Re: [Fis] Simple question: What we really see in the mirror?
Dear Lou, dear Gordanna, On 22 Oct 2017, at 05:56, Louis H Kauffman wrote: 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. That is a very nice way to solve the paradox indeed, forcing us to make a little out-of-body experience! I would say that "This statement is false" is a "genuine paradox". And the machine's solution is that "false" is not definable as predicate (tarski solution). "this statement is unbelievable" go out of the paradox, not quite unlikely this Krassimir's solution, but it makes the statement true and definitely not believable except by going out of the body again, which machines can do, by the constructive diagonal involved. Best regards, Bruno Very best regards, Lou Kauffman On Oct 21, 2017, at 12:35 PM, Krassimir Markov 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
Re: [Fis] Simple question: What we really see in the mirror?
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 “Self-reference”! 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 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? 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
Re: [Fis] Simple question: What we really see in the mirror?
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
“Self-reference”!
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
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?
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
Re: [Fis] Simple question: What we really see in the mirror?
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 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 > > > > > ___ > Fis mailing list > Fis@listas.unizar.es > http://listas.unizar.
[Fis] Simple question: What we really see in the mirror?
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 ___ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
