On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring the fact that >>> some expressions of language are simply not truth bearers.
A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring the fact that >>> some expressions of language are simply not truth bearers.
A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
On 10/21/2024 9:48 PM, Richard Damon wrote:
On 10/21/24 10:04 PM, olcott wrote:
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring the fact
that
some expressions of language are simply not truth bearers.
A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.
Only if "can not be determined" means that there isn't an actual
answer to it,
Not that we don't know the answer to it.
For instance, the Twin Primes conjecture is either True, or it is
False, it can't be a non-truth-bearer, as either there is or there
isn't a highest pair of primes that differs by two.
Sure.
The fact we don't know, and maybe can never know, doesn't make the
question incorrect.
Some truth is just unknowable.
Sure.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
Right, and a question that we don't know (or maybe can't know) but is
either true or false, is not an incorrect question.
Sure.
When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
Does D halt, is not an incorrect question, as it will halt or not.
Tarski is a simpler example for this case.
His theory rightfully cannot determine whether
the following sentence is true or false:
"This sentence is not true".
Because that sentence is not a truth bearer.
That does not mean that True(L,x) cannot be defined.
It only means that some expression ore not truth bearers.
That the H that it was built from won't give the right answer is
irrelevent.
You just don't understand what the terms mean, because you CHOSE to
make youself ignorant, and thus INTENTIONALY made yourself into a
pathetic ignorant pathological lying idiot.
Sorry, but that is the facts.
On 10/22/2024 6:22 AM, Richard Damon wrote:
On 10/21/24 11:17 PM, olcott wrote:
On 10/21/2024 9:48 PM, Richard Damon wrote:
On 10/21/24 10:04 PM, olcott wrote:
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring the
fact that
some expressions of language are simply not truth bearers.
A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.
Only if "can not be determined" means that there isn't an actual
answer to it,
Not that we don't know the answer to it.
For instance, the Twin Primes conjecture is either True, or it is
False, it can't be a non-truth-bearer, as either there is or there
isn't a highest pair of primes that differs by two.
Sure.
So, you agree your definition is wrong
The fact we don't know, and maybe can never know, doesn't make the
question incorrect.
Some truth is just unknowable.
Sure.
And again.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
Right, and a question that we don't know (or maybe can't know) but
is either true or false, is not an incorrect question.
Sure.
So you argee again that you proposition is wrong.
When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
Does D halt, is not an incorrect question, as it will halt or not.
Tarski is a simpler example for this case.
His theory rightfully cannot determine whether
the following sentence is true or false:
"This sentence is not true".
Because that sentence is not a truth bearer.
No, that isn't his statement, but of course your problem is you can't
understand his actual statement so need to paraphrase it, and that
loses some critical properties.
Haskell Curry species expressions of theory {T} that are
stipulated to be true:
Thus, given {T}, an elementary theorem is an
elementary statement which is true. https://www.liarparadox.org/Haskell_Curry_45.pdf
When we start with the foundation that True(L,x) is defined
as applying a set of truth preserving operations to a set
of expressions of language stipulated to be true Tarski's
proof fails.
We overcome Tarski Undefinability the same way that ZFC
overcame Russell's Paradox. We replace the prior foundation
with a new one.
https://liarparadox.org/Tarski_275_276.pdf
That does not mean that True(L,x) cannot be defined.
It only means that some expression ore not truth bearers.
His proof does, the fact that you don't undetstand what he is talking
about doesn't make him wrong.
You asserting he is wrong becuase you don't understand his proof makes
you wrong, and STUPID.
That the H that it was built from won't give the right answer is
irrelevent.
You just don't understand what the terms mean, because you CHOSE to
make youself ignorant, and thus INTENTIONALY made yourself into a
pathetic ignorant pathological lying idiot.
Sorry, but that is the facts.
On 10/22/2024 2:39 AM, Mikko wrote:
On 2024-10-22 02:04:14 +0000, olcott said:
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring the fact that >>>>> some expressions of language are simply not truth bearers.
A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.
There are several possibilities.
A theory may be intentionally incomplete. For example, group theory
leaves several important question unanswered. There are infinitely
may different groups and group axioms must be true in every group.
Another possibility is that a theory is poorly constructed: the
author just failed to include an important postulate.
Then there is the possibility that the purpose of the theory is
incompatible with decidability, for example arithmetic.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.
See my most recent reply to Richard it sums up
my position most succinctly.
On 10/24/2024 9:06 AM, Mikko wrote:
On 2024-10-22 15:04:37 +0000, olcott said:
On 10/22/2024 2:39 AM, Mikko wrote:
On 2024-10-22 02:04:14 +0000, olcott said:
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring the
fact that
some expressions of language are simply not truth bearers.
A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.
There are several possibilities.
A theory may be intentionally incomplete. For example, group theory
leaves several important question unanswered. There are infinitely
may different groups and group axioms must be true in every group.
Another possibility is that a theory is poorly constructed: the
author just failed to include an important postulate.
Then there is the possibility that the purpose of the theory is
incompatible with decidability, for example arithmetic.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.
See my most recent reply to Richard it sums up
my position most succinctly.
We already know that your position is uninteresting.
Don't want to bother to look at it (AKA uninteresting) is not at
all the same thing as the corrected foundation to computability
does not eliminate undecidability. It does eliminate undecidability
and not bothering to look at it is no actual rebuttal.
On 10/24/2024 9:06 AM, Mikko wrote:
On 2024-10-22 15:04:37 +0000, olcott said:
On 10/22/2024 2:39 AM, Mikko wrote:
On 2024-10-22 02:04:14 +0000, olcott said:
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring the fact that
some expressions of language are simply not truth bearers.
A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.
There are several possibilities.
A theory may be intentionally incomplete. For example, group theory
leaves several important question unanswered. There are infinitely
may different groups and group axioms must be true in every group.
Another possibility is that a theory is poorly constructed: the
author just failed to include an important postulate.
Then there is the possibility that the purpose of the theory is
incompatible with decidability, for example arithmetic.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.
See my most recent reply to Richard it sums up
my position most succinctly.
We already know that your position is uninteresting.
Don't want to bother to look at it (AKA uninteresting) is not at
all the same thing as the corrected foundation to computability
does not eliminate undecidability.
It does eliminate undecidability
and not bothering to look at it is no actual rebuttal.
On 10/25/2024 3:14 AM, Mikko wrote:
On 2024-10-24 16:07:03 +0000, olcott said:
On 10/24/2024 9:06 AM, Mikko wrote:
On 2024-10-22 15:04:37 +0000, olcott said:
On 10/22/2024 2:39 AM, Mikko wrote:
On 2024-10-22 02:04:14 +0000, olcott said:
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring the >>>>>>>>> fact that
some expressions of language are simply not truth bearers.
A formal theory is undecidable if there is no Turing machine that >>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>> theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there >>>>>>>> is not. No third possibility.
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.
There are several possibilities.
A theory may be intentionally incomplete. For example, group theory >>>>>> leaves several important question unanswered. There are infinitely >>>>>> may different groups and group axioms must be true in every group. >>>>>>
Another possibility is that a theory is poorly constructed: the
author just failed to include an important postulate.
Then there is the possibility that the purpose of the theory is
incompatible with decidability, for example arithmetic.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.
See my most recent reply to Richard it sums up
my position most succinctly.
We already know that your position is uninteresting.
Don't want to bother to look at it (AKA uninteresting) is not at
all the same thing as the corrected foundation to computability
does not eliminate undecidability.
No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.
In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.
Ae also know
that a good foundation to computability does not eliminate
undecidablility but proves it, and also proves uncomputablility
of various functions.
Whether some foundation can be correct or what it would mean to
call it so is a different problem.
It does eliminate undecidability
and not bothering to look at it is no actual rebuttal.
You may say so but you don't offer any good argument to support
that claim. Instead you offer various indications that you will
never present a good argument about anything.
On 10/25/2024 3:14 AM, Mikko wrote:
On 2024-10-24 16:07:03 +0000, olcott said:
On 10/24/2024 9:06 AM, Mikko wrote:
On 2024-10-22 15:04:37 +0000, olcott said:
On 10/22/2024 2:39 AM, Mikko wrote:
On 2024-10-22 02:04:14 +0000, olcott said:
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring the fact that
some expressions of language are simply not truth bearers.
A formal theory is undecidable if there is no Turing machine that >>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>> theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there >>>>>>>> is not. No third possibility.
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.
There are several possibilities.
A theory may be intentionally incomplete. For example, group theory >>>>>> leaves several important question unanswered. There are infinitely >>>>>> may different groups and group axioms must be true in every group. >>>>>>
Another possibility is that a theory is poorly constructed: the
author just failed to include an important postulate.
Then there is the possibility that the purpose of the theory is
incompatible with decidability, for example arithmetic.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.
See my most recent reply to Richard it sums up
my position most succinctly.
We already know that your position is uninteresting.
Don't want to bother to look at it (AKA uninteresting) is not at
all the same thing as the corrected foundation to computability
does not eliminate undecidability.
No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.
In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.
On 10/26/2024 2:52 AM, Mikko wrote:
On 2024-10-25 14:37:19 +0000, olcott said:
On 10/25/2024 3:14 AM, Mikko wrote:
On 2024-10-24 16:07:03 +0000, olcott said:
On 10/24/2024 9:06 AM, Mikko wrote:
On 2024-10-22 15:04:37 +0000, olcott said:
On 10/22/2024 2:39 AM, Mikko wrote:
On 2024-10-22 02:04:14 +0000, olcott said:
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring >>>>>>>>>>> the fact thatA formal theory is undecidable if there is no Turing machine that >>>>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>>>> theory or not. Whether an expression is a truth bearer is not >>>>>>>>>> relevant. Either there is a valid proof of that formula or there >>>>>>>>>> is not. No third possibility.
some expressions of language are simply not truth bearers. >>>>>>>>>>
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.
There are several possibilities.
A theory may be intentionally incomplete. For example, group theory >>>>>>>> leaves several important question unanswered. There are infinitely >>>>>>>> may different groups and group axioms must be true in every group. >>>>>>>>
Another possibility is that a theory is poorly constructed: the >>>>>>>> author just failed to include an important postulate.
Then there is the possibility that the purpose of the theory is >>>>>>>> incompatible with decidability, for example arithmetic.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.
See my most recent reply to Richard it sums up
my position most succinctly.
We already know that your position is uninteresting.
Don't want to bother to look at it (AKA uninteresting) is not at
all the same thing as the corrected foundation to computability
does not eliminate undecidability.
No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.
In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.
No, not in the same way.
Pathological self reference causes an issue in both cases.
This issue is resolved by disallowing it in both cases.
When we disallow the Liar Paradox then Tarski cannot derive
the first state of his proof and his proof fails.
Tarski's Liar Paradox from page 248
It would then be possible to reconstruct the antinomy of the liar
in the metalanguage, by forming in the language itself a sentence
x such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x https://liarparadox.org/Tarski_275_276.pdf
adapted to become this
x ∉ Pr if and only if p // line 1 of the proof
Here is the Tarski Undefinability Theorem proof
(1) x ∉ Provable if and only if p // assumption (see above)
(2) x ∈ True if and only if p // Tarski's convention T
(3) x ∉ Provable if and only if x ∈ True. // (1) and (2) combined
(4) either x ∉ True or x̄ ∉ True; // axiom: ~True(x) ∨ ~True(~x)
(5) if x ∈ Provable, then x ∈ True; // axiom: Provable(x) → True(x) (6) if x̄ ∈ Provable, then x̄ ∈ True; // axiom: Provable(~x) → True(~x)
(7) x ∈ True
(8) x ∉ Provable
(9) x̄ ∉ Provable
ZFC is a useful set theory for many purposes.
You don't offer any useful theory for any purpose.
If we had a True(L, x) that worked consistently and L
is formalized natural language then we could refute
all of the dangerous lies made for political gain in
real time before they gained any traction.
Because we don't have this it looks like there is a
good chance we will be seeing the rise of the Fourth
Reich in a few days.
On 10/26/2024 10:48 AM, Richard Damon wrote:
On 10/26/24 8:59 AM, olcott wrote:
On 10/26/2024 2:52 AM, Mikko wrote:
On 2024-10-25 14:37:19 +0000, olcott said:
On 10/25/2024 3:14 AM, Mikko wrote:
On 2024-10-24 16:07:03 +0000, olcott said:
On 10/24/2024 9:06 AM, Mikko wrote:
On 2024-10-22 15:04:37 +0000, olcott said:
On 10/22/2024 2:39 AM, Mikko wrote:
On 2024-10-22 02:04:14 +0000, olcott said:
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring >>>>>>>>>>>>> the fact thatA formal theory is undecidable if there is no Turing machine >>>>>>>>>>>> that
some expressions of language are simply not truth bearers. >>>>>>>>>>>>
determines whether a formula of that theory is a theorem of >>>>>>>>>>>> that
theory or not. Whether an expression is a truth bearer is not >>>>>>>>>>>> relevant. Either there is a valid proof of that formula or >>>>>>>>>>>> there
is not. No third possibility.
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y >>>>>>>>>>> cannot be determined to be yes or no then the question
itself is somehow incorrect.
There are several possibilities.
A theory may be intentionally incomplete. For example, group >>>>>>>>>> theory
leaves several important question unanswered. There are
infinitely
may different groups and group axioms must be true in every >>>>>>>>>> group.
Another possibility is that a theory is poorly constructed: the >>>>>>>>>> author just failed to include an important postulate.
Then there is the possibility that the purpose of the theory is >>>>>>>>>> incompatible with decidability, for example arithmetic.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
When "X a formula of theory Y" is neither true nor false >>>>>>>>>>> then "X a formula of theory Y" is not a truth bearer.
Whether AB = BA is not answered by group theory but is alwasy >>>>>>>>>> true or false about specific A and B and universally true in >>>>>>>>>> some groups but not all.
See my most recent reply to Richard it sums up
my position most succinctly.
We already know that your position is uninteresting.
Don't want to bother to look at it (AKA uninteresting) is not at >>>>>>> all the same thing as the corrected foundation to computability
does not eliminate undecidability.
No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.
In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.
No, not in the same way.
Pathological self reference causes an issue in both cases.
This issue is resolved by disallowing it in both cases.
Nope, because is set theory, the "self-reference"
does exist and is problematic in its several other instances.
Abolishing it in each case DOES ELIMINATE THE FREAKING PROBLEM.
On 10/26/2024 2:52 AM, Mikko wrote:
On 2024-10-25 14:37:19 +0000, olcott said:
On 10/25/2024 3:14 AM, Mikko wrote:
On 2024-10-24 16:07:03 +0000, olcott said:
On 10/24/2024 9:06 AM, Mikko wrote:
On 2024-10-22 15:04:37 +0000, olcott said:
On 10/22/2024 2:39 AM, Mikko wrote:
On 2024-10-22 02:04:14 +0000, olcott said:
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring the fact thatA formal theory is undecidable if there is no Turing machine that >>>>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>>>> theory or not. Whether an expression is a truth bearer is not >>>>>>>>>> relevant. Either there is a valid proof of that formula or there >>>>>>>>>> is not. No third possibility.
some expressions of language are simply not truth bearers. >>>>>>>>>>
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.
There are several possibilities.
A theory may be intentionally incomplete. For example, group theory >>>>>>>> leaves several important question unanswered. There are infinitely >>>>>>>> may different groups and group axioms must be true in every group. >>>>>>>>
Another possibility is that a theory is poorly constructed: the >>>>>>>> author just failed to include an important postulate.
Then there is the possibility that the purpose of the theory is >>>>>>>> incompatible with decidability, for example arithmetic.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.
See my most recent reply to Richard it sums up
my position most succinctly.
We already know that your position is uninteresting.
Don't want to bother to look at it (AKA uninteresting) is not at
all the same thing as the corrected foundation to computability
does not eliminate undecidability.
No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.
In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.
No, not in the same way.
Pathological self reference causes an issue in both cases.
This issue is resolved by disallowing it in both cases.
On 10/26/2024 8:04 PM, Richard Damon wrote:
On 10/26/24 5:57 PM, olcott wrote:
On 10/26/2024 10:48 AM, Richard Damon wrote:
On 10/26/24 8:59 AM, olcott wrote:
On 10/26/2024 2:52 AM, Mikko wrote:
On 2024-10-25 14:37:19 +0000, olcott said:
On 10/25/2024 3:14 AM, Mikko wrote:
On 2024-10-24 16:07:03 +0000, olcott said:
On 10/24/2024 9:06 AM, Mikko wrote:
On 2024-10-22 15:04:37 +0000, olcott said:
On 10/22/2024 2:39 AM, Mikko wrote:
On 2024-10-22 02:04:14 +0000, olcott said:
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in >>>>>>>>>>>>>>> ignoring the fact thatA formal theory is undecidable if there is no Turing >>>>>>>>>>>>>> machine that
some expressions of language are simply not truth bearers. >>>>>>>>>>>>>>
determines whether a formula of that theory is a theorem >>>>>>>>>>>>>> of that
theory or not. Whether an expression is a truth bearer is not >>>>>>>>>>>>>> relevant. Either there is a valid proof of that formula or >>>>>>>>>>>>>> there
is not. No third possibility.
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y >>>>>>>>>>>>> cannot be determined to be yes or no then the question >>>>>>>>>>>>> itself is somehow incorrect.
There are several possibilities.
A theory may be intentionally incomplete. For example, group >>>>>>>>>>>> theory
leaves several important question unanswered. There are >>>>>>>>>>>> infinitely
may different groups and group axioms must be true in every >>>>>>>>>>>> group.
Another possibility is that a theory is poorly constructed: the >>>>>>>>>>>> author just failed to include an important postulate.
Then there is the possibility that the purpose of the theory is >>>>>>>>>>>> incompatible with decidability, for example arithmetic. >>>>>>>>>>>>
An incorrect question is an expression of language that >>>>>>>>>>>>> is not a truth bearer translated into question form. >>>>>>>>>>>>>Whether AB = BA is not answered by group theory but is alwasy >>>>>>>>>>>> true or false about specific A and B and universally true in >>>>>>>>>>>> some groups but not all.
When "X a formula of theory Y" is neither true nor false >>>>>>>>>>>>> then "X a formula of theory Y" is not a truth bearer. >>>>>>>>>>>>
See my most recent reply to Richard it sums up
my position most succinctly.
We already know that your position is uninteresting.
Don't want to bother to look at it (AKA uninteresting) is not at >>>>>>>>> all the same thing as the corrected foundation to computability >>>>>>>>> does not eliminate undecidability.
No, but we already know that you don't offer anything interesting >>>>>>>> about foundations to computability or undecidabilty.
In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.
No, not in the same way.
Pathological self reference causes an issue in both cases.
This issue is resolved by disallowing it in both cases.
Nope, because is set theory, the "self-reference"
does exist and is problematic in its several other instances.
Abolishing it in each case DOES ELIMINATE THE FREAKING PROBLEM.
Yes, IN SET THEORY, the "self-reference" can be banned, by the nature
of the contstruction.
That seems to be the best way.
In Computation Theory it can not, without making the system less than
Turing Complete, as the structure of the Computations fundamentally
allow for it,
Sure.
and in a way that is potentially undetectable.
I really don't think so it only seems that way.
You don't seem to understand that fact, but the fundamental nature of
being able to encode your processing in the same sort of strings you
process makes this a possibility.
It does not make these things undetectable, it merely
allows failing to detect.
Dues to the nature of its relationship to Mathematics and Logic, it
turns out that and logic with certain minimal requirements can get
into a similar situation.
I think that I can see deeper than the Curry/Howard Isomorphism.
Computations and formal systems are in their most basic foundational
essence finite string transformation rules.
Your only way to remove it from these fields is to remove that source
of "power" in the systems, and the cost of that is just too high for
most people, thus you plan just fails.
Detection then rejection.
Of course, you understanding is too crude to see this issue, so it
just goes over your head, and your claims just reveal your ignorance
of the fields.
Sorry, that is just the facts, that you seem to be too stupid to
understand.
In other words you can correctly explain every single detail
conclusively proving how finite string transformation rules
are totally unrelated to either computation and formal systems.
On 10/27/2024 3:27 AM, Mikko wrote:
On 2024-10-26 12:59:33 +0000, olcott said:Godel says otherwise.
On 10/26/2024 2:52 AM, Mikko wrote:
On 2024-10-25 14:37:19 +0000, olcott said:
On 10/25/2024 3:14 AM, Mikko wrote:
On 2024-10-24 16:07:03 +0000, olcott said:
On 10/24/2024 9:06 AM, Mikko wrote:
On 2024-10-22 15:04:37 +0000, olcott said:
On 10/22/2024 2:39 AM, Mikko wrote:
On 2024-10-22 02:04:14 +0000, olcott said:
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring >>>>>>>>>>>>> the fact thatA formal theory is undecidable if there is no Turing machine >>>>>>>>>>>> that
some expressions of language are simply not truth bearers. >>>>>>>>>>>>
determines whether a formula of that theory is a theorem of >>>>>>>>>>>> that
theory or not. Whether an expression is a truth bearer is not >>>>>>>>>>>> relevant. Either there is a valid proof of that formula or >>>>>>>>>>>> there
is not. No third possibility.
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y >>>>>>>>>>> cannot be determined to be yes or no then the question
itself is somehow incorrect.
There are several possibilities.
A theory may be intentionally incomplete. For example, group >>>>>>>>>> theory
leaves several important question unanswered. There are
infinitely
may different groups and group axioms must be true in every >>>>>>>>>> group.
Another possibility is that a theory is poorly constructed: the >>>>>>>>>> author just failed to include an important postulate.
Then there is the possibility that the purpose of the theory is >>>>>>>>>> incompatible with decidability, for example arithmetic.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
When "X a formula of theory Y" is neither true nor false >>>>>>>>>>> then "X a formula of theory Y" is not a truth bearer.
Whether AB = BA is not answered by group theory but is alwasy >>>>>>>>>> true or false about specific A and B and universally true in >>>>>>>>>> some groups but not all.
See my most recent reply to Richard it sums up
my position most succinctly.
We already know that your position is uninteresting.
Don't want to bother to look at it (AKA uninteresting) is not at >>>>>>> all the same thing as the corrected foundation to computability
does not eliminate undecidability.
No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.
In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.
No, not in the same way.
Pathological self reference causes an issue in both cases.
This issue is resolved by disallowing it in both cases.
There is no self reference in a formal theory. Expressions of a formal
theory don't refer.
On 10/27/2024 3:27 AM, Mikko wrote:
On 2024-10-26 12:59:33 +0000, olcott said:Godel says otherwise.
On 10/26/2024 2:52 AM, Mikko wrote:
On 2024-10-25 14:37:19 +0000, olcott said:
On 10/25/2024 3:14 AM, Mikko wrote:
On 2024-10-24 16:07:03 +0000, olcott said:
On 10/24/2024 9:06 AM, Mikko wrote:
On 2024-10-22 15:04:37 +0000, olcott said:
On 10/22/2024 2:39 AM, Mikko wrote:
On 2024-10-22 02:04:14 +0000, olcott said:
On 10/16/2024 11:37 AM, Mikko wrote:
On 2024-10-16 14:27:09 +0000, olcott said:
The whole notion of undecidability is anchored in ignoring the fact thatA formal theory is undecidable if there is no Turing machine that >>>>>>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>>>>>> theory or not. Whether an expression is a truth bearer is not >>>>>>>>>>>> relevant. Either there is a valid proof of that formula or there >>>>>>>>>>>> is not. No third possibility.
some expressions of language are simply not truth bearers. >>>>>>>>>>>>
After being continually interrupted by emergencies
interrupting other emergencies...
If the answer to the question: Is X a formula of theory Y >>>>>>>>>>> cannot be determined to be yes or no then the question
itself is somehow incorrect.
There are several possibilities.
A theory may be intentionally incomplete. For example, group theory >>>>>>>>>> leaves several important question unanswered. There are infinitely >>>>>>>>>> may different groups and group axioms must be true in every group. >>>>>>>>>>
Another possibility is that a theory is poorly constructed: the >>>>>>>>>> author just failed to include an important postulate.
Then there is the possibility that the purpose of the theory is >>>>>>>>>> incompatible with decidability, for example arithmetic.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
When "X a formula of theory Y" is neither true nor false >>>>>>>>>>> then "X a formula of theory Y" is not a truth bearer.
Whether AB = BA is not answered by group theory but is alwasy >>>>>>>>>> true or false about specific A and B and universally true in >>>>>>>>>> some groups but not all.
See my most recent reply to Richard it sums up
my position most succinctly.
We already know that your position is uninteresting.
Don't want to bother to look at it (AKA uninteresting) is not at >>>>>>> all the same thing as the corrected foundation to computability
does not eliminate undecidability.
No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.
In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.
No, not in the same way.
Pathological self reference causes an issue in both cases.
This issue is resolved by disallowing it in both cases.
There is no self reference in a formal theory. Expressions of a formal
theory don't refer.
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