FIS Colleagues:

I offer an alternative view of the Barber’s Paradox.  The term: barber does not refer to a person per se.  Rather it refers to a relationship between two persons, one of whom, when shaving another,  has the role: barber.  By extension, a barber is a person who provides that service.   When I provide shaving services to others, I am a barber; when I shave myself, I am not a barber.  The paradox arises from not recognizing that persons and roles are different entities.  With the following rephrasing, there is no paradox.

        Bob, being the only barber in town, shaves all and only those men who do not shave themselves.

Changing the subject from a service-provider role to a person makes it is clear that Bob is one of the men who shaves himself.

John Grisinger

On 10/22/2017 6:42 AM, Bruno Marchal wrote:
Dear Krassimir and 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

Thank you.

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

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).

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?

Hmm... Let say a village exists where the barber shaves all and only men who does not shave themselves (nor beard in that village!).

Then we have the logical paradox. If he does not shave himself he has to shave himself, by definition, and if he shaves himself, he shaves someone shaving himself, which he can't do.

The solution of the paradox is simple: there is no such village. (we cannot solve so easily the paradox of the set of all set which do not belong to themselves, though).

The idea of adding a "time parameter" is good though, and that is what make the notion of enumeration of all partal computable functions possible, but with the price that the one everywhere defined will be sparsed in an non computable way, leading to incompleteness and intrinsic ignorance.

Yet, if we cannot build a machine comprehending its own semantics, we can build a machine referring to any of its parts, including the whole part of itself, by the use of the second recursion theorem of Kleene, or Gödel self-reference. The basic idea is elementary: you apply a duplicator to its self description (in some universal machinery). If D'x' = 'x'x'', D'D' gives 'D'D'' (with a reasonable notion of quoting). Similarly if D'x' gives T('x'x''), D'D' gives T applied to itself T('D'D''). With the term "human", you might have added a piece of non 3p communicable insight, in which case you were referring, I guess, partially at least, to the non nameable first person transported by that 3p self. (in machines term: you have temporarily mixed []p with []p&p, which of course looks quite alike for the ideally sound machine, but it still obey different logics).



PS a more practical question: is this post my second post of last week, or my first post of next week? To which week sunday belongs?

Friendly greetings

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