On 4/24/2024 3:35 AM, Mikko wrote:
On 2024-04-23 14:31:00 +0000, olcott said:
On 4/23/2024 3:21 AM, Mikko wrote:
On 2024-04-22 17:37:55 +0000, olcott said:
On 4/22/2024 10:27 AM, Mikko wrote:
On 2024-04-22 14:10:54 +0000, olcott said:
On 4/22/2024 4:35 AM, Mikko wrote:
On 2024-04-21 14:44:37 +0000, olcott said:
On 4/21/2024 2:57 AM, Mikko wrote:
On 2024-04-20 15:20:05 +0000, olcott said:
On 4/20/2024 2:54 AM, Mikko wrote:
On 2024-04-19 18:04:48 +0000, olcott said:
When we create a three-valued logic system that has these >>>>>>>>>>>>> three values: {True, False, Nonsense}
https://en.wikipedia.org/wiki/Three-valued_logic
Such three valued logic has the problem that a tautology of the >>>>>>>>>>>> ordinary propositional logic cannot be trusted to be true. For >>>>>>>>>>>> example, in ordinary logic A ∨ ¬A is always true. This means that
some ordinary proofs of ordinary theorems are no longer valid and >>>>>>>>>>>> you need to accept the possibility that a theory that is complete >>>>>>>>>>>> in ordinary logic is incomplete in your logic.
I only used three-valued logic as a teaching device. Whenever an >>>>>>>>>>> expression of language has the value of {Nonsense} then it is >>>>>>>>>>> rejected and not allowed to be used in any logical operations. It >>>>>>>>>>> is basically invalid input.
You cannot teach because you lack necessary skills. Therefore you >>>>>>>>>> don't need any teaching device.
That is too close to ad homimen.
If you think my reasoning is incorrect then point to the error >>>>>>>>> in my reasoning. Saying that in your opinion I am a bad teacher >>>>>>>>> is too close to ad hominem because it refers to your opinion of >>>>>>>>> me and utterly bypasses any of my reasoning.
No, it isn't. You introduced youtself as a topic of discussion so >>>>>>>> you are a legitimate topic of discussion.
I didn't claim that there be any reasoning, incorrect or otherwise. >>>>>>>>
If you claim I am a bad teacher you must point out what is wrong with >>>>>>> the lesson otherwise your claim that I am a bad teacher is essentially >>>>>>> an as hominem attack.
You are not a teacher, bad or otherwise. That you lack skills that >>>>>> happen to be necessary for teaching is obvious from you postings
here. A teacher needs to understand human psychology but you don't. >>>>>>
You may be correct that I am a terrible teacher.
None-the-less Mathematicians might not have very much understanding
of the link between proof theory and computability.
Sume mathematicians do have very much understanding of that. But that
link is not needed for understanding and solving problems separately
in the two areas.
When I refer to rejecting an invalid input math would seem to construe >>>>> this as nonsense, where as computability theory would totally understand. >>>>People working on computability theory do not understand "invalid input" >>>> as "impossible input".
The proof then shows, for any program f that might determine whether
programs halt, that a "pathological" program g, called with some input,
can pass its own source and its input to f and then specifically do the
opposite of what f predicts g will do. No f can exist that handles this
case, thus showing undecidability.
https://en.wikipedia.org/wiki/Halting_problem#
So then they must believe that there exists an H that does correctly
determine the halt status of every input, some inputs are simply
more difficult than others, no inputs are impossible.
That "must" is false as it does not follow from anything.
Sure it does. If there are no "impossible" inputs that entails
that all inputs are possible.
When all inputs are possible then
the halting problem proof is wrong.
On 4/24/2024 6:01 PM, Richard Damon wrote:
On 4/24/24 11:33 AM, olcott wrote:
On 4/24/2024 3:35 AM, Mikko wrote:
On 2024-04-23 14:31:00 +0000, olcott said:
On 4/23/2024 3:21 AM, Mikko wrote:
On 2024-04-22 17:37:55 +0000, olcott said:
On 4/22/2024 10:27 AM, Mikko wrote:
On 2024-04-22 14:10:54 +0000, olcott said:
On 4/22/2024 4:35 AM, Mikko wrote:
On 2024-04-21 14:44:37 +0000, olcott said:
On 4/21/2024 2:57 AM, Mikko wrote:
On 2024-04-20 15:20:05 +0000, olcott said:
On 4/20/2024 2:54 AM, Mikko wrote:
On 2024-04-19 18:04:48 +0000, olcott said:
When we create a three-valued logic system that has these >>>>>>>>>>>>>>> three values: {True, False, Nonsense}
https://en.wikipedia.org/wiki/Three-valued_logic
Such three valued logic has the problem that a tautology of the >>>>>>>>>>>>>> ordinary propositional logic cannot be trusted to be true. For >>>>>>>>>>>>>> example, in ordinary logic A ∨ ¬A is always true. This means that
some ordinary proofs of ordinary theorems are no longer valid and
you need to accept the possibility that a theory that is complete
in ordinary logic is incomplete in your logic.
I only used three-valued logic as a teaching device. Whenever an >>>>>>>>>>>>> expression of language has the value of {Nonsense} then it is >>>>>>>>>>>>> rejected and not allowed to be used in any logical operations. It >>>>>>>>>>>>> is basically invalid input.
You cannot teach because you lack necessary skills. Therefore you >>>>>>>>>>>> don't need any teaching device.
That is too close to ad homimen.
If you think my reasoning is incorrect then point to the error >>>>>>>>>>> in my reasoning. Saying that in your opinion I am a bad teacher >>>>>>>>>>> is too close to ad hominem because it refers to your opinion of >>>>>>>>>>> me and utterly bypasses any of my reasoning.
No, it isn't. You introduced youtself as a topic of discussion so >>>>>>>>>> you are a legitimate topic of discussion.
I didn't claim that there be any reasoning, incorrect or otherwise. >>>>>>>>>>
If you claim I am a bad teacher you must point out what is wrong with >>>>>>>>> the lesson otherwise your claim that I am a bad teacher is essentially
an as hominem attack.
You are not a teacher, bad or otherwise. That you lack skills that >>>>>>>> happen to be necessary for teaching is obvious from you postings >>>>>>>> here. A teacher needs to understand human psychology but you don't. >>>>>>>>
You may be correct that I am a terrible teacher.
None-the-less Mathematicians might not have very much understanding >>>>>>> of the link between proof theory and computability.
Sume mathematicians do have very much understanding of that. But that >>>>>> link is not needed for understanding and solving problems separately >>>>>> in the two areas.
When I refer to rejecting an invalid input math would seem to construe >>>>>>> this as nonsense, where as computability theory would totally understand.
People working on computability theory do not understand "invalid input" >>>>>> as "impossible input".
The proof then shows, for any program f that might determine whether >>>>> programs halt, that a "pathological" program g, called with some input, >>>>> can pass its own source and its input to f and then specifically do the >>>>> opposite of what f predicts g will do. No f can exist that handles this >>>>> case, thus showing undecidability.
https://en.wikipedia.org/wiki/Halting_problem#
So then they must believe that there exists an H that does correctly >>>>> determine the halt status of every input, some inputs are simply
more difficult than others, no inputs are impossible.
That "must" is false as it does not follow from anything.
Sure it does. If there are no "impossible" inputs that entails
that all inputs are possible. When all inputs are possible then
the halting problem proof is wrong.
*Termination Analyzer H is Not Fooled by Pathological Input D*
https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
Everyone that objects to the statement that H(D,D) correctly determines
the halt status of its inputs say that believe that H(D,D) must report
on the behavior of the D(D) that invokes H(D,D).
Right, because that IS the definition of a Halt Decider.
Everyone here takes the definition of a halt decider to be
required to determine the halt status of the program that
invokes this halt decider, knowing full well that the program
that invokes this halt decider IS NOT ITS INPUT.
All these same people also know the computable functions only
operate on their inputs and are not allowed to consider anything
else.
Computable functions are the formalized analogue of the intuitive notion
of algorithms, in the sense that a function is computable if there
exists an algorithm that can do the job of the function, i.e. given an
input of the function domain it can return the corresponding output. https://en.wikipedia.org/wiki/Computable_function
When the definition of a halt decider contradicts the definition of
a computable function they can't both be right.
On 4/25/2024 3:16 AM, Mikko wrote:
On 2024-04-25 00:17:57 +0000, olcott said:
On 4/24/2024 6:01 PM, Richard Damon wrote:
On 4/24/24 11:33 AM, olcott wrote:
On 4/24/2024 3:35 AM, Mikko wrote:
On 2024-04-23 14:31:00 +0000, olcott said:
On 4/23/2024 3:21 AM, Mikko wrote:
On 2024-04-22 17:37:55 +0000, olcott said:
On 4/22/2024 10:27 AM, Mikko wrote:
On 2024-04-22 14:10:54 +0000, olcott said:
On 4/22/2024 4:35 AM, Mikko wrote:
On 2024-04-21 14:44:37 +0000, olcott said:
On 4/21/2024 2:57 AM, Mikko wrote:
On 2024-04-20 15:20:05 +0000, olcott said:
On 4/20/2024 2:54 AM, Mikko wrote:
On 2024-04-19 18:04:48 +0000, olcott said:
When we create a three-valued logic system that has these >>>>>>>>>>>>>>>>> three values: {True, False, Nonsense}Such three valued logic has the problem that a tautology of the
https://en.wikipedia.org/wiki/Three-valued_logic >>>>>>>>>>>>>>>>
ordinary propositional logic cannot be trusted to be true. For >>>>>>>>>>>>>>>> example, in ordinary logic A ∨ ¬A is always true. This means that
some ordinary proofs of ordinary theorems are no longer valid and
you need to accept the possibility that a theory that is complete
in ordinary logic is incomplete in your logic. >>>>>>>>>>>>>>>>
I only used three-valued logic as a teaching device. Whenever an
expression of language has the value of {Nonsense} then it is >>>>>>>>>>>>>>> rejected and not allowed to be used in any logical operations. It
is basically invalid input.
You cannot teach because you lack necessary skills. Therefore you
don't need any teaching device.
That is too close to ad homimen.
If you think my reasoning is incorrect then point to the error >>>>>>>>>>>>> in my reasoning. Saying that in your opinion I am a bad teacher >>>>>>>>>>>>> is too close to ad hominem because it refers to your opinion of >>>>>>>>>>>>> me and utterly bypasses any of my reasoning.
No, it isn't. You introduced youtself as a topic of discussion so >>>>>>>>>>>> you are a legitimate topic of discussion.
I didn't claim that there be any reasoning, incorrect or otherwise.
If you claim I am a bad teacher you must point out what is wrong with
the lesson otherwise your claim that I am a bad teacher is essentially
an as hominem attack.
You are not a teacher, bad or otherwise. That you lack skills that >>>>>>>>>> happen to be necessary for teaching is obvious from you postings >>>>>>>>>> here. A teacher needs to understand human psychology but you don't. >>>>>>>>>>
You may be correct that I am a terrible teacher.
None-the-less Mathematicians might not have very much understanding >>>>>>>>> of the link between proof theory and computability.
Sume mathematicians do have very much understanding of that. But that >>>>>>>> link is not needed for understanding and solving problems separately >>>>>>>> in the two areas.
When I refer to rejecting an invalid input math would seem to construe
this as nonsense, where as computability theory would totally understand.
People working on computability theory do not understand "invalid input"
as "impossible input".
The proof then shows, for any program f that might determine whether >>>>>>> programs halt, that a "pathological" program g, called with some input, >>>>>>> can pass its own source and its input to f and then specifically do the >>>>>>> opposite of what f predicts g will do. No f can exist that handles this >>>>>>> case, thus showing undecidability.
https://en.wikipedia.org/wiki/Halting_problem#
So then they must believe that there exists an H that does correctly >>>>>>> determine the halt status of every input, some inputs are simply >>>>>>> more difficult than others, no inputs are impossible.
That "must" is false as it does not follow from anything.
Sure it does. If there are no "impossible" inputs that entails
that all inputs are possible. When all inputs are possible then
the halting problem proof is wrong.
*Termination Analyzer H is Not Fooled by Pathological Input D*
https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
Everyone that objects to the statement that H(D,D) correctly determines >>>>> the halt status of its inputs say that believe that H(D,D) must report >>>>> on the behavior of the D(D) that invokes H(D,D).
Right, because that IS the definition of a Halt Decider.
Everyone here takes the definition of a halt decider to be
required to determine the halt status of the program that
invokes this halt decider, knowing full well that the program
that invokes this halt decider IS NOT ITS INPUT.
All these same people also know the computable functions only
operate on their inputs and are not allowed to consider anything
else.
Computable functions are the formalized analogue of the intuitive notion >>> of algorithms, in the sense that a function is computable if there
exists an algorithm that can do the job of the function, i.e. given an
input of the function domain it can return the corresponding output.
https://en.wikipedia.org/wiki/Computable_function
When the definition of a halt decider contradicts the definition of
a computable function they can't both be right.
When the definitions of a term contradicts the definition of another term
then both of them are wrong. A correct definition does not contradict
anything other than a different definition of the same term.
*Wrong*
In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be
true in the same sense at the same time https://en.wikipedia.org/wiki/Law_of_noncontradiction
Computable functions are the formalized analogue of the intuitive notion
of algorithms, in the sense that a function is computable if there
exists an algorithm that can do the job of the function, i.e. given an
input of the function domain it can return the corresponding output. https://en.wikipedia.org/wiki/Computable_function
*That one is correct*
01 int D(ptr x) // ptr is pointer to int function
02 {
03 int Halt_Status = H(x, x);
04 if (Halt_Status)
05 HERE: goto HERE;
06 return Halt_Status;
07 }
08
09 void main()
10 {
11 D(D);
12 }
That H(D,D) must report on the behavior of its caller is the
one that is incorrect.
On 4/25/2024 3:11 AM, Mikko wrote:
However, whether there are any impossible inputs depends
on the meaning of the word "impossible". If "impossible input" means an
imput that cannot be an input then of course every input is possible.
In computability theory and computational complexity theory, an
undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes- or-no answer. https://en.wikipedia.org/wiki/Undecidable_problem
Inputs not having an algorithm leading to a correct YES/NO
answer are called impossible inputs.
On 4/26/2024 3:32 AM, Mikko wrote:
On 2024-04-25 14:15:20 +0000, olcott said:
01 int D(ptr x) // ptr is pointer to int function
02 {
03 int Halt_Status = H(x, x);
04 if (Halt_Status)
05 HERE: goto HERE;
06 return Halt_Status;
07 }
08
09 void main()
10 {
11 D(D);
12 }
That H(D,D) must report on the behavior of its caller is the
one that is incorrect.
What H(D,D) must report is independet of what procedure (if any)
calls it.
Thus when H(D,D) correctly reports that its input D(D) cannot possibly
reach its own line 6 and halt no matter what H does then H can abort its input and report that its input D(D) does not halt.
The fact that the D(D) executed in main does halt is none of H's
business because H is not allowed to report on the behavior of its
caller.
On 4/26/2024 4:16 AM, Mikko wrote:
On 2024-04-25 14:08:49 +0000, olcott said:
On 4/25/2024 3:11 AM, Mikko wrote:
However, whether there are any impossible inputs depends
on the meaning of the word "impossible". If "impossible input" means an >>>> imput that cannot be an input then of course every input is possible.
In computability theory and computational complexity theory, an
undecidable problem is a decision problem for which it is proved to be
impossible to construct an algorithm that always leads to a correct yes- >>> or-no answer. https://en.wikipedia.org/wiki/Undecidable_problem
In logic "undecidable" is more often used in the expressions like
"undecidable proposition" where it means that neither the proposition
nor its negation is provable. In the expression "undecidable problem"
the meaning of "undecidable" is different. In order to avoid confusion
it is better to use the expression "unsolvable problem".
An undecidable sentence of a theory K is a closed wf ℬ of K such that neither ℬ nor ¬ℬ is a theorem of K, that is, such that not-⊢K ℬ and not-⊢K ¬ℬ. (Mendelson: 2015:208)
AKA Undecidable(K, ℬ) ≡ ∃ℬ ∈ K ((K ⊬ ℬ) ∧ (K ⊬ ¬ℬ))
impossible to construct an algorithm that always leads to a correct yes
or-no answer is isomorphic to cannot be proved or refuted from axioms.
True(L, x) ≡ ∃x ∈ L (L ⊢ x)
False(L, x) ≡ ∃x ∈ L (L ⊢ ¬x)
Truth_Bearer(L, x) ≡ ∃x ∈ L (True(L, x) ∨ False(L, ¬x))
Because Quine convinced most people that there is no such thing as
{true on the basis of meaning} most people simply disbelieve that
expressions of language can be proved true on the basis of axioms
that formalize the meanings of these expressions.
That is like saying we cannot know that 2 + 3 = 5 because people
simply do not "believe in" numbers or arithmetic.
Inputs not having an algorithm leading to a correct YES/NO
answer are called impossible inputs.
"Inputs not having an algorithm" does not make sense. If there is an
algorithm for a problem it is for all inputs.
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof... (Gödel 1931:43-44)
epistemological antinomies (AKA Self-contradictory expressions) cannot
be proved or refuted by formal systems or algorithms because they are
neither true nor false.
When a decision problem does not reject self-contradictory expressions
then they seem to prove that this problem is undecidable.
On 4/26/2024 3:32 AM, Mikko wrote:
On 2024-04-25 14:15:20 +0000, olcott said:
On 4/25/2024 3:16 AM, Mikko wrote:
On 2024-04-25 00:17:57 +0000, olcott said:
On 4/24/2024 6:01 PM, Richard Damon wrote:
On 4/24/24 11:33 AM, olcott wrote:
On 4/24/2024 3:35 AM, Mikko wrote:
On 2024-04-23 14:31:00 +0000, olcott said:
On 4/23/2024 3:21 AM, Mikko wrote:
On 2024-04-22 17:37:55 +0000, olcott said:
On 4/22/2024 10:27 AM, Mikko wrote:
On 2024-04-22 14:10:54 +0000, olcott said:
On 4/22/2024 4:35 AM, Mikko wrote:
On 2024-04-21 14:44:37 +0000, olcott said:
On 4/21/2024 2:57 AM, Mikko wrote:
On 2024-04-20 15:20:05 +0000, olcott said:
On 4/20/2024 2:54 AM, Mikko wrote:
On 2024-04-19 18:04:48 +0000, olcott said: >>>>>>>>>>>>>>>>>>
When we create a three-valued logic system that has these >>>>>>>>>>>>>>>>>>> three values: {True, False, Nonsense}Such three valued logic has the problem that a tautology of the
https://en.wikipedia.org/wiki/Three-valued_logic >>>>>>>>>>>>>>>>>>
ordinary propositional logic cannot be trusted to be true. For
example, in ordinary logic A ∨ ¬A is always true. This means that
some ordinary proofs of ordinary theorems are no longer valid and
you need to accept the possibility that a theory that is complete
in ordinary logic is incomplete in your logic. >>>>>>>>>>>>>>>>>>
I only used three-valued logic as a teaching device. Whenever an
expression of language has the value of {Nonsense} then it is >>>>>>>>>>>>>>>>> rejected and not allowed to be used in any logical operations. It
is basically invalid input.
You cannot teach because you lack necessary skills. Therefore you
don't need any teaching device.
That is too close to ad homimen.
If you think my reasoning is incorrect then point to the error >>>>>>>>>>>>>>> in my reasoning. Saying that in your opinion I am a bad teacher >>>>>>>>>>>>>>> is too close to ad hominem because it refers to your opinion of >>>>>>>>>>>>>>> me and utterly bypasses any of my reasoning.
No, it isn't. You introduced youtself as a topic of discussion so
you are a legitimate topic of discussion.
I didn't claim that there be any reasoning, incorrect or otherwise.
If you claim I am a bad teacher you must point out what is wrong with
the lesson otherwise your claim that I am a bad teacher is essentially
an as hominem attack.
You are not a teacher, bad or otherwise. That you lack skills that >>>>>>>>>>>> happen to be necessary for teaching is obvious from you postings >>>>>>>>>>>> here. A teacher needs to understand human psychology but you don't.
You may be correct that I am a terrible teacher.
None-the-less Mathematicians might not have very much understanding >>>>>>>>>>> of the link between proof theory and computability.
Sume mathematicians do have very much understanding of that. But that
link is not needed for understanding and solving problems separately >>>>>>>>>> in the two areas.
When I refer to rejecting an invalid input math would seem to construe
this as nonsense, where as computability theory would totally understand.
People working on computability theory do not understand "invalid input"
as "impossible input".
The proof then shows, for any program f that might determine whether >>>>>>>>> programs halt, that a "pathological" program g, called with some input,
can pass its own source and its input to f and then specifically do the
opposite of what f predicts g will do. No f can exist that handles this
case, thus showing undecidability.
https://en.wikipedia.org/wiki/Halting_problem#
So then they must believe that there exists an H that does correctly >>>>>>>>> determine the halt status of every input, some inputs are simply >>>>>>>>> more difficult than others, no inputs are impossible.
That "must" is false as it does not follow from anything.
Sure it does. If there are no "impossible" inputs that entails
that all inputs are possible. When all inputs are possible then
the halting problem proof is wrong.
*Termination Analyzer H is Not Fooled by Pathological Input D*
https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
Everyone that objects to the statement that H(D,D) correctly determines >>>>>>> the halt status of its inputs say that believe that H(D,D) must report >>>>>>> on the behavior of the D(D) that invokes H(D,D).
Right, because that IS the definition of a Halt Decider.
Everyone here takes the definition of a halt decider to be
required to determine the halt status of the program that
invokes this halt decider, knowing full well that the program
that invokes this halt decider IS NOT ITS INPUT.
All these same people also know the computable functions only
operate on their inputs and are not allowed to consider anything
else.
Computable functions are the formalized analogue of the intuitive notion >>>>> of algorithms, in the sense that a function is computable if there
exists an algorithm that can do the job of the function, i.e. given an >>>>> input of the function domain it can return the corresponding output. >>>>> https://en.wikipedia.org/wiki/Computable_function
When the definition of a halt decider contradicts the definition of
a computable function they can't both be right.
When the definitions of a term contradicts the definition of another term >>>> then both of them are wrong. A correct definition does not contradict
anything other than a different definition of the same term.
*Wrong*
That "Wrong" is wrong as it refers to a true statement.
No it only proves that at least one of them are wrong.then both of them are wrong.
That is like saying we cannot know that 2 + 3 = 5 because people
simply do not "believe in" numbers or arithmetic.
On 4/27/2024 3:41 AM, Mikko wrote:
On 2024-04-26 16:21:21 +0000, olcott said:
That is like saying we cannot know that 2 + 3 = 5 because people
simply do not "believe in" numbers or arithmetic.
There really are that kind of people. They usually don't believe
that 2 + 3 = 5 because they learned it before they learned that
one can disbelieve. But people often disbelieve logical proofs
because they learned about proofs only when they already had
learned to disbelieve, and even then not very much about proofs,
just enough to disbelieve. Consequently, there are people posting
in various newgroups that they have found a solution to a problem
that is proven unsolvable.
Likewise most people have been indoctrinated to believe that the
errors of logic are not errors.
When we encode the principle of explosion as a syllogism:
Socrates is a man.
Socrates is not a man.
Therefore, Socrates is a butterfly.
The conclusion does not follow from the premises,
thus the non-sequitur error. https://en.wikipedia.org/wiki/Principle_of_explosion
In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be
true in the same sense at the same time, e. g. the two propositions "p
is the case" and "p is not the case" are mutually exclusive. https://en.wikipedia.org/wiki/Law_of_noncontradiction
{A, ~A} ⊨ FALSE fixes this problem
On 4/27/2024 3:24 AM, Mikko wrote:
On 2024-04-26 13:54:05 +0000, olcott said:
On 4/26/2024 3:32 AM, Mikko wrote:
On 2024-04-25 14:15:20 +0000, olcott said:No it only proves that at least one of them are wrong.
On 4/25/2024 3:16 AM, Mikko wrote:
On 2024-04-25 00:17:57 +0000, olcott said:
On 4/24/2024 6:01 PM, Richard Damon wrote:
On 4/24/24 11:33 AM, olcott wrote:
On 4/24/2024 3:35 AM, Mikko wrote:
On 2024-04-23 14:31:00 +0000, olcott said:
On 4/23/2024 3:21 AM, Mikko wrote:
On 2024-04-22 17:37:55 +0000, olcott said:
On 4/22/2024 10:27 AM, Mikko wrote:
On 2024-04-22 14:10:54 +0000, olcott said:
On 4/22/2024 4:35 AM, Mikko wrote:
On 2024-04-21 14:44:37 +0000, olcott said:
On 4/21/2024 2:57 AM, Mikko wrote:
On 2024-04-20 15:20:05 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 4/20/2024 2:54 AM, Mikko wrote:
On 2024-04-19 18:04:48 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
When we create a three-valued logic system that has these >>>>>>>>>>>>>>>>>>>>> three values: {True, False, Nonsense} >>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Three-valued_logic >>>>>>>>>>>>>>>>>>>>Such three valued logic has the problem that a tautology of the
ordinary propositional logic cannot be trusted to be true. For
example, in ordinary logic A ∨ ¬A is always true. This means that
some ordinary proofs of ordinary theorems are no longer valid and
you need to accept the possibility that a theory that is complete
in ordinary logic is incomplete in your logic. >>>>>>>>>>>>>>>>>>>>
I only used three-valued logic as a teaching device. Whenever an
expression of language has the value of {Nonsense} then it is
rejected and not allowed to be used in any logical operations. It
is basically invalid input.
You cannot teach because you lack necessary skills. Therefore you
don't need any teaching device.
That is too close to ad homimen.
If you think my reasoning is incorrect then point to the error
in my reasoning. Saying that in your opinion I am a bad teacher
is too close to ad hominem because it refers to your opinion of
me and utterly bypasses any of my reasoning.
No, it isn't. You introduced youtself as a topic of discussion so
you are a legitimate topic of discussion.
I didn't claim that there be any reasoning, incorrect or otherwise.
If you claim I am a bad teacher you must point out what is wrong with
the lesson otherwise your claim that I am a bad teacher is essentially
an as hominem attack.
You are not a teacher, bad or otherwise. That you lack skills that
happen to be necessary for teaching is obvious from you postings >>>>>>>>>>>>>> here. A teacher needs to understand human psychology but you don't.
You may be correct that I am a terrible teacher.
None-the-less Mathematicians might not have very much understanding
of the link between proof theory and computability.
Sume mathematicians do have very much understanding of that. But that
link is not needed for understanding and solving problems separately
in the two areas.
When I refer to rejecting an invalid input math would seem to construe
this as nonsense, where as computability theory would totally understand.
People working on computability theory do not understand "invalid input"
as "impossible input".
The proof then shows, for any program f that might determine whether
programs halt, that a "pathological" program g, called with some input,
can pass its own source and its input to f and then specifically do the
opposite of what f predicts g will do. No f can exist that handles this
case, thus showing undecidability.
https://en.wikipedia.org/wiki/Halting_problem#
So then they must believe that there exists an H that does correctly
determine the halt status of every input, some inputs are simply >>>>>>>>>>> more difficult than others, no inputs are impossible.
That "must" is false as it does not follow from anything.
Sure it does. If there are no "impossible" inputs that entails >>>>>>>>> that all inputs are possible. When all inputs are possible then >>>>>>>>> the halting problem proof is wrong.
*Termination Analyzer H is Not Fooled by Pathological Input D* >>>>>>>>> https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
Everyone that objects to the statement that H(D,D) correctly determines
the halt status of its inputs say that believe that H(D,D) must report
on the behavior of the D(D) that invokes H(D,D).
Right, because that IS the definition of a Halt Decider.
Everyone here takes the definition of a halt decider to be
required to determine the halt status of the program that
invokes this halt decider, knowing full well that the program
that invokes this halt decider IS NOT ITS INPUT.
All these same people also know the computable functions only
operate on their inputs and are not allowed to consider anything >>>>>>> else.
Computable functions are the formalized analogue of the intuitive notion
of algorithms, in the sense that a function is computable if there >>>>>>> exists an algorithm that can do the job of the function, i.e. given an >>>>>>> input of the function domain it can return the corresponding output. >>>>>>> https://en.wikipedia.org/wiki/Computable_function
When the definition of a halt decider contradicts the definition of >>>>>>> a computable function they can't both be right.
When the definitions of a term contradicts the definition of another term
then both of them are wrong. A correct definition does not contradict >>>>>> anything other than a different definition of the same term.
*Wrong*
That "Wrong" is wrong as it refers to a true statement.
then both of them are wrong.
A correct definition cannot contradict any other sentence, including
other defintions as well as any true and false claims. If a "defintion"
contradicts something then it is not really a definition.
*That is not the way that it works*
If a pair of existing definitions
contradict each other then at least one of them is incorrect.
It might
be the one that you thought was correct.
On 4/28/2024 3:36 AM, Mikko wrote:
On 2024-04-27 13:39:50 +0000, olcott said:
On 4/27/2024 3:24 AM, Mikko wrote:
On 2024-04-26 13:54:05 +0000, olcott said:
On 4/26/2024 3:32 AM, Mikko wrote:
On 2024-04-25 14:15:20 +0000, olcott said:No it only proves that at least one of them are wrong.
On 4/25/2024 3:16 AM, Mikko wrote:
On 2024-04-25 00:17:57 +0000, olcott said:
On 4/24/2024 6:01 PM, Richard Damon wrote:
On 4/24/24 11:33 AM, olcott wrote:
On 4/24/2024 3:35 AM, Mikko wrote:
On 2024-04-23 14:31:00 +0000, olcott said:
On 4/23/2024 3:21 AM, Mikko wrote:That "must" is false as it does not follow from anything. >>>>>>>>>>>>
On 2024-04-22 17:37:55 +0000, olcott said:
On 4/22/2024 10:27 AM, Mikko wrote:Sume mathematicians do have very much understanding of that. But that
On 2024-04-22 14:10:54 +0000, olcott said:
On 4/22/2024 4:35 AM, Mikko wrote:
On 2024-04-21 14:44:37 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 4/21/2024 2:57 AM, Mikko wrote:No, it isn't. You introduced youtself as a topic of discussion so
On 2024-04-20 15:20:05 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 4/20/2024 2:54 AM, Mikko wrote:
On 2024-04-19 18:04:48 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
When we create a three-valued logic system that has theseSuch three valued logic has the problem that a tautology of the
three values: {True, False, Nonsense} >>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Three-valued_logic >>>>>>>>>>>>>>>>>>>>>>
ordinary propositional logic cannot be trusted to be true. For
example, in ordinary logic A ∨ ¬A is always true. This means that
some ordinary proofs of ordinary theorems are no longer valid and
you need to accept the possibility that a theory that is complete
in ordinary logic is incomplete in your logic. >>>>>>>>>>>>>>>>>>>>>>
I only used three-valued logic as a teaching device. Whenever an
expression of language has the value of {Nonsense} then it is
rejected and not allowed to be used in any logical operations. It
is basically invalid input.
You cannot teach because you lack necessary skills. Therefore you
don't need any teaching device.
That is too close to ad homimen.
If you think my reasoning is incorrect then point to the error
in my reasoning. Saying that in your opinion I am a bad teacher
is too close to ad hominem because it refers to your opinion of
me and utterly bypasses any of my reasoning. >>>>>>>>>>>>>>>>>>
you are a legitimate topic of discussion.
I didn't claim that there be any reasoning, incorrect or otherwise.
If you claim I am a bad teacher you must point out what is wrong with
the lesson otherwise your claim that I am a bad teacher is essentially
an as hominem attack.
You are not a teacher, bad or otherwise. That you lack skills that
happen to be necessary for teaching is obvious from you postings
here. A teacher needs to understand human psychology but you don't.
You may be correct that I am a terrible teacher. >>>>>>>>>>>>>>> None-the-less Mathematicians might not have very much understanding
of the link between proof theory and computability. >>>>>>>>>>>>>>
link is not needed for understanding and solving problems separately
in the two areas.
When I refer to rejecting an invalid input math would seem to construe
this as nonsense, where as computability theory would totally understand.
People working on computability theory do not understand "invalid input"
as "impossible input".
The proof then shows, for any program f that might determine whether
programs halt, that a "pathological" program g, called with some input,
can pass its own source and its input to f and then specifically do the
opposite of what f predicts g will do. No f can exist that handles this
case, thus showing undecidability.
https://en.wikipedia.org/wiki/Halting_problem#
So then they must believe that there exists an H that does correctly
determine the halt status of every input, some inputs are simply >>>>>>>>>>>>> more difficult than others, no inputs are impossible. >>>>>>>>>>>>
Sure it does. If there are no "impossible" inputs that entails >>>>>>>>>>> that all inputs are possible. When all inputs are possible then >>>>>>>>>>> the halting problem proof is wrong.
*Termination Analyzer H is Not Fooled by Pathological Input D* >>>>>>>>>>> https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
Everyone that objects to the statement that H(D,D) correctly determines
the halt status of its inputs say that believe that H(D,D) must report
on the behavior of the D(D) that invokes H(D,D).
Right, because that IS the definition of a Halt Decider.
Everyone here takes the definition of a halt decider to be
required to determine the halt status of the program that
invokes this halt decider, knowing full well that the program >>>>>>>>> that invokes this halt decider IS NOT ITS INPUT.
All these same people also know the computable functions only >>>>>>>>> operate on their inputs and are not allowed to consider anything >>>>>>>>> else.
Computable functions are the formalized analogue of the intuitive notion
of algorithms, in the sense that a function is computable if there >>>>>>>>> exists an algorithm that can do the job of the function, i.e. given an
input of the function domain it can return the corresponding output. >>>>>>>>> https://en.wikipedia.org/wiki/Computable_function
When the definition of a halt decider contradicts the definition of >>>>>>>>> a computable function they can't both be right.
When the definitions of a term contradicts the definition of another term
then both of them are wrong. A correct definition does not contradict >>>>>>>> anything other than a different definition of the same term.
*Wrong*
That "Wrong" is wrong as it refers to a true statement.
then both of them are wrong.
A correct definition cannot contradict any other sentence, including
other defintions as well as any true and false claims. If a "defintion" >>>> contradicts something then it is not really a definition.
*That is not the way that it works*
Yes, it is. A correct definition does not claim anything, so it cannot
contradict anything.
If a pair of existing definitions
contradict each other then at least one of them is incorrect.
If a definition contradicts anything then it is incorrect.
If both of them contradict something then both are incorrect.
Are you actually paying attention or just glancing at a few
words and then spouting off something?
Translated into a syllogism:
All A are True
No A are True
Therefore B
On 4/29/2024 4:17 AM, Mikko wrote:
On 2024-04-28 13:10:29 +0000, olcott said:
On 4/28/2024 3:36 AM, Mikko wrote:
On 2024-04-27 13:39:50 +0000, olcott said:
On 4/27/2024 3:24 AM, Mikko wrote:
On 2024-04-26 13:54:05 +0000, olcott said:
On 4/26/2024 3:32 AM, Mikko wrote:
On 2024-04-25 14:15:20 +0000, olcott said:No it only proves that at least one of them are wrong.
On 4/25/2024 3:16 AM, Mikko wrote:
On 2024-04-25 00:17:57 +0000, olcott said:
On 4/24/2024 6:01 PM, Richard Damon wrote:
On 4/24/24 11:33 AM, olcott wrote:
On 4/24/2024 3:35 AM, Mikko wrote:
On 2024-04-23 14:31:00 +0000, olcott said:
On 4/23/2024 3:21 AM, Mikko wrote:That "must" is false as it does not follow from anything. >>>>>>>>>>>>>>
On 2024-04-22 17:37:55 +0000, olcott said:
On 4/22/2024 10:27 AM, Mikko wrote:Sume mathematicians do have very much understanding of that. But that
On 2024-04-22 14:10:54 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 4/22/2024 4:35 AM, Mikko wrote:
On 2024-04-21 14:44:37 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 4/21/2024 2:57 AM, Mikko wrote:No, it isn't. You introduced youtself as a topic of discussion so
On 2024-04-20 15:20:05 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
On 4/20/2024 2:54 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2024-04-19 18:04:48 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>
When we create a three-valued logic system that has theseSuch three valued logic has the problem that a tautology of the
three values: {True, False, Nonsense} >>>>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Three-valued_logic >>>>>>>>>>>>>>>>>>>>>>>>
ordinary propositional logic cannot be trusted to be true. For
example, in ordinary logic A ∨ ¬A is always true. This means that
some ordinary proofs of ordinary theorems are no longer valid and
you need to accept the possibility that a theory that is complete
in ordinary logic is incomplete in your logic. >>>>>>>>>>>>>>>>>>>>>>>>
I only used three-valued logic as a teaching device. Whenever an
expression of language has the value of {Nonsense} then it is
rejected and not allowed to be used in any logical operations. It
is basically invalid input.
You cannot teach because you lack necessary skills. Therefore you
don't need any teaching device.
That is too close to ad homimen.
If you think my reasoning is incorrect then point to the error
in my reasoning. Saying that in your opinion I am a bad teacher
is too close to ad hominem because it refers to your opinion of
me and utterly bypasses any of my reasoning. >>>>>>>>>>>>>>>>>>>>
you are a legitimate topic of discussion. >>>>>>>>>>>>>>>>>>>>
I didn't claim that there be any reasoning, incorrect or otherwise.
If you claim I am a bad teacher you must point out what is wrong with
the lesson otherwise your claim that I am a bad teacher is essentially
an as hominem attack.
You are not a teacher, bad or otherwise. That you lack skills that
happen to be necessary for teaching is obvious from you postings
here. A teacher needs to understand human psychology but you don't.
You may be correct that I am a terrible teacher. >>>>>>>>>>>>>>>>> None-the-less Mathematicians might not have very much understanding
of the link between proof theory and computability. >>>>>>>>>>>>>>>>
link is not needed for understanding and solving problems separately
in the two areas.
When I refer to rejecting an invalid input math would seem to construe
this as nonsense, where as computability theory would totally understand.
People working on computability theory do not understand "invalid input"
as "impossible input".
The proof then shows, for any program f that might determine whether
programs halt, that a "pathological" program g, called with some input,
can pass its own source and its input to f and then specifically do the
opposite of what f predicts g will do. No f can exist that handles this
case, thus showing undecidability.
https://en.wikipedia.org/wiki/Halting_problem#
So then they must believe that there exists an H that does correctly
determine the halt status of every input, some inputs are simply
more difficult than others, no inputs are impossible. >>>>>>>>>>>>>>
Sure it does. If there are no "impossible" inputs that entails >>>>>>>>>>>>> that all inputs are possible. When all inputs are possible then >>>>>>>>>>>>> the halting problem proof is wrong.
*Termination Analyzer H is Not Fooled by Pathological Input D* >>>>>>>>>>>>> https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
Everyone that objects to the statement that H(D,D) correctly determines
the halt status of its inputs say that believe that H(D,D) must report
on the behavior of the D(D) that invokes H(D,D).
Right, because that IS the definition of a Halt Decider. >>>>>>>>>>>>
Everyone here takes the definition of a halt decider to be >>>>>>>>>>> required to determine the halt status of the program that >>>>>>>>>>> invokes this halt decider, knowing full well that the program >>>>>>>>>>> that invokes this halt decider IS NOT ITS INPUT.
All these same people also know the computable functions only >>>>>>>>>>> operate on their inputs and are not allowed to consider anything >>>>>>>>>>> else.
Computable functions are the formalized analogue of the intuitive notion
of algorithms, in the sense that a function is computable if there >>>>>>>>>>> exists an algorithm that can do the job of the function, i.e. given an
input of the function domain it can return the corresponding output.
https://en.wikipedia.org/wiki/Computable_function
When the definition of a halt decider contradicts the definition of >>>>>>>>>>> a computable function they can't both be right.
When the definitions of a term contradicts the definition of another term
then both of them are wrong. A correct definition does not contradict
anything other than a different definition of the same term. >>>>>>>>>>
*Wrong*
That "Wrong" is wrong as it refers to a true statement.
then both of them are wrong.
A correct definition cannot contradict any other sentence, including >>>>>> other defintions as well as any true and false claims. If a "defintion" >>>>>> contradicts something then it is not really a definition.
*That is not the way that it works*
Yes, it is. A correct definition does not claim anything, so it cannot >>>> contradict anything.
If a pair of existing definitions
contradict each other then at least one of them is incorrect.
If a definition contradicts anything then it is incorrect.
If both of them contradict something then both are incorrect.
Are you actually paying attention or just glancing at a few
words and then spouting off something?
No reason to actually pay attention as long as observed errors remain
uncorrected.
All of the prior objections have been fully addressed yet cannot be understood until all of the preceding steps of the proof are understood.
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