Discussion:
What are the early references to self referencing sentences in literature?
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Marko Manninen
2017-12-18 11:20:32 UTC
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We know greek paradoxes in many forms like "this sentence is a lie" or "all Cretans are liars" coming from the mouth of a Cretan.

Do we have similar examples from other sources like semitic, early indo european languages, sumerian etc?

I'm also interested of the development of the language and human mind to comprehend this kind of self referencing paradoxes. If anyone can give further useful reading I'd appreciate it.

Something like answering questions about features necessary for a language to support this, do we have languages that doesnt support self reference by design, or just by the fact that people using language really just dont need it in a society they are living, etc.

BR,
Marko
Franz Gnaedinger
2017-12-21 08:19:02 UTC
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Post by Marko Manninen
We know greek paradoxes in many forms like "this sentence is a lie" or "all Cretans are liars" coming from the mouth of a Cretan.
Do we have similar examples from other sources like semitic, early indo european languages, sumerian etc?
I'm also interested of the development of the language and human mind to comprehend this kind of self referencing paradoxes. If anyone can give further useful reading I'd appreciate it.
Something like answering questions about features necessary for a language to support this, do we have languages that doesnt support self reference by design, or just by the fact that people using language really just dont need it in a society they are living, etc.
BR,
Marko
A Cretan says all Cretans are liars ... The paradox arises when you reduce
natural logic to mathematical logic

mathematical logic a = a

natural logic all is equal, all unequal ... (Goethe)

Psychologists are telling us that we lie twenty times a day or more, so we all
are liars, including the Cretans. In mathematical logic there are only false
or true statements, the false ones completely false, the true ones completely
true. Actual lies are a blend of true and false. Professional liars know that
and tell a lot of truisms in order to gain confidence, and only then place
their profitable lie that is again embedded in true statements - they don't
lie all the time as in mathematical logic.

If you ask for self-reference, you can find that in art. René Magritte
famously painted a pipe and wrote on the canvas, under the pipe: Ceci
n'est pas une pipe, This is not a pipe. Which is wrong, the picture shows
a pipe, but also true, because the pipe is not an actual pipe, just a piece
of canvas with added color.

A higher form of self-reflection is found in Leonardo da Vinci. He represented
himself as John the Baptist who announced a greater one than himself, God,
creator of the world that surpasses all human works in completeness and
brillance. Look at Leonardo's last painting. John, before leaving us, already
half caught by the dark shadows of the background, turns around once more,
smiling, pointing with his bright right hand skyward, and with his left hand
- Leonardo was a left-hander - on his own chest, but this hand, symbolizing
his own work, including his last painting, is half covered by the right arm,
and shadowy compared to the shining raised hand that symbolizes God's work,
nature.
Helmut Richter
2017-12-21 09:13:38 UTC
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Post by Franz Gnaedinger
A Cretan says all Cretans are liars ... The paradox arises when you reduce
natural logic to mathematical logic
It arises when do this reduction in a way that is wrong in either
every-day or mathematical logic.

In this case, the mistake is the missing definition of "liar". Is it a
person who consistently and reliably always utters untrue statements? Or
a person on whose statements you can never rely because you do never
know when he will lie and when not?

In daily life, a "liar" is the second type of person, and the paradox is
not a paradox any more.

Ambiguous or missing definitions are one of the main sources of wrong
logic, irrespective of whether it is clad in mathematical notation.
--
Helmut Richter
Franz Gnaedinger
2017-12-22 07:35:28 UTC
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Post by Helmut Richter
Post by Franz Gnaedinger
A Cretan says all Cretans are liars ... The paradox arises when you reduce
natural logic to mathematical logic
It arises when do this reduction in a way that is wrong in either
every-day or mathematical logic.
In this case, the mistake is the missing definition of "liar". Is it a
person who consistently and reliably always utters untrue statements? Or
a person on whose statements you can never rely because you do never
know when he will lie and when not?
In daily life, a "liar" is the second type of person, and the paradox is
not a paradox any more.
Ambiguous or missing definitions are one of the main sources of wrong
logic, irrespective of whether it is clad in mathematical notation.
That is another formulation of what I say: natural logic speaks of human
beings who embody the logic of equal unequal (Goethe: all is equal, all
unequal) and mathematical logic of abstractions, of numbers and objects
that embody the logic of a = a. A natural liar belongs to the logic of
equal unequal, a mathematically defined liar to the logic of a = a.
wugi
2017-12-31 11:57:44 UTC
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Post by Helmut Richter
Post by Franz Gnaedinger
A Cretan says all Cretans are liars ... The paradox arises when you reduce
natural logic to mathematical logic
It arises when do this reduction in a way that is wrong in either
every-day or mathematical logic.
In this case, the mistake is the missing definition of "liar". Is it a
person who consistently and reliably always utters untrue statements? Or
a person on whose statements you can never rely because you do never
know when he will lie and when not?
In daily life, a "liar" is the second type of person, and the paradox is
not a paradox any more.
Ambiguous or missing definitions are one of the main sources of wrong
logic, irrespective of whether it is clad in mathematical notation.
Ambiguous definitions are one source, ambiguous reference frames
another. I try to explain the latter:

In mathematics as well as in the 'real world', a falsifiable statement
is something (A) that is said, about something (B) else, in the world
'out there'. When I say 'The weather is nice' (A), I'm saying it about a
phenomenon, the weather (B) outside of my statement's frame; and it may
be verified independently. Similarly, when I say 'Parallel straight
curves don't intersect' (A), none of these objects and properties (B)
belong themselves to the frame of my statement A.

But when I say 'What I tell now is a lie' (A), the thing I'm talking
about (A) is not something outside there, but belongs itself to the
frame of my statement! There is no independent
falsification-verification method. It is a statement that apparently
respects linguistic and/or mathematical syntax. But it is a void
statement, nothing falsifyable.

The liars' paradoxes are in this vein of void statements. They are a
feature of self-referentiality (or mutual self-reference, eg: A says 'B
is telling the truth', B says 'A is lying').


An example of the other source of confusion, ambiguous definitions, is
in the barber paradox.
The barber shaves all men in the village who don't shave themselves.
Does the barber shave himself?
The solution is in realising that the definition is incomplete WRT the
barber himself. So, depending on the case, the statement has to be
finetuned to:
1) The barber shaves all men who don't shave themselves, AND himself. Or
2) The barber shaves all men who don't shave themselves, EXCEPT himself.


In mathematical set theory, avoiding (mutual) self-reference has to do
with the distinction between element and set. A set should be distinct
from its element(s). An element can't be identical to its defining set
and vice versa. A set mustn't be describing itself, but something 'out
there'.
And as for ambiguous definitions, the equivalence of the barber paradox
is here Bertrand Russell's set of 'All sets which don't contain
themselves as an element'. Does this set contain itself? (And my
solution is similar to the barber paradox's. But it goes against the
distinction element/set anyway :-).
--
guido wugi
Franz Gnaedinger
2018-01-04 07:30:53 UTC
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Post by wugi
An example of the other source of confusion, ambiguous definitions, is
in the barber paradox.
The barber shaves all men in the village who don't shave themselves.
Does the barber shave himself?
The solution is in realising that the definition is incomplete WRT the
barber himself. So, depending on the case, the statement has to be
1) The barber shaves all men who don't shave themselves, AND himself. Or
2) The barber shaves all men who don't shave themselves, EXCEPT himself.
Natural logic will always find a way around the barber paradox, no matter how
you formulate it:

A village has only one barber, and he shaves all men who don't shave
themselves ...

Well, a literary mind can assume that the barber grows a beard, and when he
needs a shaving he goes to the barber of the neighboring village, a friend
of his, and they use the occasion for a chat over a glass of Ouzo, or rather,
in the olden days, a mug of fermented honey mixed with water.

In the light of natural logic also Goedel becomes easily understandable.
He proved that mathematical logic is not logic per se, but a secluded realm
that is not really separated from natural logic but must be secured by strict
albeit arbitrary rules, for example divisions by zero are forbidden, because
they yield infinite, which is equal unequal in itself, and thus lead from
the mathematical logic of a = a to the natural logic of equal unequal,
as formulated by Goethe: All is equal, all unequal ...
Gerd Thieme
2018-01-04 11:11:56 UTC
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Post by wugi
The barber shaves all men in the village who don't shave themselves.
Does the barber shave himself?
The solution is in realising that the definition is incomplete WRT the
barber himself.
No, it is not incomplete at all. It is more than just complete: it’s
contradictory. The usual consequence of such a contradiction is:

_The barber does not exist._

Denying the barber’s existence solves this riddle completely. So, it’s
not even a paradox.

Gerd

Franz Gnaedinger
2017-12-22 07:45:25 UTC
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Post by Franz Gnaedinger
A Cretan says all Cretans are liars ... The paradox arises when you reduce
natural logic to mathematical logic
mathematical logic a = a
natural logic all is equal, all unequal ... (Goethe)
Psychologists are telling us that we lie twenty times a day or more, so we all
are liars, including the Cretans. In mathematical logic there are only false
or true statements, the false ones completely false, the true ones completely
true. Actual lies are a blend of true and false. Professional liars know that
and tell a lot of truisms in order to gain confidence, and only then place
their profitable lie that is again embedded in true statements - they don't
lie all the time as in mathematical logic.
If you ask for self-reference, you can find that in art. René Magritte
famously painted a pipe and wrote on the canvas, under the pipe: Ceci
n'est pas une pipe, This is not a pipe. Which is wrong, the picture shows
a pipe, but also true, because the pipe is not an actual pipe, just a piece
of canvas with added color.
A higher form of self-reflection is found in Leonardo da Vinci. He represented
himself as John the Baptist who announced a greater one than himself, God,
creator of the world that surpasses all human works in completeness and
brillance. Look at Leonardo's last painting. John, before leaving us, already
half caught by the dark shadows of the background, turns around once more,
smiling, pointing with his bright right hand skyward, and with his left hand
- Leonardo was a left-hander - on his own chest, but this hand, symbolizing
his own work, including his last painting, is half covered by the right arm,
and shadowy compared to the shining raised hand that symbolizes God's work,
nature.
Now let us go from Leonardo da Vinci to Edward de Vere alias William
Shakespeare

William
Will I am
a strong will personified
Shakespeare
shaking my spear
wielding my sword
which is my word
my elegant and powerful word

Leonardo's late drawings of storm and flood might have inspired The Tempest.
In Prospero one can recognize Leonardo, in his daughter Miranda (literally:
She to be looked at and admired as a miracle) his art, also art in general,
including the play by Shakespeare, and in her husband Ferdinand, son to
the king of Naples, political power.

What are Miranda and Ferdinand doing on their honeymoon? Play at chess!
No loving couple would do that, so they are symbols - of art and political
power respectively that maintain a complicated relationship. Edward de Vere
knew about those complications from his experience at the court of England.

I discern between art and a work of art.

Art is the human measure in a technical world, and a work of art is kind
of a formula based on the logic of equal unequal (Goethe: all is equal,
all unequal), parallel to a mathematical formula based on the logic of a = a.
Implementing art in society requires great skill. Think for example of the
Usenet, and of the Web in general.
Franz Gnaedinger
2018-01-03 08:45:12 UTC
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Post by Franz Gnaedinger
Now let us go from Leonardo da Vinci to Edward de Vere alias William
Shakespeare
William
Will I am
a strong will personified
Shakespeare
shaking my spear
wielding my sword
which is my word
my elegant and powerful word
Leonardo's late drawings of storm and flood might have inspired The Tempest.
She to be looked at and admired as a miracle) his art, also art in general,
including the play by Shakespeare, and in her husband Ferdinand, son to
the king of Naples, political power.
What are Miranda and Ferdinand doing on their honeymoon? Play at chess!
No loving couple would do that, so they are symbols - of art and political
power respectively that maintain a complicated relationship. Edward de Vere
knew about those complications from his experience at the court of England.
I discern between art and a work of art.
Art is the human measure in a technical world, and a work of art is kind
of a formula based on the logic of equal unequal (Goethe: all is equal,
all unequal), parallel to a mathematical formula based on the logic of a = a.
Implementing art in society requires great skill. Think for example of the
Usenet, and of the Web in general.
If you google for

"lying cretans in literature"

you can find for example this link

https://books.google.ch/books?id=CyxtzAVVNukC&pg=PA71&lpg=PA71&dq=lying+cretans+in+literature&source=bl&ots=z9NP0QgCEx&sig=0voEKeS9J_R-arLpipgE0O8ULOo&hl=en&sa=X&ved=0ahUKEwja5tOpr7vYAhVB2KQKHSH_AqAQ6AEIQDAE#v=onepage&q=lying%20cretans%20in%20literature&f=false

with a discussion of the lying Cretans in Ovid and in Callimachus' hymn.

From my humanistic schooldays I vaguely remember a joking reference to
the lying Cretans, but the author was not intrigued by the paradox.
Literature can't be fettered by the mathematical logic of a = a. Instead
it follows and explores the wider logic of equal unequal.

The journeys of Odysseus are dreams. Returned home, the hero - "if ever
there was such a man" - sleeps on the shore. A long series of dreams bring
him back to Troy, Troy in disguise, and blended with other places and periods
of time. In his first dream he encounters the one-eyed giant Polyphem who
resembles more a wooded mountain top than a man who eats bread - Homeric
symbol of Troy VIIa, his one eye the acropolis overlooking the wider river
plain, his body donwntown Troy VIIa that provided protected shelter for
5,000 to 10,000 people. And in his last dream he reaches the shore of pleasant
Scherie, identified as an early Troy by Eberhard Zangger. Always Troy, always
the same, each time different.

Robert Recorde, in his algebra book Whetstone of witte, London 1557,
introduced the equality sign: "I will sette as I doe often in worke use,
a paire of paralleles, or Gemowe (Twin) lines of one lengthe, thus:======,
bicause, noe.2. thynges can be moare equalle."

The rule of equation, commonly called Algebers Rule

Edward de Vere, born 1550, may have studied Recorde's book in the ample
library of his uncle, and may have objected: "noe.2. thynges" are abolutely
identical, and nothing remains unchanged forever. I shall work on another
whetstone of witte based on the logic of equal unequal, on change and
shifting identities and perpetual transformations ... Later on, in his play
As You Like It, he would have paid homage to Recorde by calling his alter ego
Touchstone, epitome or cynosure of wit.
d***@gmail.com
2018-01-01 15:31:51 UTC
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Post by Marko Manninen
We know greek paradoxes in many forms like "this sentence is a lie" or "all Cretans are liars" coming from the mouth of a Cretan.
Do we have similar examples from other sources like semitic, early indo european languages, sumerian etc?
I'm also interested of the development of the language and human mind to comprehend this kind of self referencing paradoxes. If anyone can give further useful reading I'd appreciate it.
Something like answering questions about features necessary for a language to support this, do we have languages that doesnt support self reference by design, or just by the fact that people using language really just dont need it in a society they are living, etc.
BR,
Marko
Hi Marko, you might be interested in Douglas Hofstadter's first Metamagical Themas column for Scientific American.
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