On 1/11/24 11:23 PM, olcott wrote:
> On 1/11/2024 10:11 PM, immibis wrote:
>> On 1/10/24 15:21, olcott wrote:
>>> On 1/10/2024 3:10 AM, Mikko wrote:
>>>> On 2024-01-10 07:19:25 +0000, immibis said:
>>>>
>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>> 4. A halting decider is a program or algorithm that determines
>>>>> whether P(I) halts or not.
>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>> halt is wrong.
>>>>> 6. Any algorithm that determines that a non-halting program halts
>>>>> is wrong.
>>>>
>>>> Instead of "wrong" it would be better to say "not a halting decider".
>>>>
>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>
>>>> The input should be syntactically correct. A syntax error makes the
>>>> inut invalid. If there is a syntax error in the input the decider
>>>> should halt without answering "yes" or "no" (any other behaviour is
>>>> hard to implement).
>>>>
>>>> Mikko
>>>>
>>>
>>>
>>> The above is the same as saying that every syntactically correct
>>> yes/no question has a correct answer.
>>
>> No, it isn't.
>> It's the same as saying that THE INPUT TO A HALTING DECIDER IS ANY
>> SYNTACTICALLY VALID PROGRAM AND INPUT WITH ABSOLUTELY NO EXCEPTIONS.
>>
>> Do you refute this definition?
>
> Yes I do.
>
> Self-contradictory inputs must be rejected as semantically unsound.
>
> Tarski never noticed that the Liar Paradox is not a truth bearer
> thus his Undefinability Theorem is anchored in an error.

And what is contradictory to ITSELF.

D contradicts H, not D, so not self contradictory.

On 1/11/24 11:22 PM, olcott wrote:
> On 1/11/2024 10:11 PM, immibis wrote:
>> On 1/10/24 15:34, olcott wrote:
>>> On 1/10/2024 1:19 AM, immibis wrote:
>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>> 4. A halting decider is a program or algorithm that determines
>>>> whether P(I) halts or not.
>>>> 5. Any algorithm that determines that a halting program doesn't halt
>>>> is wrong.
>>>> 6. Any algorithm that determines that a non-halting program halts is
>>>> wrong.
>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>
>>>> Which one is refuted? Please specify which point 1 through 7 is
>>>> refuted. If you cannot specify, you are being dishonest.
>>>
>>>
>>> The above is the same as saying that every syntactically correct
>>
>> Which number 1-7?
>
> 7 No one has every bothered to notice that self-contradictory inputs
> must be rejected as semantically unsound.
>
> Tarski never noticed that the Liar Paradox is not a truth bearer
> thus his Undefinability Theorem is anchored in an error.
>

And where did he do that?

SPECIFIC line in his proof.

His proof actually says that "A definition of True" (by which he means
the existance of a finite algorithm that can always determine if a
statement is true) leads to the implication that the Liar's Paradox must
be true.

On 1/11/24 11:58 PM, olcott wrote:
> On 1/11/2024 10:11 PM, immibis wrote:
>> On 1/10/24 15:34, olcott wrote:
>>> On 1/10/2024 1:19 AM, immibis wrote:
>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>> 4. A halting decider is a program or algorithm that determines
>>>> whether P(I) halts or not.
>>>> 5. Any algorithm that determines that a halting program doesn't halt
>>>> is wrong.
>>>> 6. Any algorithm that determines that a non-halting program halts is
>>>> wrong.
>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>
>>>> Which one is refuted? Please specify which point 1 through 7 is
>>>> refuted. If you cannot specify, you are being dishonest.
>>>
>>>
>>> The above is the same as saying that every syntactically correct
>>
>> Which number 1-7?
>
> This was a very helpful insight in that placing the context of the
> question directly in the question is the clearest way to explain
> these things.
>
> On 1/6/2024 1:54 PM, immibis wrote:
> > "Does the barber shave himself?" has a correct answer: it's one of
> > "yes" or "no".
> >
> > "Does a barber who shaves every man who does not shave himself shave
> > himself?" has no correct answer.
>
> *isomorphically*
>
> *The question posed by the HP*
> Does the direct execution of D(D) halt? Has a correct answer: it is yes.
>
> *The question posed to H by its counter-example input*
> What correct Boolean value does H return when D is defined to do the
> opposite of whatever value that H returns?" has no correct answer.
>
>

So, you are admitting that the problem with YOUR question (what is the
correct answer that H can return) is impossible NOT because of the
Halting question itelf (like the do x shave itself question) buut in the
assumption that there can be a machine that decides Halting, just like
there can't be the Barber you are asking about.

On 1/11/2024 11:30 PM, immibis wrote:
> On 1/12/24 05:58, olcott wrote:
>> On 1/11/2024 10:11 PM, immibis wrote:
>>> On 1/10/24 15:34, olcott wrote:
>>>> On 1/10/2024 1:19 AM, immibis wrote:
>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>> 4. A halting decider is a program or algorithm that determines
>>>>> whether P(I) halts or not.
>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>> halt is wrong.
>>>>> 6. Any algorithm that determines that a non-halting program halts
>>>>> is wrong.
>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>
>>>>> Which one is refuted? Please specify which point 1 through 7 is
>>>>> refuted. If you cannot specify, you are being dishonest.
>>>>
>>>>
>>>> The above is the same as saying that every syntactically correct
>>>
>>> Which number 1-7?
>>
>> This was a very helpful insight in that placing the context of the
>> question directly in the question is the clearest way to explain
>> these things.
>>
>> On 1/6/2024 1:54 PM, immibis wrote:
>>  > "Does the barber shave himself?" has a correct answer: it's one of
>>  > "yes" or "no".
>>  >
>>  > "Does a barber who shaves every man who does not shave himself shave
>>  > himself?" has no correct answer.
>>
>> *isomorphically*
>>
>> *The question posed by the HP*
>> Does the direct execution of D(D) halt? Has a correct answer: it is yes.

Above is where I already answered the question that you ask below.
Does the direct execution of D(D) halt? Has a correct answer: it is yes.

>>
>> *The question posed to H by its counter-example input*
>> What correct Boolean value does H return when D is defined to do the
>> opposite of whatever value that H returns?" has no correct answer.
>>
>
> Finally, Olcott has a breakthrough.
>
> Now consider points 2 and 3. Does D(D) halt?

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

On 1/12/2024 1:05 AM, immibis wrote:
> On 1/12/24 06:37, olcott wrote:
>> On 1/11/2024 11:30 PM, immibis wrote:
>>> On 1/12/24 05:58, olcott wrote:
>>>> On 1/11/2024 10:11 PM, immibis wrote:
>>>>> On 1/10/24 15:34, olcott wrote:
>>>>>> On 1/10/2024 1:19 AM, immibis wrote:
>>>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>>> whether P(I) halts or not.
>>>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>>>> halt is wrong.
>>>>>>> 6. Any algorithm that determines that a non-halting program halts
>>>>>>> is wrong.
>>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>>>
>>>>>>> Which one is refuted? Please specify which point 1 through 7 is
>>>>>>> refuted. If you cannot specify, you are being dishonest.
>>>>>>
>>>>>>
>>>>>> The above is the same as saying that every syntactically correct
>>>>>
>>>>> Which number 1-7?
>>>>
>>>> This was a very helpful insight in that placing the context of the
>>>> question directly in the question is the clearest way to explain
>>>> these things.
>>>>
>>>> On 1/6/2024 1:54 PM, immibis wrote:
>>>>  > "Does the barber shave himself?" has a correct answer: it's one of
>>>>  > "yes" or "no".
>>>>  >
>>>>  > "Does a barber who shaves every man who does not shave himself shave
>>>>  > himself?" has no correct answer.
>>>>
>>>> *isomorphically*
>>>>
>>>> *The question posed by the HP*
>>>> Does the direct execution of D(D) halt? Has a correct answer: it is
>>>> yes.
>>>>
>>>> *The question posed to H by its counter-example input*
>>>> What correct Boolean value does H return when D is defined to do the
>>>> opposite of whatever value that H returns?" has no correct answer.
>>>>
>>>
>>> Finally, Olcott has a breakthrough.
>>>
>>> Now consider points 2 and 3. Does D(D) halt?
>> I already answered that, please reread the above.
>>
>
> You didn't answer, so please answer now.
>
> >>> *The question posed to H by its counter-example input*
> >>> What correct Boolean value does H return when D is defined to do the
> >>> opposite of whatever value that H returns?" has no correct answer.
>
> This is wrong. *The question posed to H by its counter-example input*
> Does the direct execution of D(D) halt?

If that was true then the question of the barber paradox would be:
"Does the barber shave himself?" that has a correct answer of yes or no.

ignoring the context that
"the barber states that he shaves all who do not shave themselves."
https://www.britannica.com/topic/barber-paradox

Since you are refuting your own reasoning this seems to prove that you
are being disingenuous, stuck in rebuttal mode at the expense of truth.

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

On 1/12/2024 1:03 AM, immibis wrote:
> On 1/12/24 06:39, olcott wrote:
>> On 1/11/2024 11:33 PM, immibis wrote:
>>> On 1/12/24 05:23, olcott wrote:
>>>> On 1/11/2024 10:11 PM, immibis wrote:
>>>>> On 1/10/24 15:21, olcott wrote:
>>>>>> On 1/10/2024 3:10 AM, Mikko wrote:
>>>>>>> On 2024-01-10 07:19:25 +0000, immibis said:
>>>>>>>
>>>>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>>>> whether P(I) halts or not.
>>>>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>>>>> halt is wrong.
>>>>>>>> 6. Any algorithm that determines that a non-halting program
>>>>>>>> halts is wrong.
>>>>>>>
>>>>>>> Instead of "wrong" it would be better to say "not a halting
>>>>>>> decider".
>>>>>>>
>>>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>>>
>>>>>>> The input should be syntactically correct. A syntax error makes the
>>>>>>> inut invalid. If there is a syntax error in the input the decider
>>>>>>> should halt without answering "yes" or "no" (any other behaviour is
>>>>>>> hard to implement).
>>>>>>>
>>>>>>> Mikko
>>>>>>>
>>>>>>
>>>>>>
>>>>>> The above is the same as saying that every syntactically correct
>>>>>> yes/no question has a correct answer.
>>>>>
>>>>> No, it isn't.
>>>>> It's the same as saying that THE INPUT TO A HALTING DECIDER IS ANY
>>>>> SYNTACTICALLY VALID PROGRAM AND INPUT WITH ABSOLUTELY NO EXCEPTIONS.
>>>>>
>>>>> Do you refute this definition?
>>>>
>>>> Yes I do.
>>>>
>>>> Self-contradictory inputs must be rejected as semantically unsound.
>>>>
>>>> Tarski never noticed that the Liar Paradox is not a truth bearer
>>>> thus his Undefinability Theorem is anchored in an error.
>>>
>>> So which inputs are valid to a halting decider? If it isn't ALL
>>> SYNTACTICALLY VALID PROGRAMS (AND INPUTS) WITH ABSOLUTELY NO
>>> EXCEPTIONS then you are not talking about the same thing that
>>> everyone else is talking about.
>>>
>>
>> *Of course I am not, they are all incorrect*
>
> OK so you haven't solved the halting problem at all. You think you've
> solved a different problem.
When Tarski "proved" that a consistent and correct True(L,x) predicate
cannot exist on the basis of his false assumption that the Liar Paradox
is a truth bearer his mistake must be corrected and the Liar Paradox
rejected as not a truth bearer.

A decider computes the mapping from its input finite string to an accept
or reject state on the basis of a property of this input string.

When the halting problem is defined to report on the behavior of the
non-input direct execution of D(D) when deciders are defined as required
to only report on the behavior of their inputs then the computer science
of this is inconsistent and must be corrected.

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

On 1/12/2024 1:04 AM, immibis wrote:
> On 1/12/24 05:28, olcott wrote:
>> On 1/11/2024 10:17 PM, immibis wrote:
>>> On 1/10/24 19:49, Jeff Barnett wrote:
>>>> On 1/10/2024 12:19 AM, immibis wrote:
>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>> 4. A halting decider is a program or algorithm that determines
>>>>> whether P(I) halts or not.
>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>> halt is wrong.
>>>>> 6. Any algorithm that determines that a non-halting program halts
>>>>> is wrong.
>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>
>>>> Since you are have not defined "valid program", the above is fairly
>>>> weak. For example, the idiot Olcott might say that "D(D)" isn't
>>>> valid and you are right back down the crap hole.
>>>
>>> That's fine. If Olcott thinks that D is not a valid program, or D is
>>> not a valid input for program D, he needs to say that.
>>>
>>>
>>> Probably the best you can do
>>>> along these lines is say that D - your decider - accepts as input
>>>> any string D where P(S) is true and P is a decidable predicate.
>>>
>>> I repeat: THE INPUT TO A HALTING DECIDER IS ANY VALID PROGRAM (and
>>> its input but it doesn't actually matter whether you allow input or
>>> not) WITH ABSOLUTELY NO EXCEPTIONS.
>>>
>>
>> If we apply that same reasoning to this syntactically correct question:
>> What time is it (yes or no)?
>>
>> It becomes much more obvious that incorrect questions
>> do not limit anyone or anything, they are just wrong.
>>
>
> You can't even write a program that answers the question, so you can't
> input the program to the halt decider. I repeat: ANY VALID PROGRAM.

The Cyc project can write a computer program that understands that
question in their CycL language.

It is much easier to write the Liar Paradox in Prolog and see that
Prolog rejects the Liar Paradox as semantically unsound.

Tarski make the mistake of anchoring his whole Undecidability Proof
in the semantically unsound Liar Paradox.

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

On 1/12/2024 1:11 AM, immibis wrote:
> On 1/12/24 05:22, olcott wrote:
>> On 1/11/2024 10:11 PM, immibis wrote:
>>> On 1/10/24 15:34, olcott wrote:
>>>> On 1/10/2024 1:19 AM, immibis wrote:
>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>> 4. A halting decider is a program or algorithm that determines
>>>>> whether P(I) halts or not.
>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>> halt is wrong.
>>>>> 6. Any algorithm that determines that a non-halting program halts
>>>>> is wrong.
>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>
>>>>> Which one is refuted? Please specify which point 1 through 7 is
>>>>> refuted. If you cannot specify, you are being dishonest.
>>>>
>>>>
>>>> The above is the same as saying that every syntactically correct
>>>
>>> Which number 1-7?
>>
>> 7 No one has every bothered to notice that self-contradictory inputs
>> must be rejected as semantically unsound.
>>
>> Tarski never noticed that the Liar Paradox is not a truth bearer
>> thus his Undefinability Theorem is anchored in an error.
>>
>
> In the system that everyone uses, all formulas such as "∃x. x > 5" are
> either true or false. It is impossible to write a formula that isn't
> true or false.

There were able to do this by adding the million-fold degree
of purely extraneous complexity of Gödel numbers.
G is neither true nor false in PA as Wittgenstein proves:
https://www.liarparadox.org/Wittgenstein.pdf
He calls G P and he calls PA Russel's System.

Alternatively they could simply create a system of HOL that implements
the ⊢ operator, then we can write G := ~(PA ⊢ G) which is rejected
by Prolog as semantically unsound.

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

On 1/12/2024 6:31 AM, Richard Damon wrote:
> On 1/11/24 11:58 PM, olcott wrote:
>> On 1/11/2024 10:11 PM, immibis wrote:
>>> On 1/10/24 15:34, olcott wrote:
>>>> On 1/10/2024 1:19 AM, immibis wrote:
>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>> 4. A halting decider is a program or algorithm that determines
>>>>> whether P(I) halts or not.
>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>> halt is wrong.
>>>>> 6. Any algorithm that determines that a non-halting program halts
>>>>> is wrong.
>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>
>>>>> Which one is refuted? Please specify which point 1 through 7 is
>>>>> refuted. If you cannot specify, you are being dishonest.
>>>>
>>>>
>>>> The above is the same as saying that every syntactically correct
>>>
>>> Which number 1-7?
>>
>> This was a very helpful insight in that placing the context of the
>> question directly in the question is the clearest way to explain
>> these things.
>>
>> On 1/6/2024 1:54 PM, immibis wrote:
>>  > "Does the barber shave himself?" has a correct answer: it's one of
>>  > "yes" or "no".
>>  >
>>  > "Does a barber who shaves every man who does not shave himself shave
>>  > himself?" has no correct answer.
>>
>> *isomorphically*
>>
>> *The question posed by the HP*
>> Does the direct execution of D(D) halt? Has a correct answer: it is yes.
>>
>> *The question posed to H by its counter-example input*
>> What correct Boolean value does H return when D is defined to do the
>> opposite of whatever value that H returns?" has no correct answer.
>>
>>
>
> So, you are admitting that the problem with YOUR question (what is the
> correct answer that H can return) is impossible NOT because of the
> Halting question itelf (like the do x shave itself question) buut in the
> assumption that there can be a machine that decides Halting, just like
> there can't be the Barber you are asking about.

Just like no one can possibly correctly answer the question:
"What time is it (yes or no)?"
because the question itself <is> Incorrect.

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

On 1/12/24 16:50, olcott wrote:
> On 1/12/2024 1:04 AM, immibis wrote:
>> On 1/12/24 05:28, olcott wrote:
>>> On 1/11/2024 10:17 PM, immibis wrote:
>>>> On 1/10/24 19:49, Jeff Barnett wrote:
>>>>> On 1/10/2024 12:19 AM, immibis wrote:
>>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>> whether P(I) halts or not.
>>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>>> halt is wrong.
>>>>>> 6. Any algorithm that determines that a non-halting program halts
>>>>>> is wrong.
>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>
>>>>> Since you are have not defined "valid program", the above is fairly
>>>>> weak. For example, the idiot Olcott might say that "D(D)" isn't
>>>>> valid and you are right back down the crap hole.
>>>>
>>>> That's fine. If Olcott thinks that D is not a valid program, or D is
>>>> not a valid input for program D, he needs to say that.
>>>>
>>>>
>>>> Probably the best you can do
>>>>> along these lines is say that D - your decider - accepts as input
>>>>> any string D where P(S) is true and P is a decidable predicate.
>>>>
>>>> I repeat: THE INPUT TO A HALTING DECIDER IS ANY VALID PROGRAM (and
>>>> its input but it doesn't actually matter whether you allow input or
>>>> not) WITH ABSOLUTELY NO EXCEPTIONS.
>>>>
>>>
>>> If we apply that same reasoning to this syntactically correct question:
>>> What time is it (yes or no)?
>>>
>>> It becomes much more obvious that incorrect questions
>>> do not limit anyone or anything, they are just wrong.
>>>
>>
>> You can't even write a program that answers the question, so you can't
>> input the program to the halt decider. I repeat: ANY VALID PROGRAM.
>
> The Cyc project can write a computer program that understands that
> question in their CycL language.

A program that tells me the current time (yes or no)?

I'd like to see the program.

On 1/12/2024 10:27 AM, immibis wrote:
> On 1/12/24 16:50, olcott wrote:
>> On 1/12/2024 1:04 AM, immibis wrote:
>>> On 1/12/24 05:28, olcott wrote:
>>>> On 1/11/2024 10:17 PM, immibis wrote:
>>>>> On 1/10/24 19:49, Jeff Barnett wrote:
>>>>>> On 1/10/2024 12:19 AM, immibis wrote:
>>>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>>> whether P(I) halts or not.
>>>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>>>> halt is wrong.
>>>>>>> 6. Any algorithm that determines that a non-halting program halts
>>>>>>> is wrong.
>>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>>
>>>>>> Since you are have not defined "valid program", the above is
>>>>>> fairly weak. For example, the idiot Olcott might say that "D(D)"
>>>>>> isn't valid and you are right back down the crap hole.
>>>>>
>>>>> That's fine. If Olcott thinks that D is not a valid program, or D
>>>>> is not a valid input for program D, he needs to say that.
>>>>>
>>>>>
>>>>> Probably the best you can do
>>>>>> along these lines is say that D - your decider - accepts as input
>>>>>> any string D where P(S) is true and P is a decidable predicate.
>>>>>
>>>>> I repeat: THE INPUT TO A HALTING DECIDER IS ANY VALID PROGRAM (and
>>>>> its input but it doesn't actually matter whether you allow input or
>>>>> not) WITH ABSOLUTELY NO EXCEPTIONS.
>>>>>
>>>>
>>>> If we apply that same reasoning to this syntactically correct question:
>>>> What time is it (yes or no)?
>>>>
>>>> It becomes much more obvious that incorrect questions
>>>> do not limit anyone or anything, they are just wrong.
>>>>
>>>
>>> You can't even write a program that answers the question, so you
>>> can't input the program to the halt decider. I repeat: ANY VALID
>>> PROGRAM.
>>
>> The Cyc project can write a computer program that understands that
>> question in their CycL language.
>
> A program that tells me the current time (yes or no)?
>
> I'd like to see the program.

You do understand that it <is> an incorrect question don't you?
It does prove that incorrect question do exist.

It is also clear that the inability to answer incorrect questions
does not place any limit on anyone or anything.

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

On 1/12/24 15:37, olcott wrote:
> On 1/12/2024 1:05 AM, immibis wrote:
>> On 1/12/24 06:37, olcott wrote:
>>> On 1/11/2024 11:30 PM, immibis wrote:
>>>> On 1/12/24 05:58, olcott wrote:
>>>>> On 1/11/2024 10:11 PM, immibis wrote:
>>>>>> On 1/10/24 15:34, olcott wrote:
>>>>>>> On 1/10/2024 1:19 AM, immibis wrote:
>>>>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>>>> whether P(I) halts or not.
>>>>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>>>>> halt is wrong.
>>>>>>>> 6. Any algorithm that determines that a non-halting program
>>>>>>>> halts is wrong.
>>>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>>>>
>>>>>>>> Which one is refuted? Please specify which point 1 through 7 is
>>>>>>>> refuted. If you cannot specify, you are being dishonest.
>>>>>>>
>>>>>>>
>>>>>>> The above is the same as saying that every syntactically correct
>>>>>>
>>>>>> Which number 1-7?
>>>>>
>>>>> This was a very helpful insight in that placing the context of the
>>>>> question directly in the question is the clearest way to explain
>>>>> these things.
>>>>>
>>>>> On 1/6/2024 1:54 PM, immibis wrote:
>>>>>  > "Does the barber shave himself?" has a correct answer: it's one of
>>>>>  > "yes" or "no".
>>>>>  >
>>>>>  > "Does a barber who shaves every man who does not shave himself
>>>>> shave
>>>>>  > himself?" has no correct answer.
>>>>>
>>>>> *isomorphically*
>>>>>
>>>>> *The question posed by the HP*
>>>>> Does the direct execution of D(D) halt? Has a correct answer: it is
>>>>> yes.
>>>>>
>>>>> *The question posed to H by its counter-example input*
>>>>> What correct Boolean value does H return when D is defined to do
>>>>> the opposite of whatever value that H returns?" has no correct answer.
>>>>>
>>>>
>>>> Finally, Olcott has a breakthrough.
>>>>
>>>> Now consider points 2 and 3. Does D(D) halt?
>>> I already answered that, please reread the above.
>>>
>>
>> You didn't answer, so please answer now.
>>
>>  >>> *The question posed to H by its counter-example input*
>>  >>> What correct Boolean value does H return when D is defined to do the
>>  >>> opposite of whatever value that H returns?" has no correct answer.
>>
>> This is wrong. *The question posed to H by its counter-example input*
>> Does the direct execution of D(D) halt?
>
> If that was true then the question of the barber paradox would be:
> "Does the barber shave himself?" that has a correct answer of yes or no.

If that was false then the question of the halting paradox would be:
"When H correctly solves the halting problem, does the direct execution
of D(D) halt?"

On 1/12/24 17:19, olcott wrote:
> On 1/12/2024 6:31 AM, Richard Damon wrote:
>> On 1/11/24 11:58 PM, olcott wrote:
>>> On 1/11/2024 10:11 PM, immibis wrote:
>>>> On 1/10/24 15:34, olcott wrote:
>>>>> On 1/10/2024 1:19 AM, immibis wrote:
>>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>> whether P(I) halts or not.
>>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>>> halt is wrong.
>>>>>> 6. Any algorithm that determines that a non-halting program halts
>>>>>> is wrong.
>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>>
>>>>>> Which one is refuted? Please specify which point 1 through 7 is
>>>>>> refuted. If you cannot specify, you are being dishonest.
>>>>>
>>>>>
>>>>> The above is the same as saying that every syntactically correct
>>>>
>>>> Which number 1-7?
>>>
>>> This was a very helpful insight in that placing the context of the
>>> question directly in the question is the clearest way to explain
>>> these things.
>>>
>>> On 1/6/2024 1:54 PM, immibis wrote:
>>>  > "Does the barber shave himself?" has a correct answer: it's one of
>>>  > "yes" or "no".
>>>  >
>>>  > "Does a barber who shaves every man who does not shave himself shave
>>>  > himself?" has no correct answer.
>>>
>>> *isomorphically*
>>>
>>> *The question posed by the HP*
>>> Does the direct execution of D(D) halt? Has a correct answer: it is yes.
>>>
>>> *The question posed to H by its counter-example input*
>>> What correct Boolean value does H return when D is defined to do the
>>> opposite of whatever value that H returns?" has no correct answer.
>>>
>>>
>>
>> So, you are admitting that the problem with YOUR question (what is the
>> correct answer that H can return) is impossible NOT because of the
>> Halting question itelf (like the do x shave itself question) buut in
>> the assumption that there can be a machine that decides Halting, just
>> like there can't be the Barber you are asking about.
>
> Just like no one can possibly correctly answer the question:
> "What time is it (yes or no)?"
> because the question itself <is> Incorrect.
>

Prove that no computer program can tell me the time (yes or no).

On 1/12/24 17:31, olcott wrote:
> On 1/12/2024 10:27 AM, immibis wrote:
>> On 1/12/24 16:50, olcott wrote:
>>> On 1/12/2024 1:04 AM, immibis wrote:
>>>> On 1/12/24 05:28, olcott wrote:
>>>>> On 1/11/2024 10:17 PM, immibis wrote:
>>>>>> On 1/10/24 19:49, Jeff Barnett wrote:
>>>>>>> On 1/10/2024 12:19 AM, immibis wrote:
>>>>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>>>> whether P(I) halts or not.
>>>>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>>>>> halt is wrong.
>>>>>>>> 6. Any algorithm that determines that a non-halting program
>>>>>>>> halts is wrong.
>>>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>>>
>>>>>>> Since you are have not defined "valid program", the above is
>>>>>>> fairly weak. For example, the idiot Olcott might say that "D(D)"
>>>>>>> isn't valid and you are right back down the crap hole.
>>>>>>
>>>>>> That's fine. If Olcott thinks that D is not a valid program, or D
>>>>>> is not a valid input for program D, he needs to say that.
>>>>>>
>>>>>>
>>>>>> Probably the best you can do
>>>>>>> along these lines is say that D - your decider - accepts as input
>>>>>>> any string D where P(S) is true and P is a decidable predicate.
>>>>>>
>>>>>> I repeat: THE INPUT TO A HALTING DECIDER IS ANY VALID PROGRAM (and
>>>>>> its input but it doesn't actually matter whether you allow input
>>>>>> or not) WITH ABSOLUTELY NO EXCEPTIONS.
>>>>>>
>>>>>
>>>>> If we apply that same reasoning to this syntactically correct
>>>>> question:
>>>>> What time is it (yes or no)?
>>>>>
>>>>> It becomes much more obvious that incorrect questions
>>>>> do not limit anyone or anything, they are just wrong.
>>>>>
>>>>
>>>> You can't even write a program that answers the question, so you
>>>> can't input the program to the halt decider. I repeat: ANY VALID
>>>> PROGRAM.
>>>
>>> The Cyc project can write a computer program that understands that
>>> question in their CycL language.
>>
>> A program that tells me the current time (yes or no)?
>>
>> I'd like to see the program.
>
> You do understand that it <is> an incorrect question don't you?
> It does prove that incorrect question do exist.
>
> It is also clear that the inability to answer incorrect questions
> does not place any limit on anyone or anything.
>

You just told me the Cyc project could write a program that could tell
me the time (yes or no).

Please show me the program.

On 1/12/24 16:47, olcott wrote:
> On 1/12/2024 1:03 AM, immibis wrote:
>> On 1/12/24 06:39, olcott wrote:
>>> On 1/11/2024 11:33 PM, immibis wrote:
>>>> On 1/12/24 05:23, olcott wrote:
>>>>> On 1/11/2024 10:11 PM, immibis wrote:
>>>>>> On 1/10/24 15:21, olcott wrote:
>>>>>>> On 1/10/2024 3:10 AM, Mikko wrote:
>>>>>>>> On 2024-01-10 07:19:25 +0000, immibis said:
>>>>>>>>
>>>>>>>>> 1. Every P(I) either halts or doesn't halt. There is no
>>>>>>>>> in-between.
>>>>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't
>>>>>>>>> halt.
>>>>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>>>>> whether P(I) halts or not.
>>>>>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>>>>>> halt is wrong.
>>>>>>>>> 6. Any algorithm that determines that a non-halting program
>>>>>>>>> halts is wrong.
>>>>>>>>
>>>>>>>> Instead of "wrong" it would be better to say "not a halting
>>>>>>>> decider".
>>>>>>>>
>>>>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>>>>
>>>>>>>> The input should be syntactically correct. A syntax error makes the
>>>>>>>> inut invalid. If there is a syntax error in the input the decider
>>>>>>>> should halt without answering "yes" or "no" (any other behaviour is
>>>>>>>> hard to implement).
>>>>>>>>
>>>>>>>> Mikko
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> The above is the same as saying that every syntactically correct
>>>>>>> yes/no question has a correct answer.
>>>>>>
>>>>>> No, it isn't.
>>>>>> It's the same as saying that THE INPUT TO A HALTING DECIDER IS ANY
>>>>>> SYNTACTICALLY VALID PROGRAM AND INPUT WITH ABSOLUTELY NO EXCEPTIONS.
>>>>>>
>>>>>> Do you refute this definition?
>>>>>
>>>>> Yes I do.
>>>>>
>>>>> Self-contradictory inputs must be rejected as semantically unsound.
>>>>>
>>>>> Tarski never noticed that the Liar Paradox is not a truth bearer
>>>>> thus his Undefinability Theorem is anchored in an error.
>>>>
>>>> So which inputs are valid to a halting decider? If it isn't ALL
>>>> SYNTACTICALLY VALID PROGRAMS (AND INPUTS) WITH ABSOLUTELY NO
>>>> EXCEPTIONS then you are not talking about the same thing that
>>>> everyone else is talking about.
>>>>
>>>
>>> *Of course I am not, they are all incorrect*
>>
>> OK so you haven't solved the halting problem at all. You think you've
>> solved a different problem.
> When Tarski "proved" that a consistent and correct True(L,x) predicate
> cannot exist on the basis of his false assumption that the Liar Paradox
> is a truth bearer his mistake must be corrected and the Liar Paradox
> rejected as not a truth bearer.

I haven't read Tarski's proof. Didn't he convert it to an arithmtic
formula? Every arithmetic formula is a truth bearer.

On 1/12/2024 10:33 AM, immibis wrote:
> On 1/12/24 15:37, olcott wrote:
>> On 1/12/2024 1:05 AM, immibis wrote:
>>> On 1/12/24 06:37, olcott wrote:
>>>> On 1/11/2024 11:30 PM, immibis wrote:
>>>>> On 1/12/24 05:58, olcott wrote:
>>>>>> On 1/11/2024 10:11 PM, immibis wrote:
>>>>>>> On 1/10/24 15:34, olcott wrote:
>>>>>>>> On 1/10/2024 1:19 AM, immibis wrote:
>>>>>>>>> 1. Every P(I) either halts or doesn't halt. There is no
>>>>>>>>> in-between.
>>>>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't
>>>>>>>>> halt.
>>>>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>>>>> whether P(I) halts or not.
>>>>>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>>>>>> halt is wrong.
>>>>>>>>> 6. Any algorithm that determines that a non-halting program
>>>>>>>>> halts is wrong.
>>>>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>>>>>
>>>>>>>>> Which one is refuted? Please specify which point 1 through 7 is
>>>>>>>>> refuted. If you cannot specify, you are being dishonest.
>>>>>>>>
>>>>>>>>
>>>>>>>> The above is the same as saying that every syntactically correct
>>>>>>>
>>>>>>> Which number 1-7?
>>>>>>
>>>>>> This was a very helpful insight in that placing the context of the
>>>>>> question directly in the question is the clearest way to explain
>>>>>> these things.
>>>>>>
>>>>>> On 1/6/2024 1:54 PM, immibis wrote:
>>>>>>  > "Does the barber shave himself?" has a correct answer: it's one of
>>>>>>  > "yes" or "no".
>>>>>>  >
>>>>>>  > "Does a barber who shaves every man who does not shave himself
>>>>>> shave
>>>>>>  > himself?" has no correct answer.
>>>>>>
>>>>>> *isomorphically*
>>>>>>
>>>>>> *The question posed by the HP*
>>>>>> Does the direct execution of D(D) halt? Has a correct answer: it
>>>>>> is yes.
>>>>>>
>>>>>> *The question posed to H by its counter-example input*
>>>>>> What correct Boolean value does H return when D is defined to do
>>>>>> the opposite of whatever value that H returns?" has no correct
>>>>>> answer.
>>>>>>
>>>>>
>>>>> Finally, Olcott has a breakthrough.
>>>>>
>>>>> Now consider points 2 and 3. Does D(D) halt?
>>>> I already answered that, please reread the above.
>>>>
>>>
>>> You didn't answer, so please answer now.
>>>
>>>  >>> *The question posed to H by its counter-example input*
>>>  >>> What correct Boolean value does H return when D is defined to do
>>> the
>>>  >>> opposite of whatever value that H returns?" has no correct answer.
>>>
>>> This is wrong. *The question posed to H by its counter-example input*
>>> Does the direct execution of D(D) halt?
>>
>> If that was true then the question of the barber paradox would be:
>> "Does the barber shave himself?" that has a correct answer of yes or no.
>
> If that was false then the question of the halting paradox would be:
> "When H correctly solves the halting problem, does the direct execution
> of D(D) halt?"
>

I am simply using your own reasoning and putting the full context
of the question that H is being asked directly into the question
just like you did for the Barber Paradox.

That you insist on contradicting your own self proves that you are
necessarily incorrect.

H is being asked about the behavior of an input that was intentionally
defined to do the opposite of whatever value that H returns, thus the
*full context of the question MUST INCLUDE THIS*

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

On 1/12/2024 10:36 AM, immibis wrote:
> On 1/12/24 16:47, olcott wrote:
>> On 1/12/2024 1:03 AM, immibis wrote:
>>> On 1/12/24 06:39, olcott wrote:
>>>> On 1/11/2024 11:33 PM, immibis wrote:
>>>>> On 1/12/24 05:23, olcott wrote:
>>>>>> On 1/11/2024 10:11 PM, immibis wrote:
>>>>>>> On 1/10/24 15:21, olcott wrote:
>>>>>>>> On 1/10/2024 3:10 AM, Mikko wrote:
>>>>>>>>> On 2024-01-10 07:19:25 +0000, immibis said:
>>>>>>>>>
>>>>>>>>>> 1. Every P(I) either halts or doesn't halt. There is no
>>>>>>>>>> in-between.
>>>>>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't
>>>>>>>>>> halt.
>>>>>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>>>>>> whether P(I) halts or not.
>>>>>>>>>> 5. Any algorithm that determines that a halting program
>>>>>>>>>> doesn't halt is wrong.
>>>>>>>>>> 6. Any algorithm that determines that a non-halting program
>>>>>>>>>> halts is wrong.
>>>>>>>>>
>>>>>>>>> Instead of "wrong" it would be better to say "not a halting
>>>>>>>>> decider".
>>>>>>>>>
>>>>>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>>>>>
>>>>>>>>> The input should be syntactically correct. A syntax error makes
>>>>>>>>> the
>>>>>>>>> inut invalid. If there is a syntax error in the input the decider
>>>>>>>>> should halt without answering "yes" or "no" (any other
>>>>>>>>> behaviour is
>>>>>>>>> hard to implement).
>>>>>>>>>
>>>>>>>>> Mikko
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> The above is the same as saying that every syntactically correct
>>>>>>>> yes/no question has a correct answer.
>>>>>>>
>>>>>>> No, it isn't.
>>>>>>> It's the same as saying that THE INPUT TO A HALTING DECIDER IS
>>>>>>> ANY SYNTACTICALLY VALID PROGRAM AND INPUT WITH ABSOLUTELY NO
>>>>>>> EXCEPTIONS.
>>>>>>>
>>>>>>> Do you refute this definition?
>>>>>>
>>>>>> Yes I do.
>>>>>>
>>>>>> Self-contradictory inputs must be rejected as semantically unsound.
>>>>>>
>>>>>> Tarski never noticed that the Liar Paradox is not a truth bearer
>>>>>> thus his Undefinability Theorem is anchored in an error.
>>>>>
>>>>> So which inputs are valid to a halting decider? If it isn't ALL
>>>>> SYNTACTICALLY VALID PROGRAMS (AND INPUTS) WITH ABSOLUTELY NO
>>>>> EXCEPTIONS then you are not talking about the same thing that
>>>>> everyone else is talking about.
>>>>>
>>>>
>>>> *Of course I am not, they are all incorrect*
>>>
>>> OK so you haven't solved the halting problem at all. You think you've
>>> solved a different problem.
>> When Tarski "proved" that a consistent and correct True(L,x) predicate
>> cannot exist on the basis of his false assumption that the Liar Paradox
>> is a truth bearer his mistake must be corrected and the Liar Paradox
>> rejected as not a truth bearer.
>
> I haven't read Tarski's proof. Didn't he convert it to an arithmtic
> formula? Every arithmetic formula is a truth bearer.
>

He incorrectly proved that no True(L,x) predicate can possibly exist
because such a predicate cannot correctly determine whether the Liar
Paradox is true or false. He didn't seem to notice that it is neither.

He did seem to notice that the Liar Paradox applied to itself is true.
This sentence is not true: "This sentence is not true" is true.

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

On 1/12/24 11:19 AM, olcott wrote:
> On 1/12/2024 6:31 AM, Richard Damon wrote:
>> On 1/11/24 11:58 PM, olcott wrote:
>>> On 1/11/2024 10:11 PM, immibis wrote:
>>>> On 1/10/24 15:34, olcott wrote:
>>>>> On 1/10/2024 1:19 AM, immibis wrote:
>>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>> whether P(I) halts or not.
>>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>>> halt is wrong.
>>>>>> 6. Any algorithm that determines that a non-halting program halts
>>>>>> is wrong.
>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>>
>>>>>> Which one is refuted? Please specify which point 1 through 7 is
>>>>>> refuted. If you cannot specify, you are being dishonest.
>>>>>
>>>>>
>>>>> The above is the same as saying that every syntactically correct
>>>>
>>>> Which number 1-7?
>>>
>>> This was a very helpful insight in that placing the context of the
>>> question directly in the question is the clearest way to explain
>>> these things.
>>>
>>> On 1/6/2024 1:54 PM, immibis wrote:
>>>  > "Does the barber shave himself?" has a correct answer: it's one of
>>>  > "yes" or "no".
>>>  >
>>>  > "Does a barber who shaves every man who does not shave himself shave
>>>  > himself?" has no correct answer.
>>>
>>> *isomorphically*
>>>
>>> *The question posed by the HP*
>>> Does the direct execution of D(D) halt? Has a correct answer: it is yes.
>>>
>>> *The question posed to H by its counter-example input*
>>> What correct Boolean value does H return when D is defined to do the
>>> opposite of whatever value that H returns?" has no correct answer.
>>>
>>>
>>
>> So, you are admitting that the problem with YOUR question (what is the
>> correct answer that H can return) is impossible NOT because of the
>> Halting question itelf (like the do x shave itself question) buut in
>> the assumption that there can be a machine that decides Halting, just
>> like there can't be the Barber you are asking about.
>
> Just like no one can possibly correctly answer the question:
> "What time is it (yes or no)?"
> because the question itself <is> Incorrect.
>

DECEITFUL STRAMAN, indicating you have no basis for your claims.

You seem to think two things that you don't understand must be the same
thing even if they are different.

On 1/12/24 9:37 AM, olcott wrote:
> On 1/12/2024 1:05 AM, immibis wrote:
>> On 1/12/24 06:37, olcott wrote:
>>> On 1/11/2024 11:30 PM, immibis wrote:
>>>> On 1/12/24 05:58, olcott wrote:
>>>>> On 1/11/2024 10:11 PM, immibis wrote:
>>>>>> On 1/10/24 15:34, olcott wrote:
>>>>>>> On 1/10/2024 1:19 AM, immibis wrote:
>>>>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>>>> whether P(I) halts or not.
>>>>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>>>>> halt is wrong.
>>>>>>>> 6. Any algorithm that determines that a non-halting program
>>>>>>>> halts is wrong.
>>>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>>>>
>>>>>>>> Which one is refuted? Please specify which point 1 through 7 is
>>>>>>>> refuted. If you cannot specify, you are being dishonest.
>>>>>>>
>>>>>>>
>>>>>>> The above is the same as saying that every syntactically correct
>>>>>>
>>>>>> Which number 1-7?
>>>>>
>>>>> This was a very helpful insight in that placing the context of the
>>>>> question directly in the question is the clearest way to explain
>>>>> these things.
>>>>>
>>>>> On 1/6/2024 1:54 PM, immibis wrote:
>>>>>  > "Does the barber shave himself?" has a correct answer: it's one of
>>>>>  > "yes" or "no".
>>>>>  >
>>>>>  > "Does a barber who shaves every man who does not shave himself
>>>>> shave
>>>>>  > himself?" has no correct answer.
>>>>>
>>>>> *isomorphically*
>>>>>
>>>>> *The question posed by the HP*
>>>>> Does the direct execution of D(D) halt? Has a correct answer: it is
>>>>> yes.
>>>>>
>>>>> *The question posed to H by its counter-example input*
>>>>> What correct Boolean value does H return when D is defined to do
>>>>> the opposite of whatever value that H returns?" has no correct answer.
>>>>>
>>>>
>>>> Finally, Olcott has a breakthrough.
>>>>
>>>> Now consider points 2 and 3. Does D(D) halt?
>>> I already answered that, please reread the above.
>>>
>>
>> You didn't answer, so please answer now.
>>
>>  >>> *The question posed to H by its counter-example input*
>>  >>> What correct Boolean value does H return when D is defined to do the
>>  >>> opposite of whatever value that H returns?" has no correct answer.
>>
>> This is wrong. *The question posed to H by its counter-example input*
>> Does the direct execution of D(D) halt?
>
> If that was true then the question of the barber paradox would be:
> "Does the barber shave himself?" that has a correct answer of yes or no.

And it DOES if you specify an existing Barber.

It is only unanswerable when the Barber is defined by by conditions that
can not be satisifed.

Just like your H.

>
> ignoring the context that
> "the barber states that he shaves all who do not shave themselves."
> https://www.britannica.com/topic/barber-paradox

If it is just that the Barber STATES this condition, then the Barber is
know to exist, and is provn to be a liar, just like you.

>
> Since you are refuting your own reasoning this seems to prove that you
> are being disingenuous, stuck in rebuttal mode at the expense of truth.
>

No, you are just proving you are an ignorant hypocritical pathological
lying idiot that lives in a fantasy world of make beleive.

On 1/12/24 10:50 AM, olcott wrote:
> On 1/12/2024 1:04 AM, immibis wrote:
>> On 1/12/24 05:28, olcott wrote:
>>> On 1/11/2024 10:17 PM, immibis wrote:
>>>> On 1/10/24 19:49, Jeff Barnett wrote:
>>>>> On 1/10/2024 12:19 AM, immibis wrote:
>>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>> whether P(I) halts or not.
>>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>>> halt is wrong.
>>>>>> 6. Any algorithm that determines that a non-halting program halts
>>>>>> is wrong.
>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>
>>>>> Since you are have not defined "valid program", the above is fairly
>>>>> weak. For example, the idiot Olcott might say that "D(D)" isn't
>>>>> valid and you are right back down the crap hole.
>>>>
>>>> That's fine. If Olcott thinks that D is not a valid program, or D is
>>>> not a valid input for program D, he needs to say that.
>>>>
>>>>
>>>> Probably the best you can do
>>>>> along these lines is say that D - your decider - accepts as input
>>>>> any string D where P(S) is true and P is a decidable predicate.
>>>>
>>>> I repeat: THE INPUT TO A HALTING DECIDER IS ANY VALID PROGRAM (and
>>>> its input but it doesn't actually matter whether you allow input or
>>>> not) WITH ABSOLUTELY NO EXCEPTIONS.
>>>>
>>>
>>> If we apply that same reasoning to this syntactically correct question:
>>> What time is it (yes or no)?
>>>
>>> It becomes much more obvious that incorrect questions
>>> do not limit anyone or anything, they are just wrong.
>>>
>>
>> You can't even write a program that answers the question, so you can't
>> input the program to the halt decider. I repeat: ANY VALID PROGRAM.
>
> The Cyc project can write a computer program that understands that
> question in their CycL language.
>
> It is much easier to write the Liar Paradox in Prolog and see that
> Prolog rejects the Liar Paradox as semantically unsound.
>
> Tarski make the mistake of anchoring his whole Undecidability Proof
> in the semantically unsound Liar Paradox.
>

WHERE?

Exact line?

Your failure to answer is just your admission that you don't actually
understand his proof.

On 1/12/24 10:57 AM, olcott wrote:
> On 1/12/2024 1:11 AM, immibis wrote:
>> On 1/12/24 05:22, olcott wrote:
>>> On 1/11/2024 10:11 PM, immibis wrote:
>>>> On 1/10/24 15:34, olcott wrote:
>>>>> On 1/10/2024 1:19 AM, immibis wrote:
>>>>>> 1. Every P(I) either halts or doesn't halt. There is no in-between.
>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't halt.
>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>> whether P(I) halts or not.
>>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>>> halt is wrong.
>>>>>> 6. Any algorithm that determines that a non-halting program halts
>>>>>> is wrong.
>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>>
>>>>>> Which one is refuted? Please specify which point 1 through 7 is
>>>>>> refuted. If you cannot specify, you are being dishonest.
>>>>>
>>>>>
>>>>> The above is the same as saying that every syntactically correct
>>>>
>>>> Which number 1-7?
>>>
>>> 7 No one has every bothered to notice that self-contradictory inputs
>>> must be rejected as semantically unsound.
>>>
>>> Tarski never noticed that the Liar Paradox is not a truth bearer
>>> thus his Undefinability Theorem is anchored in an error.
>>>
>>
>> In the system that everyone uses, all formulas such as "∃x. x > 5" are
>> either true or false. It is impossible to write a formula that isn't
>> true or false.
>
> There were able to do this by adding the million-fold degree
> of purely extraneous complexity of Gödel numbers.
> G is neither true nor false in PA as Wittgenstein proves:
> https://www.liarparadox.org/Wittgenstein.pdf
> He calls G P and he calls PA Russel's System.
>
> Alternatively they could simply create a system of HOL that implements
> the ⊢ operator, then we can write G := ~(PA ⊢ G) which is rejected
> by Prolog as semantically unsound.
>

So, what was WRONG with any of the math that he did?

If you say that G is neither true or false, then I guess your logic
system can't handle basic mathematics or programs, because G is a simple
statement about an admittedly complicated, but computable relationship,
being that there exists no Natural Number that satisfies a particular
Primative Recursive Relationship (which is really nothing more than a
type of decider program that can be shown to ALWAYS give an answer in
finite time.

G needs none of the complexity of Godel Numbers to evaluate, just basic
mathematics and simple finitely nested finite loops.

All the complexity is to pull out the hidden meaning that is encoded in
G, which isn't actually available in the logic system that G is
expressed in.

You are rigth, we can not write the statement G := ~(PA ⊢ G) in PA, but
that isn't the statement that G is, only what can be proven with the
additional information in the meta-logic system.

So, your logic breaks as it tries to claim the proof says something it
doesn't say, because you just don't understand the logic of the systetem.

On 1/12/24 1:48 PM, olcott wrote:
> On 1/12/2024 10:36 AM, immibis wrote:
>> On 1/12/24 16:47, olcott wrote:
>>> On 1/12/2024 1:03 AM, immibis wrote:
>>>> On 1/12/24 06:39, olcott wrote:
>>>>> On 1/11/2024 11:33 PM, immibis wrote:
>>>>>> On 1/12/24 05:23, olcott wrote:
>>>>>>> On 1/11/2024 10:11 PM, immibis wrote:
>>>>>>>> On 1/10/24 15:21, olcott wrote:
>>>>>>>>> On 1/10/2024 3:10 AM, Mikko wrote:
>>>>>>>>>> On 2024-01-10 07:19:25 +0000, immibis said:
>>>>>>>>>>
>>>>>>>>>>> 1. Every P(I) either halts or doesn't halt. There is no
>>>>>>>>>>> in-between.
>>>>>>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't
>>>>>>>>>>> halt.
>>>>>>>>>>> 4. A halting decider is a program or algorithm that
>>>>>>>>>>> determines whether P(I) halts or not.
>>>>>>>>>>> 5. Any algorithm that determines that a halting program
>>>>>>>>>>> doesn't halt is wrong.
>>>>>>>>>>> 6. Any algorithm that determines that a non-halting program
>>>>>>>>>>> halts is wrong.
>>>>>>>>>>
>>>>>>>>>> Instead of "wrong" it would be better to say "not a halting
>>>>>>>>>> decider".
>>>>>>>>>>
>>>>>>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>>>>>>
>>>>>>>>>> The input should be syntactically correct. A syntax error
>>>>>>>>>> makes the
>>>>>>>>>> inut invalid. If there is a syntax error in the input the decider
>>>>>>>>>> should halt without answering "yes" or "no" (any other
>>>>>>>>>> behaviour is
>>>>>>>>>> hard to implement).
>>>>>>>>>>
>>>>>>>>>> Mikko
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> The above is the same as saying that every syntactically correct
>>>>>>>>> yes/no question has a correct answer.
>>>>>>>>
>>>>>>>> No, it isn't.
>>>>>>>> It's the same as saying that THE INPUT TO A HALTING DECIDER IS
>>>>>>>> ANY SYNTACTICALLY VALID PROGRAM AND INPUT WITH ABSOLUTELY NO
>>>>>>>> EXCEPTIONS.
>>>>>>>>
>>>>>>>> Do you refute this definition?
>>>>>>>
>>>>>>> Yes I do.
>>>>>>>
>>>>>>> Self-contradictory inputs must be rejected as semantically unsound.
>>>>>>>
>>>>>>> Tarski never noticed that the Liar Paradox is not a truth bearer
>>>>>>> thus his Undefinability Theorem is anchored in an error.
>>>>>>
>>>>>> So which inputs are valid to a halting decider? If it isn't ALL
>>>>>> SYNTACTICALLY VALID PROGRAMS (AND INPUTS) WITH ABSOLUTELY NO
>>>>>> EXCEPTIONS then you are not talking about the same thing that
>>>>>> everyone else is talking about.
>>>>>>
>>>>>
>>>>> *Of course I am not, they are all incorrect*
>>>>
>>>> OK so you haven't solved the halting problem at all. You think
>>>> you've solved a different problem.
>>> When Tarski "proved" that a consistent and correct True(L,x) predicate
>>> cannot exist on the basis of his false assumption that the Liar Paradox
>>> is a truth bearer his mistake must be corrected and the Liar Paradox
>>> rejected as not a truth bearer.
>>
>> I haven't read Tarski's proof. Didn't he convert it to an arithmtic
>> formula? Every arithmetic formula is a truth bearer.
>>
>
> He incorrectly proved that no True(L,x) predicate can possibly exist
> because such a predicate cannot correctly determine whether the Liar
> Paradox is true or false. He didn't seem to notice that it is neither.
>
> He did seem to notice that the Liar Paradox applied to itself is true.
> This sentence is not true: "This sentence is not true" is true.
>

WHERE did he do this. You have said this many times, but can't point to
the actual statement he did it in.

You Rre just proven to be a liar making untenable claims.

On 1/12/24 10:47 AM, olcott wrote:
> On 1/12/2024 1:03 AM, immibis wrote:
>> On 1/12/24 06:39, olcott wrote:
>>> On 1/11/2024 11:33 PM, immibis wrote:
>>>> On 1/12/24 05:23, olcott wrote:
>>>>> On 1/11/2024 10:11 PM, immibis wrote:
>>>>>> On 1/10/24 15:21, olcott wrote:
>>>>>>> On 1/10/2024 3:10 AM, Mikko wrote:
>>>>>>>> On 2024-01-10 07:19:25 +0000, immibis said:
>>>>>>>>
>>>>>>>>> 1. Every P(I) either halts or doesn't halt. There is no
>>>>>>>>> in-between.
>>>>>>>>> 2. P(I) halts iff the direct execution of P(I) halts.
>>>>>>>>> 3. P(I) doesn't halt iff the direct execution of P(I) doesn't
>>>>>>>>> halt.
>>>>>>>>> 4. A halting decider is a program or algorithm that determines
>>>>>>>>> whether P(I) halts or not.
>>>>>>>>> 5. Any algorithm that determines that a halting program doesn't
>>>>>>>>> halt is wrong.
>>>>>>>>> 6. Any algorithm that determines that a non-halting program
>>>>>>>>> halts is wrong.
>>>>>>>>
>>>>>>>> Instead of "wrong" it would be better to say "not a halting
>>>>>>>> decider".
>>>>>>>>
>>>>>>>>> 7. The input to a halting decider is ANY VALID PROGRAM WITH
>>>>>>>>> ABSOLUTELY NO EXCEPTIONS.
>>>>>>>>
>>>>>>>> The input should be syntactically correct. A syntax error makes the
>>>>>>>> inut invalid. If there is a syntax error in the input the decider
>>>>>>>> should halt without answering "yes" or "no" (any other behaviour is
>>>>>>>> hard to implement).
>>>>>>>>
>>>>>>>> Mikko
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> The above is the same as saying that every syntactically correct
>>>>>>> yes/no question has a correct answer.
>>>>>>
>>>>>> No, it isn't.
>>>>>> It's the same as saying that THE INPUT TO A HALTING DECIDER IS ANY
>>>>>> SYNTACTICALLY VALID PROGRAM AND INPUT WITH ABSOLUTELY NO EXCEPTIONS.
>>>>>>
>>>>>> Do you refute this definition?
>>>>>
>>>>> Yes I do.
>>>>>
>>>>> Self-contradictory inputs must be rejected as semantically unsound.
>>>>>
>>>>> Tarski never noticed that the Liar Paradox is not a truth bearer
>>>>> thus his Undefinability Theorem is anchored in an error.
>>>>
>>>> So which inputs are valid to a halting decider? If it isn't ALL
>>>> SYNTACTICALLY VALID PROGRAMS (AND INPUTS) WITH ABSOLUTELY NO
>>>> EXCEPTIONS then you are not talking about the same thing that
>>>> everyone else is talking about.
>>>>
>>>
>>> *Of course I am not, they are all incorrect*
>>
>> OK so you haven't solved the halting problem at all. You think you've
>> solved a different problem.
> When Tarski "proved" that a consistent and correct True(L,x) predicate
> cannot exist on the basis of his false assumption that the Liar Paradox
> is a truth bearer his mistake must be corrected and the Liar Paradox
> rejected as not a truth bearer.

Where does he assume the Liar Paradox is a Truth Bearer?

Exact line please, or you are just showing yourself to be a LIAR.

>
> A decider computes the mapping from its input finite string to an accept
> or reject state on the basis of a property of this input string.
>
> When the halting problem is defined to report on the behavior of the
> non-input direct execution of D(D) when deciders are defined as required
> to only report on the behavior of their inputs then the computer science
> of this is inconsistent and must be corrected.

WHy is the behavior of the program described by the input NOT a property
of that input?

That is part of the definition of a Semantic Property.

On 1/12/24 17:46, olcott wrote:
> On 1/12/2024 10:33 AM, immibis wrote:
>> On 1/12/24 15:37, olcott wrote:
>>>
>>> If that was true then the question of the barber paradox would be:
>>> "Does the barber shave himself?" that has a correct answer of yes or no.
>>
>> If that was false then the question of the halting paradox would be:
>> "When H correctly solves the halting problem, does the direct
>> execution of D(D) halt?"
>>
>
> I am simply using your own reasoning and putting the full context
> of the question that H is being asked directly into the question
> just like you did for the Barber Paradox.

No, you are putting the incorrect context in.

*The correct context is:*
"When H correctly solves the halting problem, does the direct execution
of D(D) halt?"

On 1/12/24 19:48, olcott wrote:
> He did seem to notice that the Liar Paradox applied to itself is true

HAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA

> This sentence is not true: "This sentence is not true" is true.