On 2021-08-06 09:59, olcott wrote:
> On 8/6/2021 8:09 AM, Richard Damon wrote:
>> On 8/6/21 6:56 AM, olcott wrote:
>>> On 8/6/2021 6:38 AM, Richard Damon wrote:
>>>> On 8/5/21 11:26 PM, olcott wrote:
>>>>> On 8/5/2021 10:25 PM, Richard Damon wrote:
>>>>>> On 8/5/21 8:55 PM, olcott wrote:
>>>>>>
>>>>>>> I don't refuse to respond to rebuttals. I refuse to respond to you.
>>>>>>>
>>>>>>> I also refuse to respond to dishonest dodges, changing the
>>>>>>> subject to
>>>>>>> avoid addressing the point at hand.
>>>>>>>
>>>>>>> As soon as I prove my point people change the subject.
>>>>>>> It is counter-productive for me to tolerate this.
>>>>>>>
>>>>>>> void P(u32 x)
>>>>>>> {
>>>>>>>      if (H(x, x))
>>>>>>>        HERE: goto HERE;
>>>>>>> }
>>>>>>>
>>>>>>> It took fifty exchanges for you to pay enough attention to
>>>>>>> acknowledge
>>>>>>> that int main(){ P(P); } never halts when we assume that H is only a
>>>>>>> pure simulator.
>>>>>>>
>>>>>>
>>>>>> No, you refuse to responde to rebuttals from me because I present
>>>>>> rebuttals so clear that you can't come up with an answer to them.
>>>>>>
>>>>>
>>>>> All of your "rebuttals" are entirely anchored in your inability to pay
>>>>> attention.
>>>>>
>>>>
>>>> FALSE.
>>>>
>>>> You lack of responses shows you don't understand any of the theory you
>>>> are talking about.
>>>>
>>>>>> What you call a 'dishonest dodge' is me pointing out that the Nth
>>>>>> time
>>>>>> you start an arguement, and are trying to misuse a terminology,
>>>>>> that I
>>>>>
>>>>> It does not freaking matter that I misuse terminology that is a
>>>>> freaking
>>>>> dishonest dodge. What matters is that my halt decider is correct.
>>>>>
>>>>
>>>> Only if you are misusing the word 'correct', or is it Halting.
>>>>
>>>> Misuse of terminology is Fundamentally wrong.
>>>
>>> I don't misuse those words. If I misuse terminology that it material to
>>> my proof then there is a problem.
>>
>> Yes, words like Turing Machine, or Halting, or Correct, or Equivalent,
>> or even Proof.
>>
>> You don't seem to really know what these are.
>>
>
> (1) Turing Machine, I use this term correctly no errors can be pointed out.

You've referred to C programs and to x86 programs as 'Turing Machines'.
That is definitely not correct usage/

> (2) Halting, I may have adapted the original definition, or not.
> According to André the final state of a computation must be reached for
> a computation to be considered as having halted.

Yes, but bear in mind that 'halting' refers to Turing Machines operating
on a specific input. It does not refer to simulations or what happens
inside a halting decider. It refers *only* to actual computations, i.e.
an actual Turing Machine operating on an actual input string.

> (3) Equivalent, I have adapted the original definition to apply to
> subsets of computations.

I have no idea what that's even supposed to mean.

> (4) Correct means that the condition of a conditional expression is
> satisfied.

Again, I have no idea what that's even supposed to mean.

> (5) Proof, here is what I mean by proof, it is an adaptation of the
> sound deductive inference model such that valid inference must only
> include true preserving operations.
>
> By proof I mean the application of truth preserving inference steps to
> premises that are known to be true. Since mathematical logic has some
> inference steps that are not truth preserving these are ruled out.
> https://en.wikipedia.org/wiki/Principle_of_explosion
> https://en.wikipedia.org/wiki/Paradoxes_of_material_implication
>
> Validity and Soundness
> A deductive argument is said to be valid if and only if it takes a form
> that makes it impossible for the premises to be true and the conclusion
> nevertheless to be false. Otherwise, a deductive argument is said to be
> invalid.
>
> A deductive argument is sound if and only if it is both valid, and all
> of its premises are actually true. Otherwise, a deductive argument is
> unsound. https://iep.utm.edu/val-snd/
>
> // original definition of valid  (same as P → C)
>
> Material conditional
> p   q p → q
> T   T   T
> T   F   F
> F   T   T
> F   F   T
>
> Transforming the above to become truth preserving:
>
> The definition of valid is changed to:
> p   q   p [PROVES] q
> T   T        T
> T   F        F
> F   T        F
> F   F        F

That is definitely *not* the definition of valid.

> A deductive argument is said to be valid if and only if it takes a form
> that the conclusion is only true if and only if the premises are true.
>
> All of the above is summed up as
> P [PROVES] C if and only if (True(P) ⊢ True(C) ∧ False(P) ⊢ False(C))

Again, that is definitely *not* the definition of a proof.

> modal operators are most often interpreted
> "□" for "Necessarily" and "◇" for "Possibly".
> https://en.wikipedia.org/wiki/Modal_logic
> (P [PROVES] C) ↔ (P ↔ □C)

Not only is that not the definition of proof, but your use of □ is
entirely meaningless above.

You do realise that □ conveys absolutely *no* information unless you
actually specify some sort of modal model? Unless you specify some set
of alternatives under consideration (i.e. a set of "possible worlds")
and some sort of accessibility relationship between those alternatives,
□ is completely uninterpretable.

Why do you insist on using symbols you don't understand?

> H(P,P)==0 is proven to be true on the basis that truth preserving
> operations are applied to premises that are verified as true: (P ↔ □C)

What are P and C in that example?

>>>
>>> If my misuse of terminology is immaterial to my proof then this is an
>>> side-issue that is irrelevant to my proof.
>>
>>
>>
>>>
>>> When people use irrelevant side-issues to avoid addressing the key point
>>> at hand this is a dishonest dodge.
>>
>>
>> Oh, and that is another word you misuse, 'dishonest'. It is NOT
>> dishonest to point out an error in an arguement, even if it isn't the
>> point you are trying to focus on as long as it does relate to the
>> problem at hand.
>>
>
> If an error is pointed out in the actual argument then this if valid.
> If an error is pointed that does not directly pertain to the argument
> then this is a dishonest dodge away from the point at hand.

*All* of the errors which have been pointed out to you have been errors
in the actual argument.

>> YOU use dishonest dodges to avoid having to try to deal with the
>> multitude of errors in your logic.
>>
>>>
>>>>
>>>> Glad you admit that.
>>>>
>>>> It shows you utter lack of knowledge in the field.
>>>>
>>>>
>>>
>>> It does not show an utter lack of knowledge in the field.
>>
>> Whht, like the fact that you totally don't understand what a Turing
>> Machine or a Computation is? Or Haltimg, or even what a Proof is.
>>
>> Not sure you really understand what is Truth.
>>
>>>
>>> It shows a lack of complete knowledge in the field that can effect my
>>> credibility. This lack has no effect on the validity of my proof that
>>> H(P,P)==0 is correct.
>>
>> Only that just about every statement in you 'proof' is invalid or
>> unsound.
>>
>> You don't seem to know enough to know how badly you are wrong.
>>
>>>
>>>>>> point out where you are going to in two steps change the meaning of a
>>>>>> word and still assume the arguement based on a different meaning
>>>>>> still
>>>>>> holds.
>>>>>>
>>>>>
>>>>> THIS IS THE ONLY FREAKING DETAIL THAT COUNTS.
>>>>> H(P,P)==0 is the correct halt status of the input to H.
>>>>> Everything that bypasses this point is a dishonest dodge.
>>>>
>>>> Ok, IF Halting is defined to be non-halting, then H(P,P) being
>>>> non-halting could be a correct answer in your world of inconsistent
>>>> logic.
>>>>
>>>
>>> Halting is defined as reaching the final state of the C function.
>>
>> Right, and when you run P(P) is does that.
>
> The Halting problem does not pertain to the behavior of P, it only
> pertains the behavior of the input to P.

This is absolutely, and categorically False. A halt decider is a program
which takes as its inputs a description of a Turing Machine, MD, and a
description of an input string, MI, and determines whether the actual
*machine* M described by MD halts when given the actual input string I
described by MI.

Talking about the behaviour of an input is entirely meaningless.

H(P, P) is supposed to tell us whether P(P) Halts. It is not supposed to
tell us whether the "input P" halts (whatever that is supposed to mean).
Only whether the actual turing machine described by its input halts on
the actual input string described by its input.

If H(P, P) == 0 and P(P) halts, then H(P, P) *by the very definition of
the problem* is giving the wrong answer.

>      the Turing machine halting problem. Simply stated, the problem
>      is: given the description of a Turing machine M and an input w,
>      does M, when started in the initial configuration q0w, perform a
>      computation that eventually halts? (Linz:1990:317).
>
>>>
>>> Not halting is defined as never reaching the final state of the function
>>> while H is in pure simulator mode. Not halting must be defined in terms
>>> of never reaching the final state of the function to distinguish it from
>>> functions that had their simulation aborted.
>>
>> WRONG. Not Halting is defined as never being able to reach the final
>> state of the function when fully run. The fact that a simulation doesn't
>> get there because the simulation was stopped before it happened to get
>> there proves nothing.
>>
>
> The Halting problem does not pertain to the behavior of P, it only
> pertains the behavior of the input to P.

Meaningless rubbish. Halting refers to the behaviour of actual
computations. I.e. actual turing machines operating on actual input
strings. Not to any "input". If you don't even know what the definition
of 'halting' or 'the halting problem' is, you shouldn't even be
discussing them.

>      the Turing machine halting problem. Simply stated, the problem
>      is: given the description of a Turing machine M and an input w,
>      does M, when started in the initial configuration q0w, perform a
>      computation that eventually halts? (Linz:1990:317).
>
> The input to H(P,P) does not reach its final state whether or not H ever
> aborts the simulation of this input.

The "input" to H(P, P) isn't even a computation. It is simply a pair of
strings. Strings neither halt nor don't halt. H(P, P) is supposed to be
answering a question about the *actual* computation P(P), which *does* halt.

> This is where you attention deficit disorder comes in. You can't seem to
> be able to pay attention to the steps that prove:

You don't appear to be paying attention to *any* of the errors which
have been repeatedly brought to your attention.

> the input to H(P,P) does not reach its final state whether or not H ever
> aborts the simulation of this input.

The "inout" to H is simply a set of strings. Strings don't halt. Strings
don't have final states. Strings can't be 'aborted'.

The simulation of a description of a Turing Machine and an input is
*not* the same computation as the actual Turing Machine applied to the
actual input string, and a halt decider is *defined* as something which
deals with the latter, not the former.

André

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