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).
They say this knowing full well that computable functions only operate
on their inputs. This also violates the definition of a decider that
only computes the mapping from its inputs. Thus expecting H(D,D) to
report on the behavior of the D(D) that invokes H(D,D) violates two core principles of of computer science.
Finally the behavior of the simulated D(D) before H aborts its
simulation is different than the behavior of the executed D(D) after H
has aborted its simulation. H(D,D) must report on the behavior that it actually sees.
They understand it as an input that must be
handled differently from ordinary input. Likewise, mathematicians do
understand that some inputs must be considered separately and
differently.
But mathematicians don't call those inputs "invalid".
It is so dead obvious that the whole world must be wired with a short
circuit in their brains. Formal bivalent mathematical systems of logic
must reject every expression that cannot possibly have a value of true
or false as a type mismatch error.
Gödel's completeness theorem proves that every consistent first order
theory has a model, i.e., there is an interpretation that assigns a
truth value to every formula of the theory. No such proof is known for
second or higher order theories.
By switching from model theory to proof theory we need no
interpretations. Every system of logic is simply relations
between finite strings.
To get rid of undecidability and incompleteness we simply encode all of
the facts of the general knowledge of the actual world as axioms of a
formal system of logic.
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))
A proposition is a central concept in the philosophy of language,
semantics, logic, and related fields, often characterized as the primary >>> bearer of truth or falsity. https://en.wikipedia.org/wiki/Proposition
In formal logic the corresponding concept is sentence.
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.
To say otherwise just proves you don't actually know the meanings of
the words you are using.
They say this knowing full well that computable functions only
operate on their inputs. This also violates the definition of a
decider that only computes the mapping from its inputs. Thus
expecting H(D,D) to report on the behavior of the D(D) that invokes
H(D,D) violates two core principles of of computer science.
Nope, and the fact you think so shows you don't understand those core
principles.
*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
On 4/24/2024 7:49 PM, Richard Damon wrote:
On 4/24/24 8:17 PM, olcott wrote:
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.
And what you don't seem to understand is that it *IS*.
The DEFINITION of a Halt Decider is to decide on the program described
by it input.
What else could that mean but the program described by the input?
All these same people also know the computable functions only
operate on their inputs and are not allowed to consider anything
else.
First, we don't know that a Halt Decider is a "Computable Function"
and in fact, that is the question, is the Halting Function computable?
Second, the input IS a "Description of the program" to be decided on,
so that IS the input.
You don't seem to understand the meaning of the word "description"
Everyone else is wrong about this when they allow a description
to include the program that invokes the halt decider.
These same people already know that the program that invokes
the decider is definitely not its input.
These same people also know that computable functions only
operate on their inputs.
So they are simply contradicting their own views by not paying attention.
On 4/24/2024 9:00 PM, Richard Damon wrote:
On 4/24/24 8:57 PM, olcott wrote:
On 4/24/2024 7:49 PM, Richard Damon wrote:
On 4/24/24 8:17 PM, olcott wrote:
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:Right, because that IS the definition of a Halt Decider.
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 >>>>>>>>>>>>>>>>>>> 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.
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). >>>>>>
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.
And what you don't seem to understand is that it *IS*.
The DEFINITION of a Halt Decider is to decide on the program
described by it input.
What else could that mean but the program described by the input?
All these same people also know the computable functions only
operate on their inputs and are not allowed to consider anything
else.
First, we don't know that a Halt Decider is a "Computable Function"
and in fact, that is the question, is the Halting Function computable? >>>>
Second, the input IS a "Description of the program" to be decided
on, so that IS the input.
You don't seem to understand the meaning of the word "description"
Everyone else is wrong about this when they allow a description
to include the program that invokes the halt decider.
Why?
Why can't you describe that program?
The x86 code is the only description finite string input that H is
allowed to have.
If you can't, then you have just admitted that you decider can't
handle ALL possible inputs.
The D(D) that invokes H(D,D) IS NOT ITS INPUT AND YOU KNOW THAT!
These same people already know that the program that invokes
the decider is definitely not its input.
But it IS, as that is PRECISELY the program described by the input.
The D(D) that invokes H(D,D) IS NOT ITS INPUT AND HAS DIFFERENT BEHAVIOR
the behavior of the simulated D(D) before H aborts its simulation is different than the behavior of the executed D(D) after H has aborted its simulation. H(D,D) must report on the behavior that it actually sees.
These same people also know that computable functions only
operate on their inputs.
Again, why do you FALSELY assume the function is computable?
Requiring a computation to report on the behavior its its caller
is computationally incorrect. COMPUTATIONS ARE NOT ALLOWED TO DO THAT!!!
Or why that desciption isn't the description of the program that calls H?
So they are simply contradicting their own views by not paying
attention.
Nope, YOU are the one with the contradiction.
You claim H meets the requirements, which means that it should be able
to decide about any program described by its input, and that you can
describe and program, but then say that this program can't be given to
your decider.
That is just admitting that you have been lying.
It seems, that again, you just don't understand the meaning of the
terms you are using, and just falsely accuse anything that doesn't
make sense to you as incorrect.
That just proves that you are utter ignorant about what you are
talking about and have made yourself into a pathological liar.
On 4/24/2024 10:38 PM, Richard Damon wrote:
On 4/24/24 10:16 PM, olcott wrote:
On 4/24/2024 9:00 PM, Richard Damon wrote:
On 4/24/24 8:57 PM, olcott wrote:
On 4/24/2024 7:49 PM, Richard Damon wrote:
On 4/24/24 8:17 PM, olcott wrote:
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 >>>>>>>>>>>>>>>>>>>>> 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.
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.
And what you don't seem to understand is that it *IS*.
The DEFINITION of a Halt Decider is to decide on the program
described by it input.
What else could that mean but the program described by the input?
All these same people also know the computable functions only
operate on their inputs and are not allowed to consider anything >>>>>>> else.
First, we don't know that a Halt Decider is a "Computable
Function" and in fact, that is the question, is the Halting
Function computable?
Second, the input IS a "Description of the program" to be decided
on, so that IS the input.
You don't seem to understand the meaning of the word "description" >>>>>>
Everyone else is wrong about this when they allow a description
to include the program that invokes the halt decider.
Why?
Why can't you describe that program?
The x86 code is the only description finite string input that H is
allowed to have.
And either that can describe the full program D(D), or you are just
admitting that H fails to be a Halt Decider by its own limitations.
Remember, the REQUIREMENTS prevail, if you somehow restrict H so you
can not describe some programs to it, then H BY DEFINITION fails to be
the needed decider.
If you can't, then you have just admitted that you decider can't
handle ALL possible inputs.
The D(D) that invokes H(D,D) IS NOT ITS INPUT AND YOU KNOW THAT!
Why not? The x86 code given to H it the code for it, at least if you
include ALL the x86 code of the full program D.
If YOU decided to not give it enough of the description, then you are
just admitting to LYING about what you are doing.
These same people already know that the program that invokes
the decider is definitely not its input.
But it IS, as that is PRECISELY the program described by the input.
The D(D) that invokes H(D,D) IS NOT ITS INPUT AND HAS DIFFERENT BEHAVIOR
Nope. If H is the required computation, then D is also a computation,
and all copies of it behave the same.
I guess you are just admitting that you your logic system determinism
doesn't exist, and thus a given statement might be both True or False
at the same or diffferent times. In other words, you are describe a
system without a real definiton of Truth,
That seems right for what you have described.
the behavior of the simulated D(D) before H aborts its simulation is
different than the behavior of the executed D(D) after H has aborted its >>> simulation. H(D,D) must report on the behavior that it actually sees.
Then the simulation is INCORRECT, PERIOD, BY DEFINITION.
THis is because the DEFINITION of a correct simulation is the behavior
of the actual program.
In fact, when you describe the "simulation" your program does, it
doesn't actually simulate a "Call H instruction", but instead used
INVALID and UNSOUND logic to try to "guess" what that behavior will be.
Thus, your claim of different behavior of simulation is just a LIE.
These same people also know that computable functions only
operate on their inputs.
Again, why do you FALSELY assume the function is computable?
Requiring a computation to report on the behavior its its caller
is computationally incorrect. COMPUTATIONS ARE NOT ALLOWED TO DO THAT!!!
But it isn't asked to report on the behavior of its caller,
You have been saying that it must report on the behavior of the D(D)
that calls H(D,D)
You have been saying that it must report on the behavior of the D(D)
that calls H(D,D)
You have been saying that it must report on the behavior of the D(D)
that calls H(D,D)
H(D,D) IS NOT ALLOWED TO DO THIS !!! AND YOU KNOW IT !!!
H(D,D) IS NOT ALLOWED TO DO THIS !!! AND YOU KNOW IT !!!
H(D,D) IS NOT ALLOWED TO DO THIS !!! AND YOU KNOW IT !!!
On 4/25/2024 3:11 AM, Mikko wrote:
On 2024-04-24 15:33:12 +0000, olcott said:
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.
Correct so far. 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.
When all inputs are possible then
the halting problem proof is wrong.
That is not true.
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 4/26/2024 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 4/27/2024 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 4/28/2024 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?
*Here is your reasoning*
Cats are animals
Cats are not animals
therefore Cats are Neither Animals nor Not Animals
It might
be the one that you thought was correct.
One should not think it was correct as it is not.
On 4/28/2024 9:31 AM, Ross Finlayson wrote:
On 04/28/2024 06:10 AM, olcott wrote:
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?
*Here is your reasoning*
Cats are animals
Cats are not animals
therefore Cats are Neither Animals nor Not Animals
It might
be the one that you thought was correct.
One should not think it was correct as it is not.
There are at least two kinds of Tertium Non Datur,
A xor B
both A and B
neither A nor B
Notice that it's just Tertium Non Datur about Tertium Non Datur,
and exhausts all possibilities.
If you replace terms that are so referential in their types,
or aren't, or in consequence otherwise of the entire structure
of relation all of them together, are and aren't, they do
not model each other and it's thusly not a proof, the same.
You never got around to saying that I am correct.
When a contradiction arises between two expressions
then at most one of them is correct.
I.e., to exhaust all possibilities, when possible via induction
to arrive at each and when possible via deduction to detach
from each, and each and every and any and all, for the universal
quantifier at least so many ways, and to arrive at what exists
and what exists uniquely, the existential quantifier exactly
one way, has that what you should do is entirely rely on
a _constructivist_ approach for your own setting, insofar
as _all the ways_ it's arrived at, then also to show for
the other _constructivist_ approach, the quickest way to
the "inductive impasse", then show how deduction arrives
at what cleaves to detach, the separate concerns.
On 4/28/2024 10:10 AM, Richard Damon wrote:
On 4/28/24 10:48 AM, olcott wrote:
On 4/28/2024 9:31 AM, Ross Finlayson wrote:
On 04/28/2024 06:10 AM, olcott wrote:
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: >>>>>>>>>>>>>>>>>>>>>>>> On 2024-04-20 15:20:05 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>No, it isn't. You introduced youtself as a topic of >>>>>>>>>>>>>>>>>>>>>> discussion so
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?
*Here is your reasoning*
Cats are animals
Cats are not animals
therefore Cats are Neither Animals nor Not Animals
It might
be the one that you thought was correct.
One should not think it was correct as it is not.
There are at least two kinds of Tertium Non Datur,
A xor B
both A and B
neither A nor B
Notice that it's just Tertium Non Datur about Tertium Non Datur,
and exhausts all possibilities.
If you replace terms that are so referential in their types,
or aren't, or in consequence otherwise of the entire structure
of relation all of them together, are and aren't, they do
not model each other and it's thusly not a proof, the same.
You never got around to saying that I am correct.
When a contradiction arises between two expressions
then at most one of them is correct.
Depends on the logic system.
Some logic systems allow for two contradictory expressions to both be
correct.
Of course, those logic system have a lot of different rules for how
you do logic in them.
Language can be a mere game where incoherence is allowed or it
can establish the foundation for {true on the basis of meaning}.
In the latter contradictions prove falsehood.
I.e., to exhaust all possibilities, when possible via induction
to arrive at each and when possible via deduction to detach
from each, and each and every and any and all, for the universal
quantifier at least so many ways, and to arrive at what exists
and what exists uniquely, the existential quantifier exactly
one way, has that what you should do is entirely rely on
a _constructivist_ approach for your own setting, insofar
as _all the ways_ it's arrived at, then also to show for
the other _constructivist_ approach, the quickest way to
the "inductive impasse", then show how deduction arrives
at what cleaves to detach, the separate concerns.
On 4/28/2024 11:13 AM, Richard Damon wrote:
On 4/28/24 11:27 AM, olcott wrote:
On 4/28/2024 10:10 AM, Richard Damon wrote:
On 4/28/24 10:48 AM, olcott wrote:
On 4/28/2024 9:31 AM, Ross Finlayson wrote:
On 04/28/2024 06:10 AM, olcott wrote:
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: >>>>>>>>>>>>>>>>>>>>>> On 2024-04-22 14:10:54 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>Sume mathematicians do have very much understanding of >>>>>>>>>>>>>>>>>>>> that. But that
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: >>>>>>>>>>>>>>>>>>>>>>>>>>No, it isn't. You introduced youtself as a topic of >>>>>>>>>>>>>>>>>>>>>>>> discussion so
On 4/20/2024 2:54 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2024-04-19 18:04:48 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>You cannot teach because you lack necessary >>>>>>>>>>>>>>>>>>>>>>>>>> skills.
When we create a three-valued logic system >>>>>>>>>>>>>>>>>>>>>>>>>>>>> thatSuch three valued logic has the problem that a >>>>>>>>>>>>>>>>>>>>>>>>>>>> tautology of the
has these
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. >>>>>>>>>>>>>>>>>>>>>>>>>>
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 definitionsIf a definition contradicts anything then it is incorrect.
contradict each other then at least one of them 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?
*Here is your reasoning*
Cats are animals
Cats are not animals
therefore Cats are Neither Animals nor Not Animals
It might
be the one that you thought was correct.
One should not think it was correct as it is not.
There are at least two kinds of Tertium Non Datur,
A xor B
both A and B
neither A nor B
Notice that it's just Tertium Non Datur about Tertium Non Datur,
and exhausts all possibilities.
If you replace terms that are so referential in their types,
or aren't, or in consequence otherwise of the entire structure
of relation all of them together, are and aren't, they do
not model each other and it's thusly not a proof, the same.
You never got around to saying that I am correct.
When a contradiction arises between two expressions
then at most one of them is correct.
Depends on the logic system.
Some logic systems allow for two contradictory expressions to both
be correct.
Of course, those logic system have a lot of different rules for how
you do logic in them.
Language can be a mere game where incoherence is allowed or it
can establish the foundation for {true on the basis of meaning}.
In the latter contradictions prove falsehood.
But there CAN be real meaning even in the presence of "Contradiction".
For instance, take the statements:
Light Behaves like a Particle
Light Behaves like a Wave
These are contradictory, as things acting like a particle do not act
like waves.
I think that the problem is that you are not in the ballpark of
sufficiently precise in your use of language. This causes you
to continue to make all kinds of fallacy of equivocation errors
that you blame on me.
Light behaves lie a particle and light behaves like a wave
cannot possibly be mutually exclusive of they are both true.
Light behave like a particle and light never behaves like
a particle is an actual contradiction.
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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