 
> Of course, the second!!! Barber puts the razor on his own beard and this
> way he shaves the man in the mirror.
> 
> The Barber paradox does not exist if we take in account that the barber is
> a human (a kind of Infos) and needs data.
> 
> So, the answer of the question “Does he shave himself?“ is NO!, he
> doesn’t, he shaves the man in the mirror who do not shave himself because
> the razor is in the hand of barber and no paradox exists.
> 
> Simple question: What we really see in the mirror?
> 
> Friendly greetings
> Krassimir
> 
> 
> 
> 
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