On 1/21/2024 4:32 PM, Richard Damon wrote:
> On 1/21/24 4:55 PM, olcott wrote:
>> On 1/21/2024 3:52 PM, Richard Damon wrote:
>>> On 1/21/24 3:51 PM, olcott wrote:
>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>
>>>>>>>> In the conclusion section:
>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>> cannot be
>>>>>>>> for-
>>>>>>>> malised as a consistent specification. It has no model and does not
>>>>>>>> exist as
>>>>>>>> a conceptual object. Assuming its conceptual existence leads to a
>>>>>>>> paradox.
>>>>>>>> The halting problem is universally used in university courses on
>>>>>>>> Computer
>>>>>>>> Science to illustrate the limits of computation. Hehner claims the
>>>>>>>> halting
>>>>>>>> problem is misconceived......
>>>>>>>>
>>>>>>>> It looks like what olcott now is claiming. Am I missing something?
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> I think the problem he is seeing is that the property of
>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>
>>>>>>> That is all that I can get from his statement of:
>>>>>>>
>>>>>>> The idea of a universal halting test seems reasonable, but cannot
>>>>>>> be formalised as a consistent specification.
>>>>>>>
>>>>>>> There certainly CAN be defined formal test that define Halting,
>>>>>>> the issue is that non-halting is defined by the non-existence of
>>>>>>> a number N for the number of steps needed to reach a final state.
>>>>>>>
>>>>>>> Some people just don't like the fact that it can be absolutely
>>>>>>> provable what the answer is (and thus unknowable), even if we
>>>>>>> know from the definition, that it must be one or the other.
>>>>>>>
>>>>>>> This leads us to a great divide in logics. The classical branch
>>>>>>> accepts that some truth is only established by infinite chains of
>>>>>>> connections, and thus can not be proven with a finite proof, and
>>>>>>> thus is unknowable.
>>>>>>>
>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>> established by Finite chains. The problem then is, such logic
>>>>>>> system need to greatly limit the domain they attempt to cover, as
>>>>>>> otherwise you get into endless chains of asking if a question can
>>>>>>> be asked, at which point you need to ask if you can even ask
>>>>>>> about asking the questions. Only when the domain is restricted in
>>>>>>> a way that the answer MUST be determinable with finite work, can
>>>>>>> we break the cycle.
>>>>>>>
>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>> (which could be Turing Machines with a fixed finite tape, or a
>>>>>>> classical program in a computer with limited memory) then we can
>>>>>>> be sure that the answer is determinable with a finite amount of
>>>>>>> work.
>>>>>>
>>>>>> Tarski did not understand that the Liar Paradox is not a truth bearer
>>>>>> thus cannot possibly be true or false. His ignorance got him so
>>>>>> confused
>>>>>> that he thought that he proved that True(L,x) cannot be defined
>>>>>> because
>>>>>> True(Tarski_theory, LP) does not work.
>>>>>
>>>>> I'll ask one more time, exactly WHERE in the proof did he do this?
>>>>> He shows that if True(L, x) exists that the Liar Paradox is a true
>>>>> statement, but not what you say.
>>>>
>>>> "He shows that if True(L, x) exists that the Liar Paradox is a true."
>>>>
>>>> That is a perfect paraphrase of my position of what he said.
>>>>
>>>
>>> Nope, you said that he assumed the Liars Paradox has a logic value.
>>>
>>> The assumption was just that True(L,x) existed.
>>>
>>
>> No that it only half of the assumption.
>> The other half is that True(tarski_theory, "this sentence is not true")
>> must be true or false. That half was Tarksi's fatal flaw.
>>
>
> Where do you see that as an INPUT assumption, and not a result of a proof?
>
> LINE please.

"Tarski’s undefinability theorem is really just the
ancient paradox of the liar, dressed up in formal wear."

https://web.mit.edu/24.242/www/Tarskitruth.pdf

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 1/21/2024 4:30 PM, Richard Damon wrote:
> On 1/21/24 4:50 PM, olcott wrote:
>> On 1/21/2024 3:46 PM, immibis wrote:
>>> On 1/21/24 22:15, olcott wrote:
>>>> On 1/21/2024 3:09 PM, immibis wrote:
>>>>> On 1/21/24 22:07, olcott wrote:
>>>>>> On 1/21/2024 2:54 PM, immibis wrote:
>>>>>>> On 1/21/24 21:51, olcott wrote:
>>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>
>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>> cannot be
>>>>>>>>>>>> for-
>>>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>>>> does not
>>>>>>>>>>>> exist as
>>>>>>>>>>>> a conceptual object. Assuming its conceptual existence leads
>>>>>>>>>>>> to a
>>>>>>>>>>>> paradox.
>>>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>>>> courses on
>>>>>>>>>>>> Computer
>>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>>> claims the
>>>>>>>>>>>> halting
>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>
>>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>>> something?
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>>
>>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>>
>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>>
>>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>>> non-existence of a number N for the number of steps needed to
>>>>>>>>>>> reach a final state.
>>>>>>>>>>>
>>>>>>>>>>> Some people just don't like the fact that it can be
>>>>>>>>>>> absolutely provable what the answer is (and thus unknowable),
>>>>>>>>>>> even if we know from the definition, that it must be one or
>>>>>>>>>>> the other.
>>>>>>>>>>>
>>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>>> branch accepts that some truth is only established by
>>>>>>>>>>> infinite chains of connections, and thus can not be proven
>>>>>>>>>>> with a finite proof, and thus is unknowable.
>>>>>>>>>>>
>>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>>> established by Finite chains. The problem then is, such logic
>>>>>>>>>>> system need to greatly limit the domain they attempt to
>>>>>>>>>>> cover, as otherwise you get into endless chains of asking if
>>>>>>>>>>> a question can be asked, at which point you need to ask if
>>>>>>>>>>> you can even ask about asking the questions. Only when the
>>>>>>>>>>> domain is restricted in a way that the answer MUST be
>>>>>>>>>>> determinable with finite work, can we break the cycle.
>>>>>>>>>>>
>>>>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>>>>> (which could be Turing Machines with a fixed finite tape, or
>>>>>>>>>>> a classical program in a computer with limited memory) then
>>>>>>>>>>> we can be sure that the answer is determinable with a finite
>>>>>>>>>>> amount of work.
>>>>>>>>>>
>>>>>>>>>> Tarski did not understand that the Liar Paradox is not a truth
>>>>>>>>>> bearer
>>>>>>>>>> thus cannot possibly be true or false. His ignorance got him
>>>>>>>>>> so confused
>>>>>>>>>> that he thought that he proved that True(L,x) cannot be
>>>>>>>>>> defined because
>>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>>
>>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>>> this? He shows that if True(L, x) exists that the Liar Paradox
>>>>>>>>> is a true statement, but not what you say.
>>>>>>>>
>>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a
>>>>>>>> true."
>>>>>>>>
>>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>>
>>>>>>>> Why this is nutty on his part requires you to understand a term
>>>>>>>> that is not in logic or math, it is only in philosophy of logic:
>>>>>>>> {truth bearer}.
>>>>>>>>
>>>>>>>
>>>>>>> You agree it's not in logic or math. Well he talked about logic
>>>>>>> and math, not philosophy. So you agree that in logic and math,
>>>>>>> the liar paradox is true?
>>>>>>>
>>>>>>
>>>>>> I agree that it a ridiculously foolish thing to say.
>>>>>>
>>>>>> The ignorance of logic and math does not derive any
>>>>>> sort of truth.
>>>>>
>>>>> So math does not prove that 1+1=2?
>>>>>
>>>>
>>>> Always with the strawman deception.
>>>> Do you want me to start calling you a liar?
>>>>
>>>> If you don't want me to start calling you a liar
>>>> then quit using the strawman deception.
>>>>
>>>> It was pointed out that logic and math are clueless
>>>> about the Liar Paradox.
>>>
>>> Didn't Tarski translate the Liar Paradox into logic and mathematics?
>>>
>>
>> The key thing that Tarski missed is that expressions of language
>> that are not truth bearers cannot possibly have any truth value.
>> *This was his fatal mistake*
>>
>>
>
>
> No, he FULLY understood that, so any assumption that proves that it has
> one, must be false.
>
> You just don't understand how logic works.

?- LP = not(true(LP)).
LP = not(true(LP)).

?- unify_with_occurs_check(LP, not(true(LP))).
false.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 1/21/24 5:42 PM, olcott wrote:
> On 1/21/2024 4:30 PM, Richard Damon wrote:
>> On 1/21/24 4:50 PM, olcott wrote:
>>> On 1/21/2024 3:46 PM, immibis wrote:
>>>> On 1/21/24 22:15, olcott wrote:
>>>>> On 1/21/2024 3:09 PM, immibis wrote:
>>>>>> On 1/21/24 22:07, olcott wrote:
>>>>>>> On 1/21/2024 2:54 PM, immibis wrote:
>>>>>>>> On 1/21/24 21:51, olcott wrote:
>>>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>>
>>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>>> cannot be
>>>>>>>>>>>>> for-
>>>>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>>>>> does not
>>>>>>>>>>>>> exist as
>>>>>>>>>>>>> a conceptual object. Assuming its conceptual existence
>>>>>>>>>>>>> leads to a
>>>>>>>>>>>>> paradox.
>>>>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>>>>> courses on
>>>>>>>>>>>>> Computer
>>>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>>>> claims the
>>>>>>>>>>>>> halting
>>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>>
>>>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>>>> something?
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>>>
>>>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>>>
>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>>>
>>>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>>>> non-existence of a number N for the number of steps needed
>>>>>>>>>>>> to reach a final state.
>>>>>>>>>>>>
>>>>>>>>>>>> Some people just don't like the fact that it can be
>>>>>>>>>>>> absolutely provable what the answer is (and thus
>>>>>>>>>>>> unknowable), even if we know from the definition, that it
>>>>>>>>>>>> must be one or the other.
>>>>>>>>>>>>
>>>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>>>> branch accepts that some truth is only established by
>>>>>>>>>>>> infinite chains of connections, and thus can not be proven
>>>>>>>>>>>> with a finite proof, and thus is unknowable.
>>>>>>>>>>>>
>>>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>>>> established by Finite chains. The problem then is, such
>>>>>>>>>>>> logic system need to greatly limit the domain they attempt
>>>>>>>>>>>> to cover, as otherwise you get into endless chains of asking
>>>>>>>>>>>> if a question can be asked, at which point you need to ask
>>>>>>>>>>>> if you can even ask about asking the questions. Only when
>>>>>>>>>>>> the domain is restricted in a way that the answer MUST be
>>>>>>>>>>>> determinable with finite work, can we break the cycle.
>>>>>>>>>>>>
>>>>>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>>>>>> (which could be Turing Machines with a fixed finite tape, or
>>>>>>>>>>>> a classical program in a computer with limited memory) then
>>>>>>>>>>>> we can be sure that the answer is determinable with a finite
>>>>>>>>>>>> amount of work.
>>>>>>>>>>>
>>>>>>>>>>> Tarski did not understand that the Liar Paradox is not a
>>>>>>>>>>> truth bearer
>>>>>>>>>>> thus cannot possibly be true or false. His ignorance got him
>>>>>>>>>>> so confused
>>>>>>>>>>> that he thought that he proved that True(L,x) cannot be
>>>>>>>>>>> defined because
>>>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>>>
>>>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>>>> this? He shows that if True(L, x) exists that the Liar Paradox
>>>>>>>>>> is a true statement, but not what you say.
>>>>>>>>>
>>>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a
>>>>>>>>> true."
>>>>>>>>>
>>>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>>>
>>>>>>>>> Why this is nutty on his part requires you to understand a term
>>>>>>>>> that is not in logic or math, it is only in philosophy of logic:
>>>>>>>>> {truth bearer}.
>>>>>>>>>
>>>>>>>>
>>>>>>>> You agree it's not in logic or math. Well he talked about logic
>>>>>>>> and math, not philosophy. So you agree that in logic and math,
>>>>>>>> the liar paradox is true?
>>>>>>>>
>>>>>>>
>>>>>>> I agree that it a ridiculously foolish thing to say.
>>>>>>>
>>>>>>> The ignorance of logic and math does not derive any
>>>>>>> sort of truth.
>>>>>>
>>>>>> So math does not prove that 1+1=2?
>>>>>>
>>>>>
>>>>> Always with the strawman deception.
>>>>> Do you want me to start calling you a liar?
>>>>>
>>>>> If you don't want me to start calling you a liar
>>>>> then quit using the strawman deception.
>>>>>
>>>>> It was pointed out that logic and math are clueless
>>>>> about the Liar Paradox.
>>>>
>>>> Didn't Tarski translate the Liar Paradox into logic and mathematics?
>>>>
>>>
>>> The key thing that Tarski missed is that expressions of language
>>> that are not truth bearers cannot possibly have any truth value.
>>> *This was his fatal mistake*
>>>
>>>
>>
>>
>> No, he FULLY understood that, so any assumption that proves that it
>> has one, must be false.
>>
>> You just don't understand how logic works.
>
> ?- LP = not(true(LP)).
> LP = not(true(LP)).
>
> ?- unify_with_occurs_check(LP, not(true(LP))).
> false.
>
>
>

On 1/21/2024 4:37 PM, olcott wrote:
> On 1/21/2024 4:19 PM, immibis wrote:
>> On 1/21/24 22:50, olcott wrote:
>>> On 1/21/2024 3:46 PM, immibis wrote:
>>>> On 1/21/24 22:15, olcott wrote:
>>>>> On 1/21/2024 3:09 PM, immibis wrote:
>>>>>> On 1/21/24 22:07, olcott wrote:
>>>>>>> On 1/21/2024 2:54 PM, immibis wrote:
>>>>>>>> On 1/21/24 21:51, olcott wrote:
>>>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>>
>>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>>> cannot be
>>>>>>>>>>>>> for-
>>>>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>>>>> does not
>>>>>>>>>>>>> exist as
>>>>>>>>>>>>> a conceptual object. Assuming its conceptual existence
>>>>>>>>>>>>> leads to a
>>>>>>>>>>>>> paradox.
>>>>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>>>>> courses on
>>>>>>>>>>>>> Computer
>>>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>>>> claims the
>>>>>>>>>>>>> halting
>>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>>
>>>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>>>> something?
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>>>
>>>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>>>
>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>>>
>>>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>>>> non-existence of a number N for the number of steps needed
>>>>>>>>>>>> to reach a final state.
>>>>>>>>>>>>
>>>>>>>>>>>> Some people just don't like the fact that it can be
>>>>>>>>>>>> absolutely provable what the answer is (and thus
>>>>>>>>>>>> unknowable), even if we know from the definition, that it
>>>>>>>>>>>> must be one or the other.
>>>>>>>>>>>>
>>>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>>>> branch accepts that some truth is only established by
>>>>>>>>>>>> infinite chains of connections, and thus can not be proven
>>>>>>>>>>>> with a finite proof, and thus is unknowable.
>>>>>>>>>>>>
>>>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>>>> established by Finite chains. The problem then is, such
>>>>>>>>>>>> logic system need to greatly limit the domain they attempt
>>>>>>>>>>>> to cover, as otherwise you get into endless chains of asking
>>>>>>>>>>>> if a question can be asked, at which point you need to ask
>>>>>>>>>>>> if you can even ask about asking the questions. Only when
>>>>>>>>>>>> the domain is restricted in a way that the answer MUST be
>>>>>>>>>>>> determinable with finite work, can we break the cycle.
>>>>>>>>>>>>
>>>>>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>>>>>> (which could be Turing Machines with a fixed finite tape, or
>>>>>>>>>>>> a classical program in a computer with limited memory) then
>>>>>>>>>>>> we can be sure that the answer is determinable with a finite
>>>>>>>>>>>> amount of work.
>>>>>>>>>>>
>>>>>>>>>>> Tarski did not understand that the Liar Paradox is not a
>>>>>>>>>>> truth bearer
>>>>>>>>>>> thus cannot possibly be true or false. His ignorance got him
>>>>>>>>>>> so confused
>>>>>>>>>>> that he thought that he proved that True(L,x) cannot be
>>>>>>>>>>> defined because
>>>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>>>
>>>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>>>> this? He shows that if True(L, x) exists that the Liar Paradox
>>>>>>>>>> is a true statement, but not what you say.
>>>>>>>>>
>>>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a
>>>>>>>>> true."
>>>>>>>>>
>>>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>>>
>>>>>>>>> Why this is nutty on his part requires you to understand a term
>>>>>>>>> that is not in logic or math, it is only in philosophy of logic:
>>>>>>>>> {truth bearer}.
>>>>>>>>>
>>>>>>>>
>>>>>>>> You agree it's not in logic or math. Well he talked about logic
>>>>>>>> and math, not philosophy. So you agree that in logic and math,
>>>>>>>> the liar paradox is true?
>>>>>>>>
>>>>>>>
>>>>>>> I agree that it a ridiculously foolish thing to say.
>>>>>>>
>>>>>>> The ignorance of logic and math does not derive any
>>>>>>> sort of truth.
>>>>>>
>>>>>> So math does not prove that 1+1=2?
>>>>>>
>>>>>
>>>>> Always with the strawman deception.
>>>>> Do you want me to start calling you a liar?
>>>>>
>>>>> If you don't want me to start calling you a liar
>>>>> then quit using the strawman deception.
>>>>>
>>>>> It was pointed out that logic and math are clueless
>>>>> about the Liar Paradox.
>>>>
>>>> Didn't Tarski translate the Liar Paradox into logic and mathematics?
>>>>
>>>
>>> The key thing that Tarski missed is that expressions of language
>>> that are not truth bearers cannot possibly have any truth value.
>>> *This was his fatal mistake*
>>>
>>>
>> So a statement such as "∀x (x = 5)" can be neither true nor false?
>
> Yet another strawman deception
>

On 1/21/24 23:21, olcott wrote:
> On 1/21/2024 4:17 PM, immibis wrote:
>> On 1/21/24 22:55, olcott wrote:
>>> On 1/21/2024 3:52 PM, Richard Damon wrote:
>>>> On 1/21/24 3:51 PM, olcott wrote:
>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>
>>>>>>>>> In the conclusion section:
>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>> cannot be
>>>>>>>>> for-
>>>>>>>>> malised as a consistent specification. It has no model and does
>>>>>>>>> not
>>>>>>>>> exist as
>>>>>>>>> a conceptual object. Assuming its conceptual existence leads to a
>>>>>>>>> paradox.
>>>>>>>>> The halting problem is universally used in university courses on
>>>>>>>>> Computer
>>>>>>>>> Science to illustrate the limits of computation. Hehner claims the
>>>>>>>>> halting
>>>>>>>>> problem is misconceived......
>>>>>>>>>
>>>>>>>>> It looks like what olcott now is claiming. Am I missing something?
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>
>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>
>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>
>>>>>>>> There certainly CAN be defined formal test that define Halting,
>>>>>>>> the issue is that non-halting is defined by the non-existence of
>>>>>>>> a number N for the number of steps needed to reach a final state.
>>>>>>>>
>>>>>>>> Some people just don't like the fact that it can be absolutely
>>>>>>>> provable what the answer is (and thus unknowable), even if we
>>>>>>>> know from the definition, that it must be one or the other.
>>>>>>>>
>>>>>>>> This leads us to a great divide in logics. The classical branch
>>>>>>>> accepts that some truth is only established by infinite chains
>>>>>>>> of connections, and thus can not be proven with a finite proof,
>>>>>>>> and thus is unknowable.
>>>>>>>>
>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>> established by Finite chains. The problem then is, such logic
>>>>>>>> system need to greatly limit the domain they attempt to cover,
>>>>>>>> as otherwise you get into endless chains of asking if a question
>>>>>>>> can be asked, at which point you need to ask if you can even ask
>>>>>>>> about asking the questions. Only when the domain is restricted
>>>>>>>> in a way that the answer MUST be determinable with finite work,
>>>>>>>> can we break the cycle.
>>>>>>>>
>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>> (which could be Turing Machines with a fixed finite tape, or a
>>>>>>>> classical program in a computer with limited memory) then we can
>>>>>>>> be sure that the answer is determinable with a finite amount of
>>>>>>>> work.
>>>>>>>
>>>>>>> Tarski did not understand that the Liar Paradox is not a truth
>>>>>>> bearer
>>>>>>> thus cannot possibly be true or false. His ignorance got him so
>>>>>>> confused
>>>>>>> that he thought that he proved that True(L,x) cannot be defined
>>>>>>> because
>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>
>>>>>> I'll ask one more time, exactly WHERE in the proof did he do this?
>>>>>> He shows that if True(L, x) exists that the Liar Paradox is a true
>>>>>> statement, but not what you say.
>>>>>
>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a true."
>>>>>
>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>
>>>>
>>>> Nope, you said that he assumed the Liars Paradox has a logic value.
>>>>
>>>> The assumption was just that True(L,x) existed.
>>>>
>>>
>>> No that it only half of the assumption.
>>> The other half is that True(tarski_theory, "this sentence is not true")
>>> must be true or false. That half was Tarksi's fatal flaw.
>>>
>>
>> True(tarski_theory, "this sentence is not true") is actually a
>> mathematical statement consisting of elementary operations such as
>> addition, multiplication, and quantifiers. Can you show how to use
>> these basic parts to build a statement that is not true or false?
>
> When I put the same thing into Prolog
> it is rejected as semantically unsound.
>
> ?- LP = not(true(LP)).
> LP = not(true(LP)).
>
> ?- unify_with_occurs_check(LP, not(true(LP))).
> false.
>
>

That isn't how Tarski works. No wonder you don't understand the halting
problem either.

On 1/21/2024 4:47 PM, Richard Damon wrote:
> On 1/21/24 5:42 PM, olcott wrote:
>> On 1/21/2024 4:30 PM, Richard Damon wrote:
>>> On 1/21/24 4:50 PM, olcott wrote:
>>>> On 1/21/2024 3:46 PM, immibis wrote:
>>>>> On 1/21/24 22:15, olcott wrote:
>>>>>> On 1/21/2024 3:09 PM, immibis wrote:
>>>>>>> On 1/21/24 22:07, olcott wrote:
>>>>>>>> On 1/21/2024 2:54 PM, immibis wrote:
>>>>>>>>> On 1/21/24 21:51, olcott wrote:
>>>>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>>>> cannot be
>>>>>>>>>>>>>> for-
>>>>>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>>>>>> does not
>>>>>>>>>>>>>> exist as
>>>>>>>>>>>>>> a conceptual object. Assuming its conceptual existence
>>>>>>>>>>>>>> leads to a
>>>>>>>>>>>>>> paradox.
>>>>>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>>>>>> courses on
>>>>>>>>>>>>>> Computer
>>>>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>>>>> claims the
>>>>>>>>>>>>>> halting
>>>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>>>>> something?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>>>>
>>>>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>>>>
>>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>>>>
>>>>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>>>>> non-existence of a number N for the number of steps needed
>>>>>>>>>>>>> to reach a final state.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Some people just don't like the fact that it can be
>>>>>>>>>>>>> absolutely provable what the answer is (and thus
>>>>>>>>>>>>> unknowable), even if we know from the definition, that it
>>>>>>>>>>>>> must be one or the other.
>>>>>>>>>>>>>
>>>>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>>>>> branch accepts that some truth is only established by
>>>>>>>>>>>>> infinite chains of connections, and thus can not be proven
>>>>>>>>>>>>> with a finite proof, and thus is unknowable.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>>>>> established by Finite chains. The problem then is, such
>>>>>>>>>>>>> logic system need to greatly limit the domain they attempt
>>>>>>>>>>>>> to cover, as otherwise you get into endless chains of
>>>>>>>>>>>>> asking if a question can be asked, at which point you need
>>>>>>>>>>>>> to ask if you can even ask about asking the questions. Only
>>>>>>>>>>>>> when the domain is restricted in a way that the answer MUST
>>>>>>>>>>>>> be determinable with finite work, can we break the cycle.
>>>>>>>>>>>>>
>>>>>>>>>>>>> For instance, if we limit ourselves to Finite State
>>>>>>>>>>>>> Machines (which could be Turing Machines with a fixed
>>>>>>>>>>>>> finite tape, or a classical program in a computer with
>>>>>>>>>>>>> limited memory) then we can be sure that the answer is
>>>>>>>>>>>>> determinable with a finite amount of work.
>>>>>>>>>>>>
>>>>>>>>>>>> Tarski did not understand that the Liar Paradox is not a
>>>>>>>>>>>> truth bearer
>>>>>>>>>>>> thus cannot possibly be true or false. His ignorance got him
>>>>>>>>>>>> so confused
>>>>>>>>>>>> that he thought that he proved that True(L,x) cannot be
>>>>>>>>>>>> defined because
>>>>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>>>>
>>>>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>>>>> this? He shows that if True(L, x) exists that the Liar
>>>>>>>>>>> Paradox is a true statement, but not what you say.
>>>>>>>>>>
>>>>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a
>>>>>>>>>> true."
>>>>>>>>>>
>>>>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>>>>
>>>>>>>>>> Why this is nutty on his part requires you to understand a term
>>>>>>>>>> that is not in logic or math, it is only in philosophy of logic:
>>>>>>>>>> {truth bearer}.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You agree it's not in logic or math. Well he talked about logic
>>>>>>>>> and math, not philosophy. So you agree that in logic and math,
>>>>>>>>> the liar paradox is true?
>>>>>>>>>
>>>>>>>>
>>>>>>>> I agree that it a ridiculously foolish thing to say.
>>>>>>>>
>>>>>>>> The ignorance of logic and math does not derive any
>>>>>>>> sort of truth.
>>>>>>>
>>>>>>> So math does not prove that 1+1=2?
>>>>>>>
>>>>>>
>>>>>> Always with the strawman deception.
>>>>>> Do you want me to start calling you a liar?
>>>>>>
>>>>>> If you don't want me to start calling you a liar
>>>>>> then quit using the strawman deception.
>>>>>>
>>>>>> It was pointed out that logic and math are clueless
>>>>>> about the Liar Paradox.
>>>>>
>>>>> Didn't Tarski translate the Liar Paradox into logic and mathematics?
>>>>>
>>>>
>>>> The key thing that Tarski missed is that expressions of language
>>>> that are not truth bearers cannot possibly have any truth value.
>>>> *This was his fatal mistake*
>>>>
>>>>
>>>
>>>
>>> No, he FULLY understood that, so any assumption that proves that it
>>> has one, must be false.
>>>
>>> You just don't understand how logic works.
>>
>> ?- LP = not(true(LP)).
>> LP = not(true(LP)).
>>
>> ?- unify_with_occurs_check(LP, not(true(LP))).
>> false.
>>
>>
>>
>
> So, you don't, since you didn't actually answer the comment.
>

On 1/21/24 23:41, olcott wrote:
> On 1/21/2024 4:32 PM, Richard Damon wrote:
>>
>> Where do you see that as an INPUT assumption, and not a result of a
>> proof?
>>
>> LINE please.
>
> "Tarski’s undefinability theorem is really just the
> ancient paradox of the liar, dressed up in formal wear."
>
> https://web.mit.edu/24.242/www/Tarskitruth.pdf
>

And what can we learn from this?

Tarski says that if True(L,p) exists then the liar paradox has a truth
value.

The liar paradox doesn't have a truth value, therefore True(L,p) doesn't
exist.

On 1/21/24 23:37, olcott wrote:
> On 1/21/2024 4:19 PM, immibis wrote:
>> On 1/21/24 22:50, olcott wrote:
>>> On 1/21/2024 3:46 PM, immibis wrote:
>>>> On 1/21/24 22:15, olcott wrote:
>>>>> On 1/21/2024 3:09 PM, immibis wrote:
>>>>>> On 1/21/24 22:07, olcott wrote:
>>>>>>> On 1/21/2024 2:54 PM, immibis wrote:
>>>>>>>> On 1/21/24 21:51, olcott wrote:
>>>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>>
>>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>>> cannot be
>>>>>>>>>>>>> for-
>>>>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>>>>> does not
>>>>>>>>>>>>> exist as
>>>>>>>>>>>>> a conceptual object. Assuming its conceptual existence
>>>>>>>>>>>>> leads to a
>>>>>>>>>>>>> paradox.
>>>>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>>>>> courses on
>>>>>>>>>>>>> Computer
>>>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>>>> claims the
>>>>>>>>>>>>> halting
>>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>>
>>>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>>>> something?
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>>>
>>>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>>>
>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>>>
>>>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>>>> non-existence of a number N for the number of steps needed
>>>>>>>>>>>> to reach a final state.
>>>>>>>>>>>>
>>>>>>>>>>>> Some people just don't like the fact that it can be
>>>>>>>>>>>> absolutely provable what the answer is (and thus
>>>>>>>>>>>> unknowable), even if we know from the definition, that it
>>>>>>>>>>>> must be one or the other.
>>>>>>>>>>>>
>>>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>>>> branch accepts that some truth is only established by
>>>>>>>>>>>> infinite chains of connections, and thus can not be proven
>>>>>>>>>>>> with a finite proof, and thus is unknowable.
>>>>>>>>>>>>
>>>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>>>> established by Finite chains. The problem then is, such
>>>>>>>>>>>> logic system need to greatly limit the domain they attempt
>>>>>>>>>>>> to cover, as otherwise you get into endless chains of asking
>>>>>>>>>>>> if a question can be asked, at which point you need to ask
>>>>>>>>>>>> if you can even ask about asking the questions. Only when
>>>>>>>>>>>> the domain is restricted in a way that the answer MUST be
>>>>>>>>>>>> determinable with finite work, can we break the cycle.
>>>>>>>>>>>>
>>>>>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>>>>>> (which could be Turing Machines with a fixed finite tape, or
>>>>>>>>>>>> a classical program in a computer with limited memory) then
>>>>>>>>>>>> we can be sure that the answer is determinable with a finite
>>>>>>>>>>>> amount of work.
>>>>>>>>>>>
>>>>>>>>>>> Tarski did not understand that the Liar Paradox is not a
>>>>>>>>>>> truth bearer
>>>>>>>>>>> thus cannot possibly be true or false. His ignorance got him
>>>>>>>>>>> so confused
>>>>>>>>>>> that he thought that he proved that True(L,x) cannot be
>>>>>>>>>>> defined because
>>>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>>>
>>>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>>>> this? He shows that if True(L, x) exists that the Liar Paradox
>>>>>>>>>> is a true statement, but not what you say.
>>>>>>>>>
>>>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a
>>>>>>>>> true."
>>>>>>>>>
>>>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>>>
>>>>>>>>> Why this is nutty on his part requires you to understand a term
>>>>>>>>> that is not in logic or math, it is only in philosophy of logic:
>>>>>>>>> {truth bearer}.
>>>>>>>>>
>>>>>>>>
>>>>>>>> You agree it's not in logic or math. Well he talked about logic
>>>>>>>> and math, not philosophy. So you agree that in logic and math,
>>>>>>>> the liar paradox is true?
>>>>>>>>
>>>>>>>
>>>>>>> I agree that it a ridiculously foolish thing to say.
>>>>>>>
>>>>>>> The ignorance of logic and math does not derive any
>>>>>>> sort of truth.
>>>>>>
>>>>>> So math does not prove that 1+1=2?
>>>>>>
>>>>>
>>>>> Always with the strawman deception.
>>>>> Do you want me to start calling you a liar?
>>>>>
>>>>> If you don't want me to start calling you a liar
>>>>> then quit using the strawman deception.
>>>>>
>>>>> It was pointed out that logic and math are clueless
>>>>> about the Liar Paradox.
>>>>
>>>> Didn't Tarski translate the Liar Paradox into logic and mathematics?
>>>>
>>>
>>> The key thing that Tarski missed is that expressions of language
>>> that are not truth bearers cannot possibly have any truth value.
>>> *This was his fatal mistake*
>>>
>>>
>> So a statement such as "∀x (x = 5)" can be neither true nor false?
>
> Yet another strawman deception
>
Every time you say "strawman deception" it will be read as "I, Olcott,
admit to being wrong"

On 1/21/2024 4:52 PM, immibis wrote:
> On 1/21/24 23:21, olcott wrote:
>> On 1/21/2024 4:17 PM, immibis wrote:
>>> On 1/21/24 22:55, olcott wrote:
>>>> On 1/21/2024 3:52 PM, Richard Damon wrote:
>>>>> On 1/21/24 3:51 PM, olcott wrote:
>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>
>>>>>>>>>> In the conclusion section:
>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>> cannot be
>>>>>>>>>> for-
>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>> does not
>>>>>>>>>> exist as
>>>>>>>>>> a conceptual object. Assuming its conceptual existence leads to a
>>>>>>>>>> paradox.
>>>>>>>>>> The halting problem is universally used in university courses on
>>>>>>>>>> Computer
>>>>>>>>>> Science to illustrate the limits of computation. Hehner claims
>>>>>>>>>> the
>>>>>>>>>> halting
>>>>>>>>>> problem is misconceived......
>>>>>>>>>>
>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>> something?
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>
>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>
>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>
>>>>>>>>> There certainly CAN be defined formal test that define Halting,
>>>>>>>>> the issue is that non-halting is defined by the non-existence
>>>>>>>>> of a number N for the number of steps needed to reach a final
>>>>>>>>> state.
>>>>>>>>>
>>>>>>>>> Some people just don't like the fact that it can be absolutely
>>>>>>>>> provable what the answer is (and thus unknowable), even if we
>>>>>>>>> know from the definition, that it must be one or the other.
>>>>>>>>>
>>>>>>>>> This leads us to a great divide in logics. The classical branch
>>>>>>>>> accepts that some truth is only established by infinite chains
>>>>>>>>> of connections, and thus can not be proven with a finite proof,
>>>>>>>>> and thus is unknowable.
>>>>>>>>>
>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>> established by Finite chains. The problem then is, such logic
>>>>>>>>> system need to greatly limit the domain they attempt to cover,
>>>>>>>>> as otherwise you get into endless chains of asking if a
>>>>>>>>> question can be asked, at which point you need to ask if you
>>>>>>>>> can even ask about asking the questions. Only when the domain
>>>>>>>>> is restricted in a way that the answer MUST be determinable
>>>>>>>>> with finite work, can we break the cycle.
>>>>>>>>>
>>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>>> (which could be Turing Machines with a fixed finite tape, or a
>>>>>>>>> classical program in a computer with limited memory) then we
>>>>>>>>> can be sure that the answer is determinable with a finite
>>>>>>>>> amount of work.
>>>>>>>>
>>>>>>>> Tarski did not understand that the Liar Paradox is not a truth
>>>>>>>> bearer
>>>>>>>> thus cannot possibly be true or false. His ignorance got him so
>>>>>>>> confused
>>>>>>>> that he thought that he proved that True(L,x) cannot be defined
>>>>>>>> because
>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>
>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>> this? He shows that if True(L, x) exists that the Liar Paradox is
>>>>>>> a true statement, but not what you say.
>>>>>>
>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a true."
>>>>>>
>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>
>>>>>
>>>>> Nope, you said that he assumed the Liars Paradox has a logic value.
>>>>>
>>>>> The assumption was just that True(L,x) existed.
>>>>>
>>>>
>>>> No that it only half of the assumption.
>>>> The other half is that True(tarski_theory, "this sentence is not true")
>>>> must be true or false. That half was Tarksi's fatal flaw.
>>>>
>>>
>>> True(tarski_theory, "this sentence is not true") is actually a
>>> mathematical statement consisting of elementary operations such as
>>> addition, multiplication, and quantifiers. Can you show how to use
>>> these basic parts to build a statement that is not true or false?
>>
>> When I put the same thing into Prolog
>> it is rejected as semantically unsound.
>>
>> ?- LP = not(true(LP)).
>> LP = not(true(LP)).
>>
>> ?- unify_with_occurs_check(LP, not(true(LP))).
>> false.
>>
>>
>
> That isn't how Tarski works. No wonder you don't understand the halting
> problem either.

THAT IS HOW THE LIAR PARADOX WORKS

Tarski didn't understand that the correct
evaluation of the Liar Paradox requires
an infinite cycle in the directed graph
of its evaluation sequence.

Do you know these terms:
cycle
directed graph
evaluation sequence

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 1/21/2024 4:53 PM, immibis wrote:
> On 1/21/24 23:41, olcott wrote:
>> On 1/21/2024 4:32 PM, Richard Damon wrote:
>>>
>>> Where do you see that as an INPUT assumption, and not a result of a
>>> proof?
>>>
>>> LINE please.
>>
>> "Tarski’s undefinability theorem is really just the
>> ancient paradox of the liar, dressed up in formal wear."
>>
>> https://web.mit.edu/24.242/www/Tarskitruth.pdf
>>
>
> And what can we learn from this?
>
> Tarski says that if True(L,p) exists then the liar paradox has a truth
> value.
>
> The liar paradox doesn't have a truth value, therefore True(L,p) doesn't
> exist.

That you can't see how that reasoning is unsound proves
that you don't understand these things.

That True(L, x) cannot prove that x is true or false
when x cannot possibly be true or false proves nothing
about True(L, x).

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 1/21/24 5:39 PM, olcott wrote:
> On 1/21/2024 4:32 PM, Richard Damon wrote:
>> On 1/21/24 4:55 PM, olcott wrote:
>>> On 1/21/2024 3:52 PM, Richard Damon wrote:
>>>> On 1/21/24 3:51 PM, olcott wrote:
>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>
>>>>>>>>> In the conclusion section:
>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>> cannot be
>>>>>>>>> for-
>>>>>>>>> malised as a consistent specification. It has no model and does
>>>>>>>>> not
>>>>>>>>> exist as
>>>>>>>>> a conceptual object. Assuming its conceptual existence leads to a
>>>>>>>>> paradox.
>>>>>>>>> The halting problem is universally used in university courses on
>>>>>>>>> Computer
>>>>>>>>> Science to illustrate the limits of computation. Hehner claims the
>>>>>>>>> halting
>>>>>>>>> problem is misconceived......
>>>>>>>>>
>>>>>>>>> It looks like what olcott now is claiming. Am I missing something?
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>
>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>
>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>
>>>>>>>> There certainly CAN be defined formal test that define Halting,
>>>>>>>> the issue is that non-halting is defined by the non-existence of
>>>>>>>> a number N for the number of steps needed to reach a final state.
>>>>>>>>
>>>>>>>> Some people just don't like the fact that it can be absolutely
>>>>>>>> provable what the answer is (and thus unknowable), even if we
>>>>>>>> know from the definition, that it must be one or the other.
>>>>>>>>
>>>>>>>> This leads us to a great divide in logics. The classical branch
>>>>>>>> accepts that some truth is only established by infinite chains
>>>>>>>> of connections, and thus can not be proven with a finite proof,
>>>>>>>> and thus is unknowable.
>>>>>>>>
>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>> established by Finite chains. The problem then is, such logic
>>>>>>>> system need to greatly limit the domain they attempt to cover,
>>>>>>>> as otherwise you get into endless chains of asking if a question
>>>>>>>> can be asked, at which point you need to ask if you can even ask
>>>>>>>> about asking the questions. Only when the domain is restricted
>>>>>>>> in a way that the answer MUST be determinable with finite work,
>>>>>>>> can we break the cycle.
>>>>>>>>
>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>> (which could be Turing Machines with a fixed finite tape, or a
>>>>>>>> classical program in a computer with limited memory) then we can
>>>>>>>> be sure that the answer is determinable with a finite amount of
>>>>>>>> work.
>>>>>>>
>>>>>>> Tarski did not understand that the Liar Paradox is not a truth
>>>>>>> bearer
>>>>>>> thus cannot possibly be true or false. His ignorance got him so
>>>>>>> confused
>>>>>>> that he thought that he proved that True(L,x) cannot be defined
>>>>>>> because
>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>
>>>>>> I'll ask one more time, exactly WHERE in the proof did he do this?
>>>>>> He shows that if True(L, x) exists that the Liar Paradox is a true
>>>>>> statement, but not what you say.
>>>>>
>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a true."
>>>>>
>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>
>>>>
>>>> Nope, you said that he assumed the Liars Paradox has a logic value.
>>>>
>>>> The assumption was just that True(L,x) existed.
>>>>
>>>
>>> No that it only half of the assumption.
>>> The other half is that True(tarski_theory, "this sentence is not true")
>>> must be true or false. That half was Tarksi's fatal flaw.
>>>
>>
>> Where do you see that as an INPUT assumption, and not a result of a
>> proof?
>>
>> LINE please.
>
> line (3)

You mean the (3) on page 275?

The one preeeded by: "from (1) and (2) we obtain immediately"

Thus (3) isn't an assumption but a proven statement.

Also (3) says x is not Provable if and only if x is not True

(Which applies only for a particuar x that was derived in (1).

Of course, you don't accept that statement, but you need to try to find
the error in that logic (which I doubt exists)

YOu are just showing how little you understand about how logic works.
You can't seem to read these papers and understand them.

On 1/21/24 5:41 PM, olcott wrote:
> On 1/21/2024 4:32 PM, Richard Damon wrote:
>> On 1/21/24 4:55 PM, olcott wrote:
>>> On 1/21/2024 3:52 PM, Richard Damon wrote:
>>>> On 1/21/24 3:51 PM, olcott wrote:
>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>
>>>>>>>>> In the conclusion section:
>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>> cannot be
>>>>>>>>> for-
>>>>>>>>> malised as a consistent specification. It has no model and does
>>>>>>>>> not
>>>>>>>>> exist as
>>>>>>>>> a conceptual object. Assuming its conceptual existence leads to a
>>>>>>>>> paradox.
>>>>>>>>> The halting problem is universally used in university courses on
>>>>>>>>> Computer
>>>>>>>>> Science to illustrate the limits of computation. Hehner claims the
>>>>>>>>> halting
>>>>>>>>> problem is misconceived......
>>>>>>>>>
>>>>>>>>> It looks like what olcott now is claiming. Am I missing something?
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>
>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>
>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>
>>>>>>>> There certainly CAN be defined formal test that define Halting,
>>>>>>>> the issue is that non-halting is defined by the non-existence of
>>>>>>>> a number N for the number of steps needed to reach a final state.
>>>>>>>>
>>>>>>>> Some people just don't like the fact that it can be absolutely
>>>>>>>> provable what the answer is (and thus unknowable), even if we
>>>>>>>> know from the definition, that it must be one or the other.
>>>>>>>>
>>>>>>>> This leads us to a great divide in logics. The classical branch
>>>>>>>> accepts that some truth is only established by infinite chains
>>>>>>>> of connections, and thus can not be proven with a finite proof,
>>>>>>>> and thus is unknowable.
>>>>>>>>
>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>> established by Finite chains. The problem then is, such logic
>>>>>>>> system need to greatly limit the domain they attempt to cover,
>>>>>>>> as otherwise you get into endless chains of asking if a question
>>>>>>>> can be asked, at which point you need to ask if you can even ask
>>>>>>>> about asking the questions. Only when the domain is restricted
>>>>>>>> in a way that the answer MUST be determinable with finite work,
>>>>>>>> can we break the cycle.
>>>>>>>>
>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>> (which could be Turing Machines with a fixed finite tape, or a
>>>>>>>> classical program in a computer with limited memory) then we can
>>>>>>>> be sure that the answer is determinable with a finite amount of
>>>>>>>> work.
>>>>>>>
>>>>>>> Tarski did not understand that the Liar Paradox is not a truth
>>>>>>> bearer
>>>>>>> thus cannot possibly be true or false. His ignorance got him so
>>>>>>> confused
>>>>>>> that he thought that he proved that True(L,x) cannot be defined
>>>>>>> because
>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>
>>>>>> I'll ask one more time, exactly WHERE in the proof did he do this?
>>>>>> He shows that if True(L, x) exists that the Liar Paradox is a true
>>>>>> statement, but not what you say.
>>>>>
>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a true."
>>>>>
>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>
>>>>
>>>> Nope, you said that he assumed the Liars Paradox has a logic value.
>>>>
>>>> The assumption was just that True(L,x) existed.
>>>>
>>>
>>> No that it only half of the assumption.
>>> The other half is that True(tarski_theory, "this sentence is not true")
>>> must be true or false. That half was Tarksi's fatal flaw.
>>>
>>
>> Where do you see that as an INPUT assumption, and not a result of a
>> proof?
>>
>> LINE please.
>
> "Tarski’s undefinability theorem is really just the
> ancient paradox of the liar, dressed up in formal wear."
>
> https://web.mit.edu/24.242/www/Tarskitruth.pdf
>

So, are you relying on some paper without attribution?

That sounds like appeal to Authority when you can't name the Authority.

Sounds like the opinion of some unnamed person.

On 1/21/24 6:00 PM, olcott wrote:
> On 1/21/2024 4:53 PM, immibis wrote:
>> On 1/21/24 23:41, olcott wrote:
>>> On 1/21/2024 4:32 PM, Richard Damon wrote:
>>>>
>>>> Where do you see that as an INPUT assumption, and not a result of a
>>>> proof?
>>>>
>>>> LINE please.
>>>
>>> "Tarski’s undefinability theorem is really just the
>>> ancient paradox of the liar, dressed up in formal wear."
>>>
>>> https://web.mit.edu/24.242/www/Tarskitruth.pdf
>>>
>>
>> And what can we learn from this?
>>
>> Tarski says that if True(L,p) exists then the liar paradox has a truth
>> value.
>>
>> The liar paradox doesn't have a truth value, therefore True(L,p)
>> doesn't exist.
>
> That you can't see how that reasoning is unsound proves
> that you don't understand these things.
>
> That True(L, x) cannot prove that x is true or false
> when x cannot possibly be true or false proves nothing
> about True(L, x).
>

But where did he ASK True(L, x) to resolve a statement that didn't have
a truth value?

He shows from the unprobability property that Truth can not be computed.

Asking True(L, x) on a statement x that is TRUE but not provable shows
the error.

On 1/21/2024 4:54 PM, immibis wrote:
> On 1/21/24 23:37, olcott wrote:
>> On 1/21/2024 4:19 PM, immibis wrote:
>>> On 1/21/24 22:50, olcott wrote:
>>>> On 1/21/2024 3:46 PM, immibis wrote:
>>>>> On 1/21/24 22:15, olcott wrote:
>>>>>> On 1/21/2024 3:09 PM, immibis wrote:
>>>>>>> On 1/21/24 22:07, olcott wrote:
>>>>>>>> On 1/21/2024 2:54 PM, immibis wrote:
>>>>>>>>> On 1/21/24 21:51, olcott wrote:
>>>>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>>>> cannot be
>>>>>>>>>>>>>> for-
>>>>>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>>>>>> does not
>>>>>>>>>>>>>> exist as
>>>>>>>>>>>>>> a conceptual object. Assuming its conceptual existence
>>>>>>>>>>>>>> leads to a
>>>>>>>>>>>>>> paradox.
>>>>>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>>>>>> courses on
>>>>>>>>>>>>>> Computer
>>>>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>>>>> claims the
>>>>>>>>>>>>>> halting
>>>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>>>>> something?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>>>>
>>>>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>>>>
>>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>>>>
>>>>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>>>>> non-existence of a number N for the number of steps needed
>>>>>>>>>>>>> to reach a final state.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Some people just don't like the fact that it can be
>>>>>>>>>>>>> absolutely provable what the answer is (and thus
>>>>>>>>>>>>> unknowable), even if we know from the definition, that it
>>>>>>>>>>>>> must be one or the other.
>>>>>>>>>>>>>
>>>>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>>>>> branch accepts that some truth is only established by
>>>>>>>>>>>>> infinite chains of connections, and thus can not be proven
>>>>>>>>>>>>> with a finite proof, and thus is unknowable.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>>>>> established by Finite chains. The problem then is, such
>>>>>>>>>>>>> logic system need to greatly limit the domain they attempt
>>>>>>>>>>>>> to cover, as otherwise you get into endless chains of
>>>>>>>>>>>>> asking if a question can be asked, at which point you need
>>>>>>>>>>>>> to ask if you can even ask about asking the questions. Only
>>>>>>>>>>>>> when the domain is restricted in a way that the answer MUST
>>>>>>>>>>>>> be determinable with finite work, can we break the cycle.
>>>>>>>>>>>>>
>>>>>>>>>>>>> For instance, if we limit ourselves to Finite State
>>>>>>>>>>>>> Machines (which could be Turing Machines with a fixed
>>>>>>>>>>>>> finite tape, or a classical program in a computer with
>>>>>>>>>>>>> limited memory) then we can be sure that the answer is
>>>>>>>>>>>>> determinable with a finite amount of work.
>>>>>>>>>>>>
>>>>>>>>>>>> Tarski did not understand that the Liar Paradox is not a
>>>>>>>>>>>> truth bearer
>>>>>>>>>>>> thus cannot possibly be true or false. His ignorance got him
>>>>>>>>>>>> so confused
>>>>>>>>>>>> that he thought that he proved that True(L,x) cannot be
>>>>>>>>>>>> defined because
>>>>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>>>>
>>>>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>>>>> this? He shows that if True(L, x) exists that the Liar
>>>>>>>>>>> Paradox is a true statement, but not what you say.
>>>>>>>>>>
>>>>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a
>>>>>>>>>> true."
>>>>>>>>>>
>>>>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>>>>
>>>>>>>>>> Why this is nutty on his part requires you to understand a term
>>>>>>>>>> that is not in logic or math, it is only in philosophy of logic:
>>>>>>>>>> {truth bearer}.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You agree it's not in logic or math. Well he talked about logic
>>>>>>>>> and math, not philosophy. So you agree that in logic and math,
>>>>>>>>> the liar paradox is true?
>>>>>>>>>
>>>>>>>>
>>>>>>>> I agree that it a ridiculously foolish thing to say.
>>>>>>>>
>>>>>>>> The ignorance of logic and math does not derive any
>>>>>>>> sort of truth.
>>>>>>>
>>>>>>> So math does not prove that 1+1=2?
>>>>>>>
>>>>>>
>>>>>> Always with the strawman deception.
>>>>>> Do you want me to start calling you a liar?
>>>>>>
>>>>>> If you don't want me to start calling you a liar
>>>>>> then quit using the strawman deception.
>>>>>>
>>>>>> It was pointed out that logic and math are clueless
>>>>>> about the Liar Paradox.
>>>>>
>>>>> Didn't Tarski translate the Liar Paradox into logic and mathematics?
>>>>>
>>>>
>>>> The key thing that Tarski missed is that expressions of language
>>>> that are not truth bearers cannot possibly have any truth value.
>>>> *This was his fatal mistake*
>>>>
>>>>
>>> So a statement such as "∀x (x = 5)" can be neither true nor false?
>>
>> Yet another strawman deception
>>
> Every time you say "strawman deception" it will be read as "I, Olcott,
> admit to being wrong"

On 1/21/24 5:53 PM, olcott wrote:
> On 1/21/2024 4:47 PM, Richard Damon wrote:
>> On 1/21/24 5:42 PM, olcott wrote:
>>> On 1/21/2024 4:30 PM, Richard Damon wrote:
>>>> On 1/21/24 4:50 PM, olcott wrote:
>>>>> On 1/21/2024 3:46 PM, immibis wrote:
>>>>>> On 1/21/24 22:15, olcott wrote:
>>>>>>> On 1/21/2024 3:09 PM, immibis wrote:
>>>>>>>> On 1/21/24 22:07, olcott wrote:
>>>>>>>>> On 1/21/2024 2:54 PM, immibis wrote:
>>>>>>>>>> On 1/21/24 21:51, olcott wrote:
>>>>>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>>>>> The idea of a universal halting test seems reasonable,
>>>>>>>>>>>>>>> but cannot be
>>>>>>>>>>>>>>> for-
>>>>>>>>>>>>>>> malised as a consistent specification. It has no model
>>>>>>>>>>>>>>> and does not
>>>>>>>>>>>>>>> exist as
>>>>>>>>>>>>>>> a conceptual object. Assuming its conceptual existence
>>>>>>>>>>>>>>> leads to a
>>>>>>>>>>>>>>> paradox.
>>>>>>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>>>>>>> courses on
>>>>>>>>>>>>>>> Computer
>>>>>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>>>>>> claims the
>>>>>>>>>>>>>>> halting
>>>>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>>>>>> something?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>>>>>> non-existence of a number N for the number of steps needed
>>>>>>>>>>>>>> to reach a final state.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Some people just don't like the fact that it can be
>>>>>>>>>>>>>> absolutely provable what the answer is (and thus
>>>>>>>>>>>>>> unknowable), even if we know from the definition, that it
>>>>>>>>>>>>>> must be one or the other.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>>>>>> branch accepts that some truth is only established by
>>>>>>>>>>>>>> infinite chains of connections, and thus can not be proven
>>>>>>>>>>>>>> with a finite proof, and thus is unknowable.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>>>>>> established by Finite chains. The problem then is, such
>>>>>>>>>>>>>> logic system need to greatly limit the domain they attempt
>>>>>>>>>>>>>> to cover, as otherwise you get into endless chains of
>>>>>>>>>>>>>> asking if a question can be asked, at which point you need
>>>>>>>>>>>>>> to ask if you can even ask about asking the questions.
>>>>>>>>>>>>>> Only when the domain is restricted in a way that the
>>>>>>>>>>>>>> answer MUST be determinable with finite work, can we break
>>>>>>>>>>>>>> the cycle.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> For instance, if we limit ourselves to Finite State
>>>>>>>>>>>>>> Machines (which could be Turing Machines with a fixed
>>>>>>>>>>>>>> finite tape, or a classical program in a computer with
>>>>>>>>>>>>>> limited memory) then we can be sure that the answer is
>>>>>>>>>>>>>> determinable with a finite amount of work.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Tarski did not understand that the Liar Paradox is not a
>>>>>>>>>>>>> truth bearer
>>>>>>>>>>>>> thus cannot possibly be true or false. His ignorance got
>>>>>>>>>>>>> him so confused
>>>>>>>>>>>>> that he thought that he proved that True(L,x) cannot be
>>>>>>>>>>>>> defined because
>>>>>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>>>>>
>>>>>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>>>>>> this? He shows that if True(L, x) exists that the Liar
>>>>>>>>>>>> Paradox is a true statement, but not what you say.
>>>>>>>>>>>
>>>>>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is
>>>>>>>>>>> a true."
>>>>>>>>>>>
>>>>>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>>>>>
>>>>>>>>>>> Why this is nutty on his part requires you to understand a term
>>>>>>>>>>> that is not in logic or math, it is only in philosophy of logic:
>>>>>>>>>>> {truth bearer}.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> You agree it's not in logic or math. Well he talked about
>>>>>>>>>> logic and math, not philosophy. So you agree that in logic and
>>>>>>>>>> math, the liar paradox is true?
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> I agree that it a ridiculously foolish thing to say.
>>>>>>>>>
>>>>>>>>> The ignorance of logic and math does not derive any
>>>>>>>>> sort of truth.
>>>>>>>>
>>>>>>>> So math does not prove that 1+1=2?
>>>>>>>>
>>>>>>>
>>>>>>> Always with the strawman deception.
>>>>>>> Do you want me to start calling you a liar?
>>>>>>>
>>>>>>> If you don't want me to start calling you a liar
>>>>>>> then quit using the strawman deception.
>>>>>>>
>>>>>>> It was pointed out that logic and math are clueless
>>>>>>> about the Liar Paradox.
>>>>>>
>>>>>> Didn't Tarski translate the Liar Paradox into logic and mathematics?
>>>>>>
>>>>>
>>>>> The key thing that Tarski missed is that expressions of language
>>>>> that are not truth bearers cannot possibly have any truth value.
>>>>> *This was his fatal mistake*
>>>>>
>>>>>
>>>>
>>>>
>>>> No, he FULLY understood that, so any assumption that proves that it
>>>> has one, must be false.
>>>>
>>>> You just don't understand how logic works.
>>>
>>> ?- LP = not(true(LP)).
>>> LP = not(true(LP)).
>>>
>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>> false.
>>>
>>>
>>>
>>
>> So, you don't, since you didn't actually answer the comment.
>>
>
> That you can't comprehend Prolog does not mean that I am wrong.
>

On 1/21/24 5:56 PM, olcott wrote:
> On 1/21/2024 4:52 PM, immibis wrote:
>> On 1/21/24 23:21, olcott wrote:
>>> On 1/21/2024 4:17 PM, immibis wrote:
>>>> On 1/21/24 22:55, olcott wrote:
>>>>> On 1/21/2024 3:52 PM, Richard Damon wrote:
>>>>>> On 1/21/24 3:51 PM, olcott wrote:
>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>
>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>> cannot be
>>>>>>>>>>> for-
>>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>>> does not
>>>>>>>>>>> exist as
>>>>>>>>>>> a conceptual object. Assuming its conceptual existence leads
>>>>>>>>>>> to a
>>>>>>>>>>> paradox.
>>>>>>>>>>> The halting problem is universally used in university courses on
>>>>>>>>>>> Computer
>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>> claims the
>>>>>>>>>>> halting
>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>
>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>> something?
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>
>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>
>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>
>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>> non-existence of a number N for the number of steps needed to
>>>>>>>>>> reach a final state.
>>>>>>>>>>
>>>>>>>>>> Some people just don't like the fact that it can be absolutely
>>>>>>>>>> provable what the answer is (and thus unknowable), even if we
>>>>>>>>>> know from the definition, that it must be one or the other.
>>>>>>>>>>
>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>> branch accepts that some truth is only established by infinite
>>>>>>>>>> chains of connections, and thus can not be proven with a
>>>>>>>>>> finite proof, and thus is unknowable.
>>>>>>>>>>
>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>> established by Finite chains. The problem then is, such logic
>>>>>>>>>> system need to greatly limit the domain they attempt to cover,
>>>>>>>>>> as otherwise you get into endless chains of asking if a
>>>>>>>>>> question can be asked, at which point you need to ask if you
>>>>>>>>>> can even ask about asking the questions. Only when the domain
>>>>>>>>>> is restricted in a way that the answer MUST be determinable
>>>>>>>>>> with finite work, can we break the cycle.
>>>>>>>>>>
>>>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>>>> (which could be Turing Machines with a fixed finite tape, or a
>>>>>>>>>> classical program in a computer with limited memory) then we
>>>>>>>>>> can be sure that the answer is determinable with a finite
>>>>>>>>>> amount of work.
>>>>>>>>>
>>>>>>>>> Tarski did not understand that the Liar Paradox is not a truth
>>>>>>>>> bearer
>>>>>>>>> thus cannot possibly be true or false. His ignorance got him so
>>>>>>>>> confused
>>>>>>>>> that he thought that he proved that True(L,x) cannot be defined
>>>>>>>>> because
>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>
>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>> this? He shows that if True(L, x) exists that the Liar Paradox
>>>>>>>> is a true statement, but not what you say.
>>>>>>>
>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a
>>>>>>> true."
>>>>>>>
>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>
>>>>>>
>>>>>> Nope, you said that he assumed the Liars Paradox has a logic value.
>>>>>>
>>>>>> The assumption was just that True(L,x) existed.
>>>>>>
>>>>>
>>>>> No that it only half of the assumption.
>>>>> The other half is that True(tarski_theory, "this sentence is not
>>>>> true")
>>>>> must be true or false. That half was Tarksi's fatal flaw.
>>>>>
>>>>
>>>> True(tarski_theory, "this sentence is not true") is actually a
>>>> mathematical statement consisting of elementary operations such as
>>>> addition, multiplication, and quantifiers. Can you show how to use
>>>> these basic parts to build a statement that is not true or false?
>>>
>>> When I put the same thing into Prolog
>>> it is rejected as semantically unsound.
>>>
>>> ?- LP = not(true(LP)).
>>> LP = not(true(LP)).
>>>
>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>> false.
>>>
>>>
>>
>> That isn't how Tarski works. No wonder you don't understand the
>> halting problem either.
>
> THAT IS HOW THE LIAR PARADOX WORKS
>
> Tarski didn't understand that the correct
> evaluation of the Liar Paradox requires
> an infinite cycle in the directed graph
> of its evaluation sequence.
>
> Do you know these terms:
> cycle
> directed graph
> evaluation sequence
>

And where did he do that?

Not line (3)

On 1/21/2024 5:00 PM, Richard Damon wrote:
> On 1/21/24 5:39 PM, olcott wrote:
>> On 1/21/2024 4:32 PM, Richard Damon wrote:
>>> On 1/21/24 4:55 PM, olcott wrote:
>>>> On 1/21/2024 3:52 PM, Richard Damon wrote:
>>>>> On 1/21/24 3:51 PM, olcott wrote:
>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>
>>>>>>>>>> In the conclusion section:
>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>> cannot be
>>>>>>>>>> for-
>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>> does not
>>>>>>>>>> exist as
>>>>>>>>>> a conceptual object. Assuming its conceptual existence leads to a
>>>>>>>>>> paradox.
>>>>>>>>>> The halting problem is universally used in university courses on
>>>>>>>>>> Computer
>>>>>>>>>> Science to illustrate the limits of computation. Hehner claims
>>>>>>>>>> the
>>>>>>>>>> halting
>>>>>>>>>> problem is misconceived......
>>>>>>>>>>
>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>> something?
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>
>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>
>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>
>>>>>>>>> There certainly CAN be defined formal test that define Halting,
>>>>>>>>> the issue is that non-halting is defined by the non-existence
>>>>>>>>> of a number N for the number of steps needed to reach a final
>>>>>>>>> state.
>>>>>>>>>
>>>>>>>>> Some people just don't like the fact that it can be absolutely
>>>>>>>>> provable what the answer is (and thus unknowable), even if we
>>>>>>>>> know from the definition, that it must be one or the other.
>>>>>>>>>
>>>>>>>>> This leads us to a great divide in logics. The classical branch
>>>>>>>>> accepts that some truth is only established by infinite chains
>>>>>>>>> of connections, and thus can not be proven with a finite proof,
>>>>>>>>> and thus is unknowable.
>>>>>>>>>
>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>> established by Finite chains. The problem then is, such logic
>>>>>>>>> system need to greatly limit the domain they attempt to cover,
>>>>>>>>> as otherwise you get into endless chains of asking if a
>>>>>>>>> question can be asked, at which point you need to ask if you
>>>>>>>>> can even ask about asking the questions. Only when the domain
>>>>>>>>> is restricted in a way that the answer MUST be determinable
>>>>>>>>> with finite work, can we break the cycle.
>>>>>>>>>
>>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>>> (which could be Turing Machines with a fixed finite tape, or a
>>>>>>>>> classical program in a computer with limited memory) then we
>>>>>>>>> can be sure that the answer is determinable with a finite
>>>>>>>>> amount of work.
>>>>>>>>
>>>>>>>> Tarski did not understand that the Liar Paradox is not a truth
>>>>>>>> bearer
>>>>>>>> thus cannot possibly be true or false. His ignorance got him so
>>>>>>>> confused
>>>>>>>> that he thought that he proved that True(L,x) cannot be defined
>>>>>>>> because
>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>
>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>> this? He shows that if True(L, x) exists that the Liar Paradox is
>>>>>>> a true statement, but not what you say.
>>>>>>
>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a true."
>>>>>>
>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>
>>>>>
>>>>> Nope, you said that he assumed the Liars Paradox has a logic value.
>>>>>
>>>>> The assumption was just that True(L,x) existed.
>>>>>
>>>>
>>>> No that it only half of the assumption.
>>>> The other half is that True(tarski_theory, "this sentence is not true")
>>>> must be true or false. That half was Tarksi's fatal flaw.
>>>>
>>>
>>> Where do you see that as an INPUT assumption, and not a result of a
>>> proof?
>>>
>>> LINE please.
>>
>> line (3)
>
> You mean the (3) on page 275?
>
> The one preeeded by: "from (1) and (2) we obtain immediately"
>
> Thus (3) isn't an assumption but a proven statement.
>
> Also (3) says x is not Provable if and only if x is not True
>
> (Which applies only for a particuar x that was derived in (1).
>
>
> Of course, you don't accept that statement, but you need to try to find
> the error in that logic (which I doubt exists)
>
> YOu are just showing how little you understand about how logic works.
> You can't seem to read these papers and understand them.

(3) x ∉ Provable if and only if x ∈ True.

Is like assuming that cows are dogs because it rejects
the way that an actual True(L, x) predicate works:
∀x ∈ L (True(L,x) ≡ (L ⊢ x))

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 1/21/2024 5:14 PM, Richard Damon wrote:
> On 1/21/24 5:56 PM, olcott wrote:
>> On 1/21/2024 4:52 PM, immibis wrote:
>>> On 1/21/24 23:21, olcott wrote:
>>>> On 1/21/2024 4:17 PM, immibis wrote:
>>>>> On 1/21/24 22:55, olcott wrote:
>>>>>> On 1/21/2024 3:52 PM, Richard Damon wrote:
>>>>>>> On 1/21/24 3:51 PM, olcott wrote:
>>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>
>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>> cannot be
>>>>>>>>>>>> for-
>>>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>>>> does not
>>>>>>>>>>>> exist as
>>>>>>>>>>>> a conceptual object. Assuming its conceptual existence leads
>>>>>>>>>>>> to a
>>>>>>>>>>>> paradox.
>>>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>>>> courses on
>>>>>>>>>>>> Computer
>>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>>> claims the
>>>>>>>>>>>> halting
>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>
>>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>>> something?
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>>
>>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>>
>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>>
>>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>>> non-existence of a number N for the number of steps needed to
>>>>>>>>>>> reach a final state.
>>>>>>>>>>>
>>>>>>>>>>> Some people just don't like the fact that it can be
>>>>>>>>>>> absolutely provable what the answer is (and thus unknowable),
>>>>>>>>>>> even if we know from the definition, that it must be one or
>>>>>>>>>>> the other.
>>>>>>>>>>>
>>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>>> branch accepts that some truth is only established by
>>>>>>>>>>> infinite chains of connections, and thus can not be proven
>>>>>>>>>>> with a finite proof, and thus is unknowable.
>>>>>>>>>>>
>>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>>> established by Finite chains. The problem then is, such logic
>>>>>>>>>>> system need to greatly limit the domain they attempt to
>>>>>>>>>>> cover, as otherwise you get into endless chains of asking if
>>>>>>>>>>> a question can be asked, at which point you need to ask if
>>>>>>>>>>> you can even ask about asking the questions. Only when the
>>>>>>>>>>> domain is restricted in a way that the answer MUST be
>>>>>>>>>>> determinable with finite work, can we break the cycle.
>>>>>>>>>>>
>>>>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>>>>> (which could be Turing Machines with a fixed finite tape, or
>>>>>>>>>>> a classical program in a computer with limited memory) then
>>>>>>>>>>> we can be sure that the answer is determinable with a finite
>>>>>>>>>>> amount of work.
>>>>>>>>>>
>>>>>>>>>> Tarski did not understand that the Liar Paradox is not a truth
>>>>>>>>>> bearer
>>>>>>>>>> thus cannot possibly be true or false. His ignorance got him
>>>>>>>>>> so confused
>>>>>>>>>> that he thought that he proved that True(L,x) cannot be
>>>>>>>>>> defined because
>>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>>
>>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>>> this? He shows that if True(L, x) exists that the Liar Paradox
>>>>>>>>> is a true statement, but not what you say.
>>>>>>>>
>>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a
>>>>>>>> true."
>>>>>>>>
>>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>>
>>>>>>>
>>>>>>> Nope, you said that he assumed the Liars Paradox has a logic value.
>>>>>>>
>>>>>>> The assumption was just that True(L,x) existed.
>>>>>>>
>>>>>>
>>>>>> No that it only half of the assumption.
>>>>>> The other half is that True(tarski_theory, "this sentence is not
>>>>>> true")
>>>>>> must be true or false. That half was Tarksi's fatal flaw.
>>>>>>
>>>>>
>>>>> True(tarski_theory, "this sentence is not true") is actually a
>>>>> mathematical statement consisting of elementary operations such as
>>>>> addition, multiplication, and quantifiers. Can you show how to use
>>>>> these basic parts to build a statement that is not true or false?
>>>>
>>>> When I put the same thing into Prolog
>>>> it is rejected as semantically unsound.
>>>>
>>>> ?- LP = not(true(LP)).
>>>> LP = not(true(LP)).
>>>>
>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>> false.
>>>>
>>>>
>>>
>>> That isn't how Tarski works. No wonder you don't understand the
>>> halting problem either.
>>
>> THAT IS HOW THE LIAR PARADOX WORKS
>>
>> Tarski didn't understand that the correct
>> evaluation of the Liar Paradox requires
>> an infinite cycle in the directed graph
>> of its evaluation sequence.
>>
>> Do you know these terms:
>> cycle
>> directed graph
>> evaluation sequence
>>
>
> And where did he do that?
>
> Not line (3)

Where did Tarski say that i=he didn't understand things?

He never understood that his understanding was incorrect
so there is no place where he says that.

My Prolog proves that the Liar Paradox is neither
true nor false. Tarski never understood that.

On 1/21/24 23:49, olcott wrote:
> On 1/21/2024 4:37 PM, olcott wrote:
>> On 1/21/2024 4:19 PM, immibis wrote:
>>> On 1/21/24 22:50, olcott wrote:
>>>> On 1/21/2024 3:46 PM, immibis wrote:
>>>>> On 1/21/24 22:15, olcott wrote:
>>>>>> On 1/21/2024 3:09 PM, immibis wrote:
>>>>>>> On 1/21/24 22:07, olcott wrote:
>>>>>>>> On 1/21/2024 2:54 PM, immibis wrote:
>>>>>>>>> On 1/21/24 21:51, olcott wrote:
>>>>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>>>> cannot be
>>>>>>>>>>>>>> for-
>>>>>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>>>>>> does not
>>>>>>>>>>>>>> exist as
>>>>>>>>>>>>>> a conceptual object. Assuming its conceptual existence
>>>>>>>>>>>>>> leads to a
>>>>>>>>>>>>>> paradox.
>>>>>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>>>>>> courses on
>>>>>>>>>>>>>> Computer
>>>>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>>>>> claims the
>>>>>>>>>>>>>> halting
>>>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>>>>> something?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>>>>
>>>>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>>>>
>>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>>>>
>>>>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>>>>> non-existence of a number N for the number of steps needed
>>>>>>>>>>>>> to reach a final state.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Some people just don't like the fact that it can be
>>>>>>>>>>>>> absolutely provable what the answer is (and thus
>>>>>>>>>>>>> unknowable), even if we know from the definition, that it
>>>>>>>>>>>>> must be one or the other.
>>>>>>>>>>>>>
>>>>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>>>>> branch accepts that some truth is only established by
>>>>>>>>>>>>> infinite chains of connections, and thus can not be proven
>>>>>>>>>>>>> with a finite proof, and thus is unknowable.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>>>>> established by Finite chains. The problem then is, such
>>>>>>>>>>>>> logic system need to greatly limit the domain they attempt
>>>>>>>>>>>>> to cover, as otherwise you get into endless chains of
>>>>>>>>>>>>> asking if a question can be asked, at which point you need
>>>>>>>>>>>>> to ask if you can even ask about asking the questions. Only
>>>>>>>>>>>>> when the domain is restricted in a way that the answer MUST
>>>>>>>>>>>>> be determinable with finite work, can we break the cycle.
>>>>>>>>>>>>>
>>>>>>>>>>>>> For instance, if we limit ourselves to Finite State
>>>>>>>>>>>>> Machines (which could be Turing Machines with a fixed
>>>>>>>>>>>>> finite tape, or a classical program in a computer with
>>>>>>>>>>>>> limited memory) then we can be sure that the answer is
>>>>>>>>>>>>> determinable with a finite amount of work.
>>>>>>>>>>>>
>>>>>>>>>>>> Tarski did not understand that the Liar Paradox is not a
>>>>>>>>>>>> truth bearer
>>>>>>>>>>>> thus cannot possibly be true or false. His ignorance got him
>>>>>>>>>>>> so confused
>>>>>>>>>>>> that he thought that he proved that True(L,x) cannot be
>>>>>>>>>>>> defined because
>>>>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>>>>
>>>>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>>>>> this? He shows that if True(L, x) exists that the Liar
>>>>>>>>>>> Paradox is a true statement, but not what you say.
>>>>>>>>>>
>>>>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a
>>>>>>>>>> true."
>>>>>>>>>>
>>>>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>>>>
>>>>>>>>>> Why this is nutty on his part requires you to understand a term
>>>>>>>>>> that is not in logic or math, it is only in philosophy of logic:
>>>>>>>>>> {truth bearer}.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You agree it's not in logic or math. Well he talked about logic
>>>>>>>>> and math, not philosophy. So you agree that in logic and math,
>>>>>>>>> the liar paradox is true?
>>>>>>>>>
>>>>>>>>
>>>>>>>> I agree that it a ridiculously foolish thing to say.
>>>>>>>>
>>>>>>>> The ignorance of logic and math does not derive any
>>>>>>>> sort of truth.
>>>>>>>
>>>>>>> So math does not prove that 1+1=2?
>>>>>>>
>>>>>>
>>>>>> Always with the strawman deception.
>>>>>> Do you want me to start calling you a liar?
>>>>>>
>>>>>> If you don't want me to start calling you a liar
>>>>>> then quit using the strawman deception.
>>>>>>
>>>>>> It was pointed out that logic and math are clueless
>>>>>> about the Liar Paradox.
>>>>>
>>>>> Didn't Tarski translate the Liar Paradox into logic and mathematics?
>>>>>
>>>>
>>>> The key thing that Tarski missed is that expressions of language
>>>> that are not truth bearers cannot possibly have any truth value.
>>>> *This was his fatal mistake*
>>>>
>>>>
>>> So a statement such as "∀x (x = 5)" can be neither true nor false?
>>
>> Yet another strawman deception
>>
>
> ∀x ∈ ℕ (x = 5) is false
>

On 1/21/24 23:56, olcott wrote:
> On 1/21/2024 4:52 PM, immibis wrote:
>> On 1/21/24 23:21, olcott wrote:
>>> On 1/21/2024 4:17 PM, immibis wrote:
>>>> On 1/21/24 22:55, olcott wrote:
>>>>> On 1/21/2024 3:52 PM, Richard Damon wrote:
>>>>>> On 1/21/24 3:51 PM, olcott wrote:
>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>
>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>> cannot be
>>>>>>>>>>> for-
>>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>>> does not
>>>>>>>>>>> exist as
>>>>>>>>>>> a conceptual object. Assuming its conceptual existence leads
>>>>>>>>>>> to a
>>>>>>>>>>> paradox.
>>>>>>>>>>> The halting problem is universally used in university courses on
>>>>>>>>>>> Computer
>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>> claims the
>>>>>>>>>>> halting
>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>
>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>> something?
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>
>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>
>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>
>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>> non-existence of a number N for the number of steps needed to
>>>>>>>>>> reach a final state.
>>>>>>>>>>
>>>>>>>>>> Some people just don't like the fact that it can be absolutely
>>>>>>>>>> provable what the answer is (and thus unknowable), even if we
>>>>>>>>>> know from the definition, that it must be one or the other.
>>>>>>>>>>
>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>> branch accepts that some truth is only established by infinite
>>>>>>>>>> chains of connections, and thus can not be proven with a
>>>>>>>>>> finite proof, and thus is unknowable.
>>>>>>>>>>
>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>> established by Finite chains. The problem then is, such logic
>>>>>>>>>> system need to greatly limit the domain they attempt to cover,
>>>>>>>>>> as otherwise you get into endless chains of asking if a
>>>>>>>>>> question can be asked, at which point you need to ask if you
>>>>>>>>>> can even ask about asking the questions. Only when the domain
>>>>>>>>>> is restricted in a way that the answer MUST be determinable
>>>>>>>>>> with finite work, can we break the cycle.
>>>>>>>>>>
>>>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>>>> (which could be Turing Machines with a fixed finite tape, or a
>>>>>>>>>> classical program in a computer with limited memory) then we
>>>>>>>>>> can be sure that the answer is determinable with a finite
>>>>>>>>>> amount of work.
>>>>>>>>>
>>>>>>>>> Tarski did not understand that the Liar Paradox is not a truth
>>>>>>>>> bearer
>>>>>>>>> thus cannot possibly be true or false. His ignorance got him so
>>>>>>>>> confused
>>>>>>>>> that he thought that he proved that True(L,x) cannot be defined
>>>>>>>>> because
>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>
>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>> this? He shows that if True(L, x) exists that the Liar Paradox
>>>>>>>> is a true statement, but not what you say.
>>>>>>>
>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a
>>>>>>> true."
>>>>>>>
>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>
>>>>>>
>>>>>> Nope, you said that he assumed the Liars Paradox has a logic value.
>>>>>>
>>>>>> The assumption was just that True(L,x) existed.
>>>>>>
>>>>>
>>>>> No that it only half of the assumption.
>>>>> The other half is that True(tarski_theory, "this sentence is not
>>>>> true")
>>>>> must be true or false. That half was Tarksi's fatal flaw.
>>>>>
>>>>
>>>> True(tarski_theory, "this sentence is not true") is actually a
>>>> mathematical statement consisting of elementary operations such as
>>>> addition, multiplication, and quantifiers. Can you show how to use
>>>> these basic parts to build a statement that is not true or false?
>>>
>>> When I put the same thing into Prolog
>>> it is rejected as semantically unsound.
>>>
>>> ?- LP = not(true(LP)).
>>> LP = not(true(LP)).
>>>
>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>> false.
>>>
>>>
>>
>> That isn't how Tarski works. No wonder you don't understand the
>> halting problem either.
>
> THAT IS HOW THE LIAR PARADOX WORKS

It isn't how Tarski works.

>
> Tarski didn't understand that the correct
> evaluation of the Liar Paradox requires
> an infinite cycle in the directed graph
> of its evaluation sequence.

You don't understand the difference between diagonalization and infinite
recursion.

Do you think the real numbers are countable?

On 1/22/24 00:17, olcott wrote:
> On 1/21/2024 5:00 PM, Richard Damon wrote:
>> On 1/21/24 5:39 PM, olcott wrote:
>>> On 1/21/2024 4:32 PM, Richard Damon wrote:
>>>> On 1/21/24 4:55 PM, olcott wrote:
>>>>> On 1/21/2024 3:52 PM, Richard Damon wrote:
>>>>>> On 1/21/24 3:51 PM, olcott wrote:
>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>
>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>> cannot be
>>>>>>>>>>> for-
>>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>>> does not
>>>>>>>>>>> exist as
>>>>>>>>>>> a conceptual object. Assuming its conceptual existence leads
>>>>>>>>>>> to a
>>>>>>>>>>> paradox.
>>>>>>>>>>> The halting problem is universally used in university courses on
>>>>>>>>>>> Computer
>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>> claims the
>>>>>>>>>>> halting
>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>
>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>> something?
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>
>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>
>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>
>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>> non-existence of a number N for the number of steps needed to
>>>>>>>>>> reach a final state.
>>>>>>>>>>
>>>>>>>>>> Some people just don't like the fact that it can be absolutely
>>>>>>>>>> provable what the answer is (and thus unknowable), even if we
>>>>>>>>>> know from the definition, that it must be one or the other.
>>>>>>>>>>
>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>> branch accepts that some truth is only established by infinite
>>>>>>>>>> chains of connections, and thus can not be proven with a
>>>>>>>>>> finite proof, and thus is unknowable.
>>>>>>>>>>
>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>> established by Finite chains. The problem then is, such logic
>>>>>>>>>> system need to greatly limit the domain they attempt to cover,
>>>>>>>>>> as otherwise you get into endless chains of asking if a
>>>>>>>>>> question can be asked, at which point you need to ask if you
>>>>>>>>>> can even ask about asking the questions. Only when the domain
>>>>>>>>>> is restricted in a way that the answer MUST be determinable
>>>>>>>>>> with finite work, can we break the cycle.
>>>>>>>>>>
>>>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>>>> (which could be Turing Machines with a fixed finite tape, or a
>>>>>>>>>> classical program in a computer with limited memory) then we
>>>>>>>>>> can be sure that the answer is determinable with a finite
>>>>>>>>>> amount of work.
>>>>>>>>>
>>>>>>>>> Tarski did not understand that the Liar Paradox is not a truth
>>>>>>>>> bearer
>>>>>>>>> thus cannot possibly be true or false. His ignorance got him so
>>>>>>>>> confused
>>>>>>>>> that he thought that he proved that True(L,x) cannot be defined
>>>>>>>>> because
>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>
>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>> this? He shows that if True(L, x) exists that the Liar Paradox
>>>>>>>> is a true statement, but not what you say.
>>>>>>>
>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a
>>>>>>> true."
>>>>>>>
>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>
>>>>>>
>>>>>> Nope, you said that he assumed the Liars Paradox has a logic value.
>>>>>>
>>>>>> The assumption was just that True(L,x) existed.
>>>>>>
>>>>>
>>>>> No that it only half of the assumption.
>>>>> The other half is that True(tarski_theory, "this sentence is not
>>>>> true")
>>>>> must be true or false. That half was Tarksi's fatal flaw.
>>>>>
>>>>
>>>> Where do you see that as an INPUT assumption, and not a result of a
>>>> proof?
>>>>
>>>> LINE please.
>>>
>>> line (3)
>>
>> You mean the (3) on page 275?
>>
>> The one preeeded by: "from (1) and (2) we obtain immediately"
>>
>> Thus (3) isn't an assumption but a proven statement.
>>
>> Also (3) says x is not Provable if and only if x is not True
>>
>> (Which applies only for a particuar x that was derived in (1).
>>
>>
>> Of course, you don't accept that statement, but you need to try to
>> find the error in that logic (which I doubt exists)
>>
>> YOu are just showing how little you understand about how logic works.
>> You can't seem to read these papers and understand them.
>
> (3) x ∉ Provable if and only if x ∈ True.
>
> Is like assuming that cows are dogs because it rejects
> the way that an actual True(L, x) predicate works:
> ∀x ∈ L (True(L,x) ≡ (L ⊢ x))
>

So you don't understand the proof and you just argue because you don't
like the conclusion.

Which is ironic, because you also make conclusions that nobody else
likes. You think that a halting program is non-halting.

On 1/21/2024 6:00 PM, immibis wrote:
> On 1/21/24 23:49, olcott wrote:
>> On 1/21/2024 4:37 PM, olcott wrote:
>>> On 1/21/2024 4:19 PM, immibis wrote:
>>>> On 1/21/24 22:50, olcott wrote:
>>>>> On 1/21/2024 3:46 PM, immibis wrote:
>>>>>> On 1/21/24 22:15, olcott wrote:
>>>>>>> On 1/21/2024 3:09 PM, immibis wrote:
>>>>>>>> On 1/21/24 22:07, olcott wrote:
>>>>>>>>> On 1/21/2024 2:54 PM, immibis wrote:
>>>>>>>>>> On 1/21/24 21:51, olcott wrote:
>>>>>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>>>>> The idea of a universal halting test seems reasonable,
>>>>>>>>>>>>>>> but cannot be
>>>>>>>>>>>>>>> for-
>>>>>>>>>>>>>>> malised as a consistent specification. It has no model
>>>>>>>>>>>>>>> and does not
>>>>>>>>>>>>>>> exist as
>>>>>>>>>>>>>>> a conceptual object. Assuming its conceptual existence
>>>>>>>>>>>>>>> leads to a
>>>>>>>>>>>>>>> paradox.
>>>>>>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>>>>>>> courses on
>>>>>>>>>>>>>>> Computer
>>>>>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>>>>>> claims the
>>>>>>>>>>>>>>> halting
>>>>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>>>>>> something?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>>>>>> non-existence of a number N for the number of steps needed
>>>>>>>>>>>>>> to reach a final state.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Some people just don't like the fact that it can be
>>>>>>>>>>>>>> absolutely provable what the answer is (and thus
>>>>>>>>>>>>>> unknowable), even if we know from the definition, that it
>>>>>>>>>>>>>> must be one or the other.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>>>>>> branch accepts that some truth is only established by
>>>>>>>>>>>>>> infinite chains of connections, and thus can not be proven
>>>>>>>>>>>>>> with a finite proof, and thus is unknowable.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>>>>>> established by Finite chains. The problem then is, such
>>>>>>>>>>>>>> logic system need to greatly limit the domain they attempt
>>>>>>>>>>>>>> to cover, as otherwise you get into endless chains of
>>>>>>>>>>>>>> asking if a question can be asked, at which point you need
>>>>>>>>>>>>>> to ask if you can even ask about asking the questions.
>>>>>>>>>>>>>> Only when the domain is restricted in a way that the
>>>>>>>>>>>>>> answer MUST be determinable with finite work, can we break
>>>>>>>>>>>>>> the cycle.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> For instance, if we limit ourselves to Finite State
>>>>>>>>>>>>>> Machines (which could be Turing Machines with a fixed
>>>>>>>>>>>>>> finite tape, or a classical program in a computer with
>>>>>>>>>>>>>> limited memory) then we can be sure that the answer is
>>>>>>>>>>>>>> determinable with a finite amount of work.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Tarski did not understand that the Liar Paradox is not a
>>>>>>>>>>>>> truth bearer
>>>>>>>>>>>>> thus cannot possibly be true or false. His ignorance got
>>>>>>>>>>>>> him so confused
>>>>>>>>>>>>> that he thought that he proved that True(L,x) cannot be
>>>>>>>>>>>>> defined because
>>>>>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>>>>>
>>>>>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>>>>>> this? He shows that if True(L, x) exists that the Liar
>>>>>>>>>>>> Paradox is a true statement, but not what you say.
>>>>>>>>>>>
>>>>>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is
>>>>>>>>>>> a true."
>>>>>>>>>>>
>>>>>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>>>>>
>>>>>>>>>>> Why this is nutty on his part requires you to understand a term
>>>>>>>>>>> that is not in logic or math, it is only in philosophy of logic:
>>>>>>>>>>> {truth bearer}.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> You agree it's not in logic or math. Well he talked about
>>>>>>>>>> logic and math, not philosophy. So you agree that in logic and
>>>>>>>>>> math, the liar paradox is true?
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> I agree that it a ridiculously foolish thing to say.
>>>>>>>>>
>>>>>>>>> The ignorance of logic and math does not derive any
>>>>>>>>> sort of truth.
>>>>>>>>
>>>>>>>> So math does not prove that 1+1=2?
>>>>>>>>
>>>>>>>
>>>>>>> Always with the strawman deception.
>>>>>>> Do you want me to start calling you a liar?
>>>>>>>
>>>>>>> If you don't want me to start calling you a liar
>>>>>>> then quit using the strawman deception.
>>>>>>>
>>>>>>> It was pointed out that logic and math are clueless
>>>>>>> about the Liar Paradox.
>>>>>>
>>>>>> Didn't Tarski translate the Liar Paradox into logic and mathematics?
>>>>>>
>>>>>
>>>>> The key thing that Tarski missed is that expressions of language
>>>>> that are not truth bearers cannot possibly have any truth value.
>>>>> *This was his fatal mistake*
>>>>>
>>>>>
>>>> So a statement such as "∀x (x = 5)" can be neither true nor false?
>>>
>>> Yet another strawman deception
>>>
>>
>> ∀x ∈ ℕ (x = 5) is false
>>
>
> Is there a way to make it neither true nor false?
No that is why it is the strawman deception

On 1/21/2024 6:04 PM, immibis wrote:
> On 1/21/24 23:56, olcott wrote:
>> On 1/21/2024 4:52 PM, immibis wrote:
>>> On 1/21/24 23:21, olcott wrote:
>>>> On 1/21/2024 4:17 PM, immibis wrote:
>>>>> On 1/21/24 22:55, olcott wrote:
>>>>>> On 1/21/2024 3:52 PM, Richard Damon wrote:
>>>>>>> On 1/21/24 3:51 PM, olcott wrote:
>>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>
>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>> cannot be
>>>>>>>>>>>> for-
>>>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>>>> does not
>>>>>>>>>>>> exist as
>>>>>>>>>>>> a conceptual object. Assuming its conceptual existence leads
>>>>>>>>>>>> to a
>>>>>>>>>>>> paradox.
>>>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>>>> courses on
>>>>>>>>>>>> Computer
>>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>>> claims the
>>>>>>>>>>>> halting
>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>
>>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>>> something?
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>>
>>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>>
>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>>
>>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>>> non-existence of a number N for the number of steps needed to
>>>>>>>>>>> reach a final state.
>>>>>>>>>>>
>>>>>>>>>>> Some people just don't like the fact that it can be
>>>>>>>>>>> absolutely provable what the answer is (and thus unknowable),
>>>>>>>>>>> even if we know from the definition, that it must be one or
>>>>>>>>>>> the other.
>>>>>>>>>>>
>>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>>> branch accepts that some truth is only established by
>>>>>>>>>>> infinite chains of connections, and thus can not be proven
>>>>>>>>>>> with a finite proof, and thus is unknowable.
>>>>>>>>>>>
>>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>>> established by Finite chains. The problem then is, such logic
>>>>>>>>>>> system need to greatly limit the domain they attempt to
>>>>>>>>>>> cover, as otherwise you get into endless chains of asking if
>>>>>>>>>>> a question can be asked, at which point you need to ask if
>>>>>>>>>>> you can even ask about asking the questions. Only when the
>>>>>>>>>>> domain is restricted in a way that the answer MUST be
>>>>>>>>>>> determinable with finite work, can we break the cycle.
>>>>>>>>>>>
>>>>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>>>>> (which could be Turing Machines with a fixed finite tape, or
>>>>>>>>>>> a classical program in a computer with limited memory) then
>>>>>>>>>>> we can be sure that the answer is determinable with a finite
>>>>>>>>>>> amount of work.
>>>>>>>>>>
>>>>>>>>>> Tarski did not understand that the Liar Paradox is not a truth
>>>>>>>>>> bearer
>>>>>>>>>> thus cannot possibly be true or false. His ignorance got him
>>>>>>>>>> so confused
>>>>>>>>>> that he thought that he proved that True(L,x) cannot be
>>>>>>>>>> defined because
>>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>>
>>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>>> this? He shows that if True(L, x) exists that the Liar Paradox
>>>>>>>>> is a true statement, but not what you say.
>>>>>>>>
>>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a
>>>>>>>> true."
>>>>>>>>
>>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>>
>>>>>>>
>>>>>>> Nope, you said that he assumed the Liars Paradox has a logic value.
>>>>>>>
>>>>>>> The assumption was just that True(L,x) existed.
>>>>>>>
>>>>>>
>>>>>> No that it only half of the assumption.
>>>>>> The other half is that True(tarski_theory, "this sentence is not
>>>>>> true")
>>>>>> must be true or false. That half was Tarksi's fatal flaw.
>>>>>>
>>>>>
>>>>> True(tarski_theory, "this sentence is not true") is actually a
>>>>> mathematical statement consisting of elementary operations such as
>>>>> addition, multiplication, and quantifiers. Can you show how to use
>>>>> these basic parts to build a statement that is not true or false?
>>>>
>>>> When I put the same thing into Prolog
>>>> it is rejected as semantically unsound.
>>>>
>>>> ?- LP = not(true(LP)).
>>>> LP = not(true(LP)).
>>>>
>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>> false.
>>>>
>>>>
>>>
>>> That isn't how Tarski works. No wonder you don't understand the
>>> halting problem either.
>>
>> THAT IS HOW THE LIAR PARADOX WORKS
>
> It isn't how Tarski works.
>
>>
>> Tarski didn't understand that the correct
>> evaluation of the Liar Paradox requires
>> an infinite cycle in the directed graph
>> of its evaluation sequence.
>
> You don't understand the difference between diagonalization and infinite
> recursion.
>
> Do you think the real numbers are countable?

Diagonalization is a process by which we know that
x is unprovable in L that makes sure to ignore the
reason why x is unprovable in L.

unify_with_occurs_check(LP, not(true(LP))).
correctly determines that LP is unprovable
BECAUSE the directed graph of its evaluation
sequence contains an infinite cycle.

On 1/21/24 6:09 PM, olcott wrote:
> On 1/21/2024 4:54 PM, immibis wrote:
>> On 1/21/24 23:37, olcott wrote:
>>> On 1/21/2024 4:19 PM, immibis wrote:
>>>> On 1/21/24 22:50, olcott wrote:
>>>>> On 1/21/2024 3:46 PM, immibis wrote:
>>>>>> On 1/21/24 22:15, olcott wrote:
>>>>>>> On 1/21/2024 3:09 PM, immibis wrote:
>>>>>>>> On 1/21/24 22:07, olcott wrote:
>>>>>>>>> On 1/21/2024 2:54 PM, immibis wrote:
>>>>>>>>>> On 1/21/24 21:51, olcott wrote:
>>>>>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>>>>> The idea of a universal halting test seems reasonable,
>>>>>>>>>>>>>>> but cannot be
>>>>>>>>>>>>>>> for-
>>>>>>>>>>>>>>> malised as a consistent specification. It has no model
>>>>>>>>>>>>>>> and does not
>>>>>>>>>>>>>>> exist as
>>>>>>>>>>>>>>> a conceptual object. Assuming its conceptual existence
>>>>>>>>>>>>>>> leads to a
>>>>>>>>>>>>>>> paradox.
>>>>>>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>>>>>>> courses on
>>>>>>>>>>>>>>> Computer
>>>>>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>>>>>> claims the
>>>>>>>>>>>>>>> halting
>>>>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>>>>>> something?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>>>>>> non-existence of a number N for the number of steps needed
>>>>>>>>>>>>>> to reach a final state.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Some people just don't like the fact that it can be
>>>>>>>>>>>>>> absolutely provable what the answer is (and thus
>>>>>>>>>>>>>> unknowable), even if we know from the definition, that it
>>>>>>>>>>>>>> must be one or the other.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>>>>>> branch accepts that some truth is only established by
>>>>>>>>>>>>>> infinite chains of connections, and thus can not be proven
>>>>>>>>>>>>>> with a finite proof, and thus is unknowable.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>>>>>> established by Finite chains. The problem then is, such
>>>>>>>>>>>>>> logic system need to greatly limit the domain they attempt
>>>>>>>>>>>>>> to cover, as otherwise you get into endless chains of
>>>>>>>>>>>>>> asking if a question can be asked, at which point you need
>>>>>>>>>>>>>> to ask if you can even ask about asking the questions.
>>>>>>>>>>>>>> Only when the domain is restricted in a way that the
>>>>>>>>>>>>>> answer MUST be determinable with finite work, can we break
>>>>>>>>>>>>>> the cycle.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> For instance, if we limit ourselves to Finite State
>>>>>>>>>>>>>> Machines (which could be Turing Machines with a fixed
>>>>>>>>>>>>>> finite tape, or a classical program in a computer with
>>>>>>>>>>>>>> limited memory) then we can be sure that the answer is
>>>>>>>>>>>>>> determinable with a finite amount of work.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Tarski did not understand that the Liar Paradox is not a
>>>>>>>>>>>>> truth bearer
>>>>>>>>>>>>> thus cannot possibly be true or false. His ignorance got
>>>>>>>>>>>>> him so confused
>>>>>>>>>>>>> that he thought that he proved that True(L,x) cannot be
>>>>>>>>>>>>> defined because
>>>>>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>>>>>
>>>>>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>>>>>> this? He shows that if True(L, x) exists that the Liar
>>>>>>>>>>>> Paradox is a true statement, but not what you say.
>>>>>>>>>>>
>>>>>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is
>>>>>>>>>>> a true."
>>>>>>>>>>>
>>>>>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>>>>>
>>>>>>>>>>> Why this is nutty on his part requires you to understand a term
>>>>>>>>>>> that is not in logic or math, it is only in philosophy of logic:
>>>>>>>>>>> {truth bearer}.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> You agree it's not in logic or math. Well he talked about
>>>>>>>>>> logic and math, not philosophy. So you agree that in logic and
>>>>>>>>>> math, the liar paradox is true?
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> I agree that it a ridiculously foolish thing to say.
>>>>>>>>>
>>>>>>>>> The ignorance of logic and math does not derive any
>>>>>>>>> sort of truth.
>>>>>>>>
>>>>>>>> So math does not prove that 1+1=2?
>>>>>>>>
>>>>>>>
>>>>>>> Always with the strawman deception.
>>>>>>> Do you want me to start calling you a liar?
>>>>>>>
>>>>>>> If you don't want me to start calling you a liar
>>>>>>> then quit using the strawman deception.
>>>>>>>
>>>>>>> It was pointed out that logic and math are clueless
>>>>>>> about the Liar Paradox.
>>>>>>
>>>>>> Didn't Tarski translate the Liar Paradox into logic and mathematics?
>>>>>>
>>>>>
>>>>> The key thing that Tarski missed is that expressions of language
>>>>> that are not truth bearers cannot possibly have any truth value.
>>>>> *This was his fatal mistake*
>>>>>
>>>>>
>>>> So a statement such as "∀x (x = 5)" can be neither true nor false?
>>>
>>> Yet another strawman deception
>>>
>> Every time you say "strawman deception" it will be read as "I, Olcott,
>> admit to being wrong"
>
> I provide an example that cannot possibly be true or false
> and you provide a counter-example as a rebuttal that is
> definitely false: ∀x ∈ ℕ (x = 5) is false
>
> THAT IS THE STRAWMAN DECEPTION
>

On 1/21/2024 6:06 PM, immibis wrote:
> On 1/22/24 00:17, olcott wrote:
>> On 1/21/2024 5:00 PM, Richard Damon wrote:
>>> On 1/21/24 5:39 PM, olcott wrote:
>>>> On 1/21/2024 4:32 PM, Richard Damon wrote:
>>>>> On 1/21/24 4:55 PM, olcott wrote:
>>>>>> On 1/21/2024 3:52 PM, Richard Damon wrote:
>>>>>>> On 1/21/24 3:51 PM, olcott wrote:
>>>>>>>> On 1/21/2024 2:43 PM, Richard Damon wrote:
>>>>>>>>> On 1/21/24 3:15 PM, olcott wrote:
>>>>>>>>>> On 1/21/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/21/24 2:22 PM, wij wrote:
>>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>
>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>> cannot be
>>>>>>>>>>>> for-
>>>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>>>> does not
>>>>>>>>>>>> exist as
>>>>>>>>>>>> a conceptual object. Assuming its conceptual existence leads
>>>>>>>>>>>> to a
>>>>>>>>>>>> paradox.
>>>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>>>> courses on
>>>>>>>>>>>> Computer
>>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>>> claims the
>>>>>>>>>>>> halting
>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>
>>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>>> something?
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> I think the problem he is seeing is that the property of
>>>>>>>>>>> "Halting" can not be uniformly determined in Finite Time.
>>>>>>>>>>>
>>>>>>>>>>> That is all that I can get from his statement of:
>>>>>>>>>>>
>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>> cannot be formalised as a consistent specification.
>>>>>>>>>>>
>>>>>>>>>>> There certainly CAN be defined formal test that define
>>>>>>>>>>> Halting, the issue is that non-halting is defined by the
>>>>>>>>>>> non-existence of a number N for the number of steps needed to
>>>>>>>>>>> reach a final state.
>>>>>>>>>>>
>>>>>>>>>>> Some people just don't like the fact that it can be
>>>>>>>>>>> absolutely provable what the answer is (and thus unknowable),
>>>>>>>>>>> even if we know from the definition, that it must be one or
>>>>>>>>>>> the other.
>>>>>>>>>>>
>>>>>>>>>>> This leads us to a great divide in logics. The classical
>>>>>>>>>>> branch accepts that some truth is only established by
>>>>>>>>>>> infinite chains of connections, and thus can not be proven
>>>>>>>>>>> with a finite proof, and thus is unknowable.
>>>>>>>>>>>
>>>>>>>>>>> Others don't accept that, and require Truth to be only
>>>>>>>>>>> established by Finite chains. The problem then is, such logic
>>>>>>>>>>> system need to greatly limit the domain they attempt to
>>>>>>>>>>> cover, as otherwise you get into endless chains of asking if
>>>>>>>>>>> a question can be asked, at which point you need to ask if
>>>>>>>>>>> you can even ask about asking the questions. Only when the
>>>>>>>>>>> domain is restricted in a way that the answer MUST be
>>>>>>>>>>> determinable with finite work, can we break the cycle.
>>>>>>>>>>>
>>>>>>>>>>> For instance, if we limit ourselves to Finite State Machines
>>>>>>>>>>> (which could be Turing Machines with a fixed finite tape, or
>>>>>>>>>>> a classical program in a computer with limited memory) then
>>>>>>>>>>> we can be sure that the answer is determinable with a finite
>>>>>>>>>>> amount of work.
>>>>>>>>>>
>>>>>>>>>> Tarski did not understand that the Liar Paradox is not a truth
>>>>>>>>>> bearer
>>>>>>>>>> thus cannot possibly be true or false. His ignorance got him
>>>>>>>>>> so confused
>>>>>>>>>> that he thought that he proved that True(L,x) cannot be
>>>>>>>>>> defined because
>>>>>>>>>> True(Tarski_theory, LP) does not work.
>>>>>>>>>
>>>>>>>>> I'll ask one more time, exactly WHERE in the proof did he do
>>>>>>>>> this? He shows that if True(L, x) exists that the Liar Paradox
>>>>>>>>> is a true statement, but not what you say.
>>>>>>>>
>>>>>>>> "He shows that if True(L, x) exists that the Liar Paradox is a
>>>>>>>> true."
>>>>>>>>
>>>>>>>> That is a perfect paraphrase of my position of what he said.
>>>>>>>>
>>>>>>>
>>>>>>> Nope, you said that he assumed the Liars Paradox has a logic value.
>>>>>>>
>>>>>>> The assumption was just that True(L,x) existed.
>>>>>>>
>>>>>>
>>>>>> No that it only half of the assumption.
>>>>>> The other half is that True(tarski_theory, "this sentence is not
>>>>>> true")
>>>>>> must be true or false. That half was Tarksi's fatal flaw.
>>>>>>
>>>>>
>>>>> Where do you see that as an INPUT assumption, and not a result of a
>>>>> proof?
>>>>>
>>>>> LINE please.
>>>>
>>>> line (3)
>>>
>>> You mean the (3) on page 275?
>>>
>>> The one preeeded by: "from (1) and (2) we obtain immediately"
>>>
>>> Thus (3) isn't an assumption but a proven statement.
>>>
>>> Also (3) says x is not Provable if and only if x is not True
>>>
>>> (Which applies only for a particuar x that was derived in (1).
>>>
>>>
>>> Of course, you don't accept that statement, but you need to try to
>>> find the error in that logic (which I doubt exists)
>>>
>>> YOu are just showing how little you understand about how logic works.
>>> You can't seem to read these papers and understand them.
>>
>> (3) x ∉ Provable if and only if x ∈ True.
>>
>> Is like assuming that cows are dogs because it rejects
>> the way that an actual True(L, x) predicate works:
>> ∀x ∈ L (True(L,x) ≡ (L ⊢ x))
>>
>
> So you don't understand the proof and you just argue because you don't
> like the conclusion.

Not at all. After 10,000 hours of careful thought over many years
I have determined this: ∀x ∈ L (True(L,x) ≡ (L ⊢ x))
is the correct way to encode a consistent and correct Truth(L,x)
predicate. It even works correctly with natural language
that has been formalized with something like Montague Grammar.