Re: ZFC solution to incorrect questions: reject them

On 3/14/24 12:32 PM, olcott wrote:

On 3/14/2024 12:33 PM, Richard Damon wrote:

On 3/13/24 4:04 PM, olcott wrote:

On 3/13/2024 5:43 PM, Richard Damon wrote:

On 3/13/24 2:54 PM, olcott wrote:

On 3/13/2024 4:39 PM, Richard Damon wrote:

On 3/13/24 1:52 PM, olcott wrote:

On 3/13/2024 12:52 PM, Richard Damon wrote:

On 3/13/24 10:08 AM, olcott wrote:

On 3/13/2024 11:44 AM, immibis wrote:

On 13/03/24 04:55, olcott wrote:

On 3/12/2024 10:49 PM, Richard Damon wrote:

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Not quite. It always gets the wrong answer, but only one of them for each quesiton.
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They all gets the wrong answer on a whole class of questions

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Wrong. You said. yourself. that H1 gets the right answer for D.
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Since it is a logical impossibility to determine the truth
value of a self-contradictory expression the requirement
for H to do this is bogus.

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Shows you are just a LIAR, as there IS a truth value to the expression that is the requirment for ANY SPECIFIC H.
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*Lying about me being a liar may possibly cost your soul*
*Lying about me being a liar may possibly cost your soul*
*Lying about me being a liar may possibly cost your soul*
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There is no mapping from H(D,D) to Halts(D,D) that exists.
This proves that H(D,D) is being asked an incorrect question.
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Why, because it is NOT a LIE.
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You don't even know the definiton of an incorrect question.
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I invented it so I get to stipulate its meaning.
https://groups.google.com/g/sci.lang/c/AO5Vlupeelo/m/nxJy7N2vULwJ

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Nope, common technical term.
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Cite a source.
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The fact that there DOES exist a mapping Halt(M,d) that maps all Turing Machines and there input to a result of Halting / Non-Halting for EVERY member of that input set, means tha Halts is a valid mapping to ask a decider to try to decider.
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That part is true.
Likewise when you ask a man that has never been married:
Have you stopped beating tour wife?
There are some men that have stopped beating their wife.

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Right, because that question include a presumption of something not actually present.
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Although there is a mapping from some men to YES/NO
there is no mapping from never unmarried men to YES/NO
thus the question is incorrect for all unmarried men.
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Although there is a mapping from some TM/input pairs to YES/NO
there is no mapping from H/D to YES/NO
thus the question is incorrect for H/D
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Except that the mapping requested is about the INPUTS to H, not H itsef.
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 In order to see that it is an incorrect question we must examine
the question in detail. Making sure to always ignore this key detail
<is> cheating.
 Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ does not halt
∀Ĥ.H (Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ != Halts(⟨Ĥ⟩, ⟨Ĥ⟩))

Which isn;t the question at all, so you are just shown to be a stupid liar.
The QUESTION is:
Does the machine and input described by this input, Halt when run?
That is the question, and exactly the question.
THis question produces a mapping of M, d -> HALTS(M,d) where Halts it True if the machine M applied to the input d will Halt, and false otherwise.
When then get to the PROBLEM (which is different then the QUESTION), can we produce a Turing Machine to compute this.
 From the definition of the Question, we can derive the REQUIREMENT for a Turing Machine H that satisfies the problem, that would be that:
For ALL <M> and d, H <M> d |-> Qy if M d will halt, and |-> Qn if it will not
There is NOTHING in this, so far, that has mention H^ at all.
H^ is just a sample input that we can TEST H with
H^ isn't a "decider" and doesn't have "requirements" that it must met, (except that it is a Turing Machine and does what it is programmed to do).
Thus arguing from REQUIREMENT on H^ are incorrect.
Note, for any specific test, H^ is a SPECIFIC machine built from a specific decider to test it, other decider can of course try to decide it, but their results are not meaningful for the proof.
Linz shows (copying from the earlier work of Turing) that no matter what H you try to choose, and no matter how it tries to come to its decision, NO H can give the correct answer for the H^ built on it.
This doesn't mean the Question was invalid, as for EVERY instance of the question (a seperate one for each decider H that we start with), the machine H^ <H^> always has definite behavior, we have the mapping from
H^ <H^> -> Halts(H^ <H^> exists, so the orignal question is still valid.
YOU keep on trying to change the question to a DIFFERENT question, about the behavior of the NON-TURING MACHINE "template", which never was an allowable input in the halting problem, as no Turing Machine can know about if or what nachine is trying to decide on it (like the ^ template become in you case).
So, you are just showing that you have FUNDAMENTAL misconception about how Computation Theory works, which means you have a lot of work to try to come up with a "replacement" of convincing people of the need for one.

 

THERE IS a mapping from ALL inputs to H(<M>,d) to a corrct Yes/No answer as determined by Halts(M,d), or in this specific case the inputs to H(D,D) to Halts (D,D).
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If H(D,D) returns 0, then the Mapping of the input D,D to Halts(D,D) is to Yes.
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If H(D,D) returns 1, then the Mapping of the input D,D to Halts(D,D) is No.
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So, the mapping asked for in the ACTUAL question exist.
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That H(D,D) doesn't give the right answer just shows that H is wrong for the input.
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The fact that there exists a D for every H such that it will get the answer wrong proves the Mapping described in the Halting Problem is uncomputable, not "invalid" (the fact that it actually exists, makes it valid).