It's all a mystery really.....

Originally posted by knightmeister
Whatever is true is true. That's ultimately the truth.

Let's leave out the word "ultimate" for a minute

One could say "there is no such thing as truth".....

The problem is that this statement is either true or not true. It's it's own paradox.

If it is true then it cannot be true , if it is not true then there is such a thing as truth. The The truth is whatever is true at the end of the day. The brute fact of existence.

…
One could say "there is no such thing as truth".....

The problem is that this statement is either true or not true.
….

Wrong!!! Your blatant illogic totally horrifies me;

….It's it's own paradox.

If it is true then it cannot be true , if it is not true then there is such a thing as truth.
...…

-Precisely!!! -THEREFORE, the statement "there is no such thing as truth" is NOT either true or false! - because if it was either true of false then this will lead to a self-contradiction.
Therefore the statement "there is no such thing as truth" is NOT a “proposition“ ( I mean “Proposition” as in formal logic and NOT to be confused with “proposed action“ )

http://en.wikipedia.org/wiki/Proposition

“….Propositions in either case are intended to be truth-bearers, that is, they are either true or false….”

THEREFORE, if a statement cannot have a truth value of either true or false (as demonstrated in this case ) then it is NOT a proposition but rather a nonsense statement -it is just like saying “P and not P” which is a self-contradiction and thus CANNOT be either true or false and thus this it is just a nonsense statement.

…The only way out is to say

"there is no such thing as truth , except for this statement which is true "
..…

No no no! the only LOGICAL way out is to point out the fact that it CANNOT be either true or false because it is a self-contradiction and thus a nonsense statement.

…. Goedel's incompleteness theorem (which mathematically is beyond me) was expressed philosophically as "this statement is false" or "I always lie"

It drove Goedel mad I think.
.…

No, it didn’t!!! why would you think that?
Goedel proved that certain mathematical theorems cannot be proven even if they are true -he merely accepted this thus this didn’t “drive him mad” and this has absolutely nothing to do with statements like "I always lie" or "this statement is false" anyway!!!

Originally posted by Andrew Hamilton
[b]…
One could say "there is no such thing as truth".....

The problem is that this statement is either true or not true.
….

Wrong!!! Your blatant illogic totally horrifies me;

….It's it's own paradox.

If it is true then it cannot be true , if it is not true then there is such a thing as truth.
...…

-Precisely!!! -THE ...[text shortened]... do with statements like "I always lie" or "this statement is false" anyway!!![/b]

No no no! the only LOGICAL way out is to point out the fact that it CANNOT be either true or false because it is a self-contradiction and thus a nonsense statement----------hammy--------------------------

It cannot be true because it is self contradictory - but I see no reason why it cannot be false - please explain.

Surely , it's only self contradictory if it is true. If it is false there is nothing to contradict.

Originally posted by Andrew Hamilton
[b]…
One could say "there is no such thing as truth".....

The problem is that this statement is either true or not true.
….

Wrong!!! Your blatant illogic totally horrifies me;

….It's it's own paradox.

If it is true then it cannot be true , if it is not true then there is such a thing as truth.
...…

-Precisely!!! -THE ...[text shortened]... do with statements like "I always lie" or "this statement is false" anyway!!![/b]

Goedel proved that certain mathematical theorems cannot be proven even if they are true -he merely accepted this thus this didn’t “drive him mad” and this has absolutely nothing to do with statements like "I always lie" or "this statement is false" anyway!!![/b]
---------------------hammy-----------------------------


REALLY? NOTHING AT ALL?

"Relation to the liar paradox

The liar paradox is the sentence "This sentence is false." An analysis of the liar sentence shows that it cannot be true (for then, as it asserts, it is false), nor can it be false (for then, it is true). A Gödel sentence G for a theory T makes a similar assertion to the liar sentence, but with truth replaced by provability: G says "G is not provable in the theory T." The analysis of the truth and provability of G is a formalized version of the analysis of the truth of the liar sentence.

It is not possible to replace "not provable" with "false" in a Gödel sentence because the predicate "Q is the Gödel number of a false formula" cannot be represented as a formula of arithmetic. This result, known as Tarski's undefinability theorem, was discovered independently by Gödel (when he was working on the proof of the incompleteness theorem) and by Alfred Tarski."

---------------wikipedia---------------

Originally posted by Andrew Hamilton
[b]…
One could say "there is no such thing as truth".....

The problem is that this statement is either true or not true.
….

Wrong!!! Your blatant illogic totally horrifies me;

….It's it's own paradox.

If it is true then it cannot be true , if it is not true then there is such a thing as truth.
...…

-Precisely!!! -THE ...[text shortened]... do with statements like "I always lie" or "this statement is false" anyway!!![/b]

It drove Goedel mad I think.---KM
.…[/b]

No, it didn’t!!! why would you think that? ---hammy-------


During his many years at the Institute, Gödel's interests turned to philosophy and physics. He studied and admired the works of Gottfried Leibniz, but came to believe that a hostile conspiracy had caused some of Leibniz's works to be suppressed.In later life, Gödel suffered periods of mental instability and illness. He had an obsessive fear of being poisoned; he wouldn't eat unless his wife, Adele, tasted his food for him. Late in 1977, Adele was hospitalized for six months and could not taste Gödel's food anymore. In her absence, he refused to eat, eventually starving himself to death. He weighed 65 pounds (approximately 30 kg) when he died. His death certificate reported that he died of "malnutrition and inanition caused by personality disturbance" in Princeton Hospital on January 14, 1978.[
------wiki---------

Originally posted by Andrew Hamilton
[b]…
One could say "there is no such thing as truth".....

The problem is that this statement is either true or not true.
….

Wrong!!! Your blatant illogic totally horrifies me;

….It's it's own paradox.

If it is true then it cannot be true , if it is not true then there is such a thing as truth.
...…

-Precisely!!! -THE ...[text shortened]... do with statements like "I always lie" or "this statement is false" anyway!!![/b]

THEREFORE, if a statement cannot have a truth value of either true or false (as demonstrated in this case ) then it is NOT a proposition but rather a nonsense statement -it is just like saying “P and not P” which is a self-contradiction and thus CANNOT be either true or false and thus this it is just a nonsense statement----------hammy------------------

You cannot compare the statement "P and not P" with "there is no such thing as truth"

"P and not P" does not even say what it is that it is proposing and thus is not a proposition. It can't even be self contradictory because, as you say it is nonesense. However, the statement " there is no such thing as truth" is different because it is a proposition that is intelligible. It's not nonsense , it's self contradictory.

If I say " the pink always elephant never has pink" -THAT'S nonsense. You can't even say whether it's true or false because it doesn't make sense.

If I say " the pink elephant never was pink" it's not nonsense it's just self contradictory. If it was nonsense you wouldn't be able to work out that it was self contradictory. You can say that it must be false.

Do you see the subtle difference?

Originally posted by knightmeister
It drove Goedel mad I think.---KM
.…

No, it didn’t!!! why would you think that? ---hammy-------


During his many years at the Institute, Gödel's interests turned to philosophy and physics. He studied and admired the works of Gottfried Leibniz, but came to believe that a hostile conspiracy had caused some of Leibniz's works to be suppresse ...[text shortened]... personality disturbance" in Princeton Hospital on January 14, 1978.[
------wiki---------[/b]

And all of this was caused by him being “driven mad” by statements such as "This sentence is false" !!!? 😛

-is there any shred of evidence or premise to believe that it is this or his theorems that are what caused him to go paranoid or to starve himself to death? -if so, explain to me this evidence.

Originally posted by knightmeister
Goedel proved that certain mathematical theorems cannot be proven even if they are true -he merely accepted this thus this didn’t “drive him mad” and this has absolutely nothing to do with statements like "I always lie" or "this statement is false" anyway!!!
---------------------hammy-----------------------------


REALLY? NOTHING AT ALL?

" s theorem) and by Alfred Tarski."

---------------wikipedia---------------[/b]

…
The liar paradox is the sentence "This sentence is false." An analysis of the liar sentence shows that it cannot be true (for then, as it asserts, it is false), nor can it be false (for then, it is true).
….

-so now you backtrack by saying it IS possible for a statement to be neither true or false!?

Reminder of your original statement:

….…
One could say "there is no such thing as truth".....

The problem is that this statement is either true or not true.
….
...…

Well, though you haven’t admitted that you were wrong, at least now we are getting somewhere.

…A Gödel sentence G for a theory T makes a similar assertion to the liar sentence, but with truth replaced by provability: G says "G is not provable in the theory T." The analysis of the truth and provability of G is a formalized version of the analysis of the truth of the liar sentence.

..…

This is a rather weak connection -the only connection is that the two are examples of proof by contradiction and proof by contradiction is EXTREMELY commonly used in logic as it is one of the most common forms of proof used.

Originally posted by knightmeister
THEREFORE, if a statement cannot have a truth value of either true or false (as demonstrated in this case ) then it is NOT a proposition but rather a nonsense statement -it is just like saying “P and not P” which is a self-contradiction and thus CANNOT be either true or false and thus this it is just a nonsense statement----------hammy----------------- . You can say that it must be false.

Do you see the subtle difference?

…
"P and not P" does not even say what it is that it is proposing and thus is not a proposition. ….

But this is NOT a statement in everyday English but rather IS a statement in formal logic and, in formal logic, it IS proposing something and thus it IS a proposition.
It is proposing that there is a proposition P that is both true and not true.

Haven’t you heard of the “Law of non-contradiction” ?

http://en.wikipedia.org/wiki/Principle_of_bivalence

“…Law of non-contradiction:
For any proposition P, it is not the case that both P is true and 'not-P' is true.
…”

….It can't even be self contradictory because, as you say it is nonsense.
...…

No -it makes sense IN FORMAL LOGIC -I have just proved that with a link. The rest of your post is flawed because of this.

Originally posted by Andrew Hamilton
[b]…
"P and not P" does not even say what it is that it is proposing and thus is not a proposition. ….

But this is NOT a statement in everyday English but rather IS a statement in formal logic and, in formal logic, it IS proposing something and thus it IS a proposition.
It is proposing that there is a proposition P that is both true and no ...[text shortened]... OGIC -I have just proved that with a link. The rest of your post is flawed because of this.[/b]

I did not realised you had switched from everyday english to formal logic - it wasn't clear.Just as it wasn't clear that you were using your own eccentric definition of "inexplicable" rather than the dictionary one.


Our previous discourse went....

-------------------------------------------------------------------------------
One could say "there is no such thing as truth"..... KM

The problem is that this statement is either true or not true. KM
….

Wrong!!! Your blatant illogic totally horrifies me; HAM

-------------------------------------------------------------------------------

You have still yet to explain how the statement "there is no such thing as truth" cannot be false. I understand that it cannot be true because it is self contradictory , but why can't it be false?

Isn't saying it is nonsense the same as saying it is false? If there is such a thing as truth (or ultimate truth) then it is false is it not?

Originally posted by Andrew Hamilton
[b]…
The liar paradox is the sentence "This sentence is false." An analysis of the liar sentence shows that it cannot be true (for then, as it asserts, it is false), nor can it be false (for then, it is true).
….

-so now you backtrack by saying it IS possible for a statement to be neither true or false!?

Reminder of your original statem ...[text shortened]... n is EXTREMELY commonly used in logic as it is one of the most common forms of proof used.[/b]

This is a rather weak connection -the only connection is that the two are examples of proof by contradiction and proof by contradiction is EXTREMELY commonly used in logic as it is one of the most common forms of proof [WORD TOO LONG]

Despite what you say it's pretty clear that most thinkers feel that Goedel's work was more than just mere maths.......


"In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations, called axioms, were shaking with inconsistency and lurking paradox. And so, at that conference, a young man called David Hilbert set out a plan to rebuild them – to make them consistent, all encompassing and without any hint of a paradox.

Hilbert was one of the greatest mathematicians that ever lived, but his plan failed, spectacularly, and it did so because of the incompleteness theorems. These were the work of Kurt Gödel and they changed the way we understand maths, took us to the very limits of logic and sent challenges spilling out into the worlds of physics, philosophy and beyond. " BBC RADIO 4

Originally posted by Andrew Hamilton
[b]…
The liar paradox is the sentence "This sentence is false." An analysis of the liar sentence shows that it cannot be true (for then, as it asserts, it is false), nor can it be false (for then, it is true).
….

-so now you backtrack by saying it IS possible for a statement to be neither true or false!?

Reminder of your original statem ...[text shortened]... n is EXTREMELY commonly used in logic as it is one of the most common forms of proof used.[/b]

Well, though you haven’t admitted that you were wrong, at least now we are getting somewhere. -----------------hammy--------------------

Firstly you re-write the dictionary definition of "inexplicable" , then you say that a self contradictory statement cannot be false? You also claim that I am wrong to call something taht cannot be explained "inexplicable"? Then you want me to say I am wrong? It's you that's in the hole my friend.

Originally posted by Andrew Hamilton
[b]…
The liar paradox is the sentence "This sentence is false." An analysis of the liar sentence shows that it cannot be true (for then, as it asserts, it is false), nor can it be false (for then, it is true).
….

-so now you backtrack by saying it IS possible for a statement to be neither true or false!?

Reminder of your original statem n is EXTREMELY commonly used in logic as it is one of the most common forms of proof used.[/b]

so now you backtrack by saying it IS possible for a statement to be neither true or false!? ---------hammy------------------

No , I DID NOT SAY that it was impossible for "a" statement to be neither true or false. The sentence "this sentence is false" fits that catagory.

What I said was refering to the PARTICULAR statement " there is no such thing as truth" . There are great similarities between the two sentences but they are not the same. Please read more carefully . I did not say what you think I said.

"this sentence is false" is a direct self contradiction of itself but also works the other way as well. It cannot be true or false.

"there is no such thing as truth" is a bit subtler and less clear. I don't think it can be true because if there is no such thing as truth at all (catagorically) then the sentence itself cannot be true either. But if there is such a thing as truth then the sentence can be false.

Before we go any further can you..................

a) read more carefully what I am saying without assuming things.

b) try to appreciate the subtle distinctions in certain things , it seems to be a weakness of yours.

Originally posted by Andrew Hamilton
And all of this was caused by him being “driven mad” by statements such as "This sentence is false" !!!? 😛

-is there any shred of evidence or premise to believe that it is this or his theorems that are what caused him to go paranoid or to starve himself to death? -if so, explain to me this evidence.

Look up Dangerous Knowledge on youtube a BBC documentary. Part 10 of 10 is on Goedel.
-----------------------------------------------------------------------------
DANGEROUS KNOWLEDGE
BBC Two: Wednesday 11 June 2008 11.30pm

In this one-off documentary, David Malone looks at four brilliant mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing - whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide.


The film begins with Georg Cantor, the great mathematician whose work proved to be the foundation for much of the 20th-century mathematics. He believed he was God's messenger and was eventually driven insane trying to prove his theories of infinity.




"MY BEAUTIFUL PROOF
LIES ALL IN RUINS"
Presenter David Malone reads letters which demonstrate Cantor's crumbling self-belief.
Watch a clip from Dangerous Knowledge




Ludwig Boltzmann's struggle to prove the existence of atoms and probability eventually drove him to suicide. Kurt Gödel, the introverted confidant of Einstein, proved that there would always be problems which were outside human logic. His life ended in a sanatorium where he starved himself to death.

Finally, Alan Turing, the great Bletchley Park code breaker, father of computer science and homosexual, died trying to prove that some things are fundamentally unprovable.

The film also talks to the latest in the line of thinkers who have continued to pursue the question of whether there are things that mathematics and the human mind cannot know. They include Greg Chaitin, mathematician at the IBM TJ Watson Research Center, New York, and Roger Penrose.

Dangerous Knowledge tackles some of the profound questions about the true nature of reality that mathematical thinkers are still trying to answer today.
------------------------------------------------------------------------------

Originally posted by knightmeister
I did not realised you had switched from everyday english to formal logic - it wasn't clear.Just as it wasn't clear that you were using your own eccentric definition of "inexplicable" rather than the dictionary one.


Our previous discourse went....

-------------------------------------------------------------------------------
One could say lse? If there is such a thing as truth (or ultimate truth) then it is false is it not?

…
You have still yet to explain how the statement "there is no such thing as truth" cannot be false. I understand that it cannot be true because it is self contradictory , but why can't it be false?
...…

I don’t know why you ask this as it was YOU who said that it can't be false.
Reminder of your quote :

…One could say "there is no such thing as truth".....

The problem is that this statement is either true or NOT true. ..… (my emphasis)

Doesn't "NOT true" mean "false" here?

Anyway, we where BOTH wrong back then 😛 because I erroneously failed to spot your above mistake! -because, as you have just correctly pointed out now, there is no reason why "there is no such thing as truth" cannot be false! 🙂

…. Isn't saying it is nonsense the same as saying it is false?
.…

Not necessarily -as all examples of statements explicitly propose something ( so excluding statements that just say “ouch“ or “hello“ etc ) that cannot be either true or false shows.

…If there is such a thing as truth (or ultimate truth) then it is false is it not?
.…

What?

Originally posted by knightmeister
This is a rather weak connection -the only connection is that the two are examples of proof by contradiction and proof by contradiction is EXTREMELY commonly used in logic as it is one of the most common forms of proof [WORD TOO LONG] ...[text shortened]... ent challenges spilling out into the worlds of physics, philosophy and beyond. " BBC RADIO 4

…
DESPITE what you say it's pretty clear that most thinkers feel that Goedel's work was more than just mere maths.......
...… (my emphasis)

did I say or imply it wasn’t? OBVIOUSLY I don’t think this because his works must have some implications outside maths.