Discussion:
The error of the Liar Paradox and Gödel's 1931 Incompleteness Theorem.
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p***@gmail.com
2020-02-24 18:41:30 UTC
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The error of the Liar Paradox and Gödel's 1931 Incompleteness Theorem.

Here is the kind of self reference that creates the liar "paradox".

void main()
{
bool LP = !(LP == true);
}

Before LP is defined to have any value, this non-existent value is tested to see if it is equal to true.

This is like asking a person that does not own a car: How many feet long is your car?

Or asking someone that has never been married: Have you stopped beating your spouse yet?

The problem with the Liar Paradox is that its value is only defined on the basis of testing this value before it has been defined.

We can see that this same reasoning also applies to Gödel's 1931 Incompleteness Theorem.

void main()
{
bool G = !(G == Provable(G));
}

Copyright 2016 and 2020 Pete Olcott
p***@gmail.com
2020-02-24 19:57:23 UTC
Permalink
Post by p***@gmail.com
The error of the Liar Paradox and Gödel's 1931 Incompleteness Theorem.
Here is the kind of self reference that creates the liar "paradox".
void main()
{
bool LP = !(LP == true);
}
Before LP is defined to have any value, this non-existent value is tested to see if it is equal to true.
This is like asking a person that does not own a car: How many feet long is your car?
Or asking someone that has never been married: Have you stopped beating your spouse yet?
The problem with the Liar Paradox is that its value is only defined on the basis of testing this value before it has been defined.
We can see that this same reasoning also applies to Gödel's 1931 Incompleteness Theorem.
void main()
{
bool G = !(G == Provable(G));
}
Copyright 2016 and 2020 Pete Olcott
Before LP is defined to have any value, this non-existent value is tested to see if it is equal to true. It is easy to see this through the "C" program because "C" has precisely defined and fully elaborated semantics.

When we understand that the above "C" program accurately captures the essence of the Liar Paradox we see that the problem with the Liar Paradox is that its value is only defined on the basis of testing this value before it has been defined.

"This sentence is not true". It not a truth bearer because it does not specify a relation between things that can be tested that resolves to a single Boolean value.

"This sentence is a bag of green onions". Is a truth bearer because it specifies a relation between things that can be tested that resolves to a single Boolean value.

https://plato.stanford.edu/entries/truthmakers/ This much is agreed: “x makes it true that p” is a construction that signifies, if it signifies anything at all, a relation borne to a truth-bearer by something else, a truth-maker.

"This sentence is not true". Has no object of truth, there is only a relation between the negation of the Boolean value of TRUE and an undefined Boolean value.

"This sentence is a bag of green onions". Has an object of truth, when we test the assertion that the abstraction of the sentence (having no physical existence) is a member of the set of a specific set of physically existing things we find that the answer is Boolean false.
p***@gmail.com
2020-02-25 00:46:33 UTC
Permalink
Post by p***@gmail.com
The error of the Liar Paradox and Gödel's 1931 Incompleteness Theorem.
Here is the kind of self reference that creates the liar "paradox".
void main()
{
bool LP = !(LP == true);
}
Before LP is defined to have any value, this non-existent value is tested to see if it is equal to true.
This is like asking a person that does not own a car: How many feet long is your car?
Or asking someone that has never been married: Have you stopped beating your spouse yet?
The problem with the Liar Paradox is that its value is only defined on the basis of testing this value before it has been defined.
We can see that this same reasoning also applies to Gödel's 1931 Incompleteness Theorem.
void main()
{
bool G = !(G == Provable(G));
}
Copyright 2016 and 2020 Pete Olcott
A Truth Bearer is an analytical expression of formal or natural language that specifies a relation that can be tested and resolved to a single Boolean value.
Zelos Malum
2020-02-25 06:32:30 UTC
Permalink
Post by p***@gmail.com
The error of the Liar Paradox and Gödel's 1931 Incompleteness Theorem.
Here is the kind of self reference that creates the liar "paradox".
void main()
{
bool LP = !(LP == true);
}
Before LP is defined to have any value, this non-existent value is tested to see if it is equal to true.
This is like asking a person that does not own a car: How many feet long is your car?
Or asking someone that has never been married: Have you stopped beating your spouse yet?
The problem with the Liar Paradox is that its value is only defined on the basis of testing this value before it has been defined.
We can see that this same reasoning also applies to Gödel's 1931 Incompleteness Theorem.
void main()
{
bool G = !(G == Provable(G));
}
Copyright 2016 and 2020 Pete Olcott
Gödels is not applicable to that, geezes christ
p***@gmail.com
2020-02-25 06:37:37 UTC
Permalink
Post by Zelos Malum
Post by p***@gmail.com
The error of the Liar Paradox and Gödel's 1931 Incompleteness Theorem.
Here is the kind of self reference that creates the liar "paradox".
void main()
{
bool LP = !(LP == true);
}
Before LP is defined to have any value, this non-existent value is tested to see if it is equal to true.
This is like asking a person that does not own a car: How many feet long is your car?
Or asking someone that has never been married: Have you stopped beating your spouse yet?
The problem with the Liar Paradox is that its value is only defined on the basis of testing this value before it has been defined.
We can see that this same reasoning also applies to Gödel's 1931 Incompleteness Theorem.
void main()
{
bool G = !(G == Provable(G));
}
Copyright 2016 and 2020 Pete Olcott
Gödels is not applicable to that, geezes christ
Gödel sure as Hell is applicable to that, I explain it another way here:

https://www.researchgate.net/publication/333907915_Proof_that_Wittgenstein_is_correct_about_Godel
Samuel Allan
2020-02-25 14:27:32 UTC
Permalink
Post by p***@gmail.com
The error of the Liar Paradox and Gödel's 1931 Incompleteness Theorem.
Here is the kind of self reference that creates the liar "paradox".
void main()
{
bool LP = !(LP == true);
}
Before LP is defined to have any value, this non-existent value is tested to see if it is equal to true.
This is like asking a person that does not own a car: How many feet long is your car?
Or asking someone that has never been married: Have you stopped beating your spouse yet?
The problem with the Liar Paradox is that its value is only defined on the basis of testing this value before it has been defined.
We can see that this same reasoning also applies to Gödel's 1931 Incompleteness Theorem.
void main()
{
bool G = !(G == Provable(G));
}
Copyright 2016 and 2020 Pete Olcott
Gödel's Incompleteness Theorem never uses self-referential statements in
the direct way in which you use them, in fact self-referential
statements can sometimes be quite useful mathematical theorems, see
(https://en.wikipedia.org/wiki/Paris%E2%80%93Harrington_theorem).

In order to properly understand his incompleteness theorem (which has
been criticized and is indeed bullet-proof), you need to read his paper
completely. He uses 'Godel numbers' to demonstrate that there always
exists a *well-defined* (contrary to your example) statement, which
still violates the consistency.

The twin primes, for instance, could be one such statement, which has no
resolution (although I don't believe this, there is no way to show
otherwise without proving it).
pete olcott
2020-02-25 17:34:51 UTC
Permalink
Post by Samuel Allan
Post by p***@gmail.com
The error of the Liar Paradox and Gödel's 1931 Incompleteness Theorem.
Here is the kind of self reference that creates the liar "paradox".
void main()
{
bool LP = !(LP == true);
}
Before LP is defined to have any value, this non-existent value is tested to see if it is equal to true.
This is like asking a person that does not own a car: How many feet long is your car?
Or asking someone that has never been married: Have you stopped beating your spouse yet?
The problem with the Liar Paradox is that its value is only defined on the basis of testing this value before it has been defined.
We can see that this same reasoning also applies to Gödel's 1931 Incompleteness Theorem.
void main()
{
bool G = !(G == Provable(G));
}
Copyright 2016 and 2020 Pete Olcott
Gödel's Incompleteness Theorem never uses self-referential statements in
the direct way in which you use them, in fact self-referential
statements can sometimes be quite useful mathematical theorems, see
(https://en.wikipedia.org/wiki/Paris%E2%80%93Harrington_theorem).
In order to properly understand his incompleteness theorem (which has
been criticized and is indeed bullet-proof), you need to read his paper
completely. He uses 'Godel numbers' to demonstrate that there always
exists a *well-defined* (contrary to your example) statement, which
still violates the consistency.
The twin primes, for instance, could be one such statement, which has no
resolution (although I don't believe this, there is no way to show
otherwise without proving it).
As it turns out to actually be the case the entire body of all conceptual truth is entirely comprised of expressions of language that have been stipulated to have the semantic property of Boolean true (paraphrase of Curry 1977:45) and truth preserving operations applied to this set.

When these truth preserving operations are defined as finite string transformation rules we establish a bijection such that truth and provability cannot diverge.

When we do this we retain all of the original expressiveness of formal systems and screen out semantic paradoxes as ill-formed truth bearers. This allows the universal truth predicate that Tarski proved to not exist to be defined as:
∀x (True(RS, x) := (RS ⊢ x))

Copyright 2018, 2019, 2020 Peter Olcott

This has been rewritten and contains the Haskell Curry quotes
https://www.researchgate.net/publication/333907915_Proof_that_Wittgenstein_is_correct_about_Godel
pete olcott
2020-02-25 17:42:13 UTC
Permalink
Post by pete olcott
Post by Samuel Allan
Post by p***@gmail.com
The error of the Liar Paradox and Gödel's 1931 Incompleteness Theorem.
Here is the kind of self reference that creates the liar "paradox".
void main()
{
bool LP = !(LP == true);
}
Before LP is defined to have any value, this non-existent value is tested to see if it is equal to true.
This is like asking a person that does not own a car: How many feet long is your car?
Or asking someone that has never been married: Have you stopped beating your spouse yet?
The problem with the Liar Paradox is that its value is only defined on the basis of testing this value before it has been defined.
We can see that this same reasoning also applies to Gödel's 1931 Incompleteness Theorem.
void main()
{
bool G = !(G == Provable(G));
}
Copyright 2016 and 2020 Pete Olcott
Gödel's Incompleteness Theorem never uses self-referential statements in
the direct way in which you use them, in fact self-referential
statements can sometimes be quite useful mathematical theorems, see
(https://en.wikipedia.org/wiki/Paris%E2%80%93Harrington_theorem).
In order to properly understand his incompleteness theorem (which has
been criticized and is indeed bullet-proof), you need to read his paper
completely. He uses 'Godel numbers' to demonstrate that there always
exists a *well-defined* (contrary to your example) statement, which
still violates the consistency.
The twin primes, for instance, could be one such statement, which has no
resolution (although I don't believe this, there is no way to show
otherwise without proving it).
As it turns out to actually be the case the entire body of all conceptual truth is entirely comprised of expressions of language that have been stipulated to have the semantic property of Boolean true (paraphrase of Curry 1977:45) and truth preserving operations applied to this set.
When these truth preserving operations are defined as finite string transformation rules we establish a bijection such that truth and provability cannot diverge.
∀x (True(RS, x) := (RS ⊢ x))
Copyright 2018, 2019, 2020 Peter Olcott
This has been rewritten and contains the Haskell Curry quotes
https://www.researchgate.net/publication/333907915_Proof_that_Wittgenstein_is_correct_about_Godel
Curry, Haskell 1977. Foundations of Mathematical Logic. New York: Dover Publications, 45

We begin by postulating a certain non void, definite
class {E} of statements, which we call elementary
statements...

The statements of {E} are called elementary statements
to distinguish them from other statements which we may
form from them or about them in the U language...

Then the elementary statements which belong to {T} we
shall call the elementary theorems of {T}; we also say
that these elementary statements are true for {T}. Thus,
given {T}, an elementary theorem is an elementary
statement which is true. A theory is thus a way of
picking out from the statements of {E} a certain subclass
of true statements...

The terminology which has just been used implies that the
elementary statements are not such that their truth and
falsity are known to us without reference to {T}.

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