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Re: On recursion and infinite recursion (reprise)
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olcott
May 3, 2022, 11:19:33 AM5/3/22
to
On 5/3/2022 9:47 AM, Dennis Bush wrote:
> On Tuesday, May 3, 2022 at 10:31:21 AM UTC-4, olcott wrote:
>> On 5/3/2022 7:12 AM, wij wij wrote:
>>> Richard Damon 在 2022年5月3日 星期二上午8:48:57 [UTC+8] 的信中寫道：
>>>> On 5/2/22 8:35 PM, olcott wrote:
>>>>> On 5/2/2022 5:47 PM, Mr Flibble wrote:
>>>>>> On Mon, 2 May 2022 18:46:00 -0400
>>>>>> Richard Damon wrote:
>>>>>>
>>>>>>> On 5/2/22 6:38 PM, Mr Flibble wrote:
>>>>>>>> On Mon, 2 May 2022 18:32:16 -0400
>>>>>>>> Richard Damon wrote:
>>>>>>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
>>>>>>>>>> Not all infinitely recursive definitions are invalid however
>>>>>>>>>> infinitely recursive definitions that arise out of a category
>>>>>>>>>> error (as is the case with the halting problem) are invalid.
>>>>>>>>>>
>>>>>>>>>> The halting problem (as currently defined) is invalid due to the
>>>>>>>>>> invalid "impossible program" [Strachey, 1965] that is actually
>>>>>>>>>> impossible due to the category error present in its definition and
>>>>>>>>>> *not* because of any function call-like recursion; confusion
>>>>>>>>>> between these two types of recursion are why Olcott is having
>>>>>>>>>> difficulty communicating his ideas with the rest of you shower.
>>>>>>>>>>
>>>>>>>>>> The categories involved in the category error are the decider and
>>>>>>>>>> that which is being decided. Currently extant attempts to
>>>>>>>>>> conflate the decider with that which is being decided are
>>>>>>>>>> infinitely recursive and thus invalid.
>>>>>>>>>>
>>>>>>>>>> /Flibble
>>>>>>>>>
>>>>>>>>> Except that the "impossible program" isn't part of the definition
>>>>>>>>> of the Halting Problem.
>>>>>>>>
>>>>>>>> It is according to [Wikipedia, 2022].
>>>>>>>>
>>>>>>>> /Flibble
>>>>>>>
>>>>>>> Nope, you comprehend worse that PO.
>>>>>>>
>>>>>>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
>>>>>>> definition but a full article explaining the subject.
>>>>>>>
>>>>>>> Maybe if you look for a FORMAL source, that states what is the ACTUAL
>>>>>>> definition, you would learn something.
>>>>>>
>>>>>> If Wikipedia is wrong then correct it and have your corrections
>>>>>> reviewed; until then please shut the fuck up.
>>>>>>
>>>>>> /Flibble
>>>>>>
>>>>>
>>>>> I think that the problem is that Richard has disagreeably as his highest
>>>>> priority, thus doesn't really give a rat's ass for the truth. An
>>>>>
>>>>> An impossible program C. Strachey
>>>>> The Computer Journal, Volume 7, Issue 4, January 1965, Page 313,
>>>>> Published: 01 January 1965
>>>>> https://academic.oup.com/comjnl/article/7/4/313/354243
>>>>>
>>>>> It is very common knowledge that the Wikipedia description is true and
>>>>> this is affirmed in Sipser.
>>>>>
>>>>> For any program f that might determine if programs halt, a
>>>>> "pathological" program g, called with some input, can pass its own
>>>>> source and its input to f and then specifically do the opposite of what
>>>>> f predicts g will do. https://en.wikipedia.org/wiki/Halting_problem
>>>>>
>>>>> Now we construct a new Turing machine D with H as a subroutine. This new
>>>>> TM calls H to determine what M does when the input to M is its own
>>>>> description ⟨M⟩. Once D has determined this information, it does the
>>>>> opposite. https://www.liarparadox.org/Sipser_165_167.pdf
>>>>>
>>>>>
>>>> Thus you have shown you don't even know what a "Definition" is, so it is
>>>> impossible for you to reason by the meaning of the words.
>>>>
>>>> You have just proved yourself to be an IDIOT.
>>>
>>> PO is incapable of logic reasoning (PO had shown he cannot even get the truth
>>> table of logical implication/AND right). All he said is delusion including when
>>> words from him happen to be correct to others (no real meaning).
>>>
>>> IIRC, PO's revision that H(P,P) has no relation with P(P) is deliberately
>>> fabricated this recent year after PO ran out his reasons to explain why HP is
>>> wrong and he is correct. PO has no trouble to 'lie' to his bible (he can read
>>> it his way), the HP thing is just piece of cake.
>> It is an easily verified fact that P(P) and the correct simulation of
>> the input to H(P,P) specify different sequences of configurations, thus
>> have different halting behavior.
>
> The easily verified fact is that the correct simulation to H(P,P) is performed by Hb(P,P) (which simulates for k more steps than H) which remains in UTM mode while simulating the same input to a final state.
>
I have no idea what you mean.
> Because H and Hb and both simulating halt deciders and are given the same input, they are deciding on the same sequence of configurations (namely starting with the first instruction of P). Because one answers false and one answers true, one must be wrong.
>
It is ridiculously stupid to assume that an input having pathological
self-reference to its decider would have the same behavior as an input
NOT having pathological to its decider.
> Since a simulating halt decider that simulates its input to a final state while remaining in UTM mode is necessarily correct, this proves that Hb(P,P) == true is correct and that H(P,P) == false is incorrect, and that H(P,P) does *not* in fact perform a correct simulation of its input because it aborts too soon.
>
It is very easy to verify the fact that the simulated input to H(P,P)
would never stop unless aborted. It is pretty psychotic that many of my
reviewers deny easily verified facts.
> You've been asked several times what input must be given to H to determine if P(P) halts. It turns out that the input (P,P) can be given to Hb to determine exactly that, so the fact that H can't give the same result for the same input just shows that it is wrong and that the halting problem is unsolvable as the existing proofs show.
>
It is ridiculously stupid to assume that an input having pathological
self-reference to its decider would have the same behavior as an input
NOT having pathological to its decider.
It is an easily verified fact that H does correctly reject its input and
that deciders only compute the mapping from their inputs.
>> That several people here deny easily
>> verified facts is a little psychotic on their part.
>
> You're projecting. Again. In fact you're *so* good a projecting that if you opened a movie theater I'll bet the picture quality would be second to none.
Anyone that denies easily verified facts has (by definition) a break
from reality.
--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer
> On Tuesday, May 3, 2022 at 10:31:21 AM UTC-4, olcott wrote:
>> On 5/3/2022 7:12 AM, wij wij wrote:
>>> Richard Damon 在 2022年5月3日 星期二上午8:48:57 [UTC+8] 的信中寫道：
>>>> On 5/2/22 8:35 PM, olcott wrote:
>>>>> On 5/2/2022 5:47 PM, Mr Flibble wrote:
>>>>>> On Mon, 2 May 2022 18:46:00 -0400
>>>>>> Richard Damon wrote:
>>>>>>
>>>>>>> On 5/2/22 6:38 PM, Mr Flibble wrote:
>>>>>>>> On Mon, 2 May 2022 18:32:16 -0400
>>>>>>>> Richard Damon wrote:
>>>>>>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
>>>>>>>>>> Not all infinitely recursive definitions are invalid however
>>>>>>>>>> infinitely recursive definitions that arise out of a category
>>>>>>>>>> error (as is the case with the halting problem) are invalid.
>>>>>>>>>>
>>>>>>>>>> The halting problem (as currently defined) is invalid due to the
>>>>>>>>>> invalid "impossible program" [Strachey, 1965] that is actually
>>>>>>>>>> impossible due to the category error present in its definition and
>>>>>>>>>> *not* because of any function call-like recursion; confusion
>>>>>>>>>> between these two types of recursion are why Olcott is having
>>>>>>>>>> difficulty communicating his ideas with the rest of you shower.
>>>>>>>>>>
>>>>>>>>>> The categories involved in the category error are the decider and
>>>>>>>>>> that which is being decided. Currently extant attempts to
>>>>>>>>>> conflate the decider with that which is being decided are
>>>>>>>>>> infinitely recursive and thus invalid.
>>>>>>>>>>
>>>>>>>>>> /Flibble
>>>>>>>>>
>>>>>>>>> Except that the "impossible program" isn't part of the definition
>>>>>>>>> of the Halting Problem.
>>>>>>>>
>>>>>>>> It is according to [Wikipedia, 2022].
>>>>>>>>
>>>>>>>> /Flibble
>>>>>>>
>>>>>>> Nope, you comprehend worse that PO.
>>>>>>>
>>>>>>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
>>>>>>> definition but a full article explaining the subject.
>>>>>>>
>>>>>>> Maybe if you look for a FORMAL source, that states what is the ACTUAL
>>>>>>> definition, you would learn something.
>>>>>>
>>>>>> If Wikipedia is wrong then correct it and have your corrections
>>>>>> reviewed; until then please shut the fuck up.
>>>>>>
>>>>>> /Flibble
>>>>>>
>>>>>
>>>>> I think that the problem is that Richard has disagreeably as his highest
>>>>> priority, thus doesn't really give a rat's ass for the truth. An
>>>>>
>>>>> An impossible program C. Strachey
>>>>> The Computer Journal, Volume 7, Issue 4, January 1965, Page 313,
>>>>> Published: 01 January 1965
>>>>> https://academic.oup.com/comjnl/article/7/4/313/354243
>>>>>
>>>>> It is very common knowledge that the Wikipedia description is true and
>>>>> this is affirmed in Sipser.
>>>>>
>>>>> For any program f that might determine if programs halt, a
>>>>> "pathological" program g, called with some input, can pass its own
>>>>> source and its input to f and then specifically do the opposite of what
>>>>> f predicts g will do. https://en.wikipedia.org/wiki/Halting_problem
>>>>>
>>>>> Now we construct a new Turing machine D with H as a subroutine. This new
>>>>> TM calls H to determine what M does when the input to M is its own
>>>>> description ⟨M⟩. Once D has determined this information, it does the
>>>>> opposite. https://www.liarparadox.org/Sipser_165_167.pdf
>>>>>
>>>>>
>>>> Thus you have shown you don't even know what a "Definition" is, so it is
>>>> impossible for you to reason by the meaning of the words.
>>>>
>>>> You have just proved yourself to be an IDIOT.
>>>
>>> PO is incapable of logic reasoning (PO had shown he cannot even get the truth
>>> table of logical implication/AND right). All he said is delusion including when
>>> words from him happen to be correct to others (no real meaning).
>>>
>>> IIRC, PO's revision that H(P,P) has no relation with P(P) is deliberately
>>> fabricated this recent year after PO ran out his reasons to explain why HP is
>>> wrong and he is correct. PO has no trouble to 'lie' to his bible (he can read
>>> it his way), the HP thing is just piece of cake.
>> It is an easily verified fact that P(P) and the correct simulation of
>> the input to H(P,P) specify different sequences of configurations, thus
>> have different halting behavior.
>
> The easily verified fact is that the correct simulation to H(P,P) is performed by Hb(P,P) (which simulates for k more steps than H) which remains in UTM mode while simulating the same input to a final state.
>
I have no idea what you mean.
> Because H and Hb and both simulating halt deciders and are given the same input, they are deciding on the same sequence of configurations (namely starting with the first instruction of P). Because one answers false and one answers true, one must be wrong.
>
It is ridiculously stupid to assume that an input having pathological
self-reference to its decider would have the same behavior as an input
NOT having pathological to its decider.
> Since a simulating halt decider that simulates its input to a final state while remaining in UTM mode is necessarily correct, this proves that Hb(P,P) == true is correct and that H(P,P) == false is incorrect, and that H(P,P) does *not* in fact perform a correct simulation of its input because it aborts too soon.
>
It is very easy to verify the fact that the simulated input to H(P,P)
would never stop unless aborted. It is pretty psychotic that many of my
reviewers deny easily verified facts.
> You've been asked several times what input must be given to H to determine if P(P) halts. It turns out that the input (P,P) can be given to Hb to determine exactly that, so the fact that H can't give the same result for the same input just shows that it is wrong and that the halting problem is unsolvable as the existing proofs show.
>
It is ridiculously stupid to assume that an input having pathological
self-reference to its decider would have the same behavior as an input
NOT having pathological to its decider.
It is an easily verified fact that H does correctly reject its input and
that deciders only compute the mapping from their inputs.
>> That several people here deny easily
>> verified facts is a little psychotic on their part.
>
> You're projecting. Again. In fact you're *so* good a projecting that if you opened a movie theater I'll bet the picture quality would be second to none.
Anyone that denies easily verified facts has (by definition) a break
from reality.
--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer
olcott
May 3, 2022, 12:39:48 PM5/3/22
to
On 5/3/2022 10:36 AM, Dennis Bush wrote:
> In other words you don't want to admit that this proves you are wrong.
>
No I can't understand what you mean.
I think that I see it now, I had forgotten the notation.
An input having a pathological self-reference relationship to its
decider H would necessarily derive a different halt status than an input
not having a pathological self-reference relationship to its decider Hb.
The P having a pathological self-reference relationship to H is not the
same as the Px NOT having a pathological self-reference relationship to
Hb. Because P.H calls itself and Px.Hb does not call itself P is not the
same input as Px.
>
>>> Because H and Hb and both simulating halt deciders and are given the same input, they are deciding on the same sequence of configurations (namely starting with the first instruction of P). Because one answers false and one answers true, one must be wrong.
>>>
>> It is ridiculously stupid to assume that an input having pathological
>> self-reference to its decider would have the same behavior as an input
>> NOT having pathological to its decider.
>
> Which is another way of saying that H can't give a correct answer for (P,P).
>
Different computations must give different answers.
That you don't fully understand all of the nuances of how this applies
to H/P and Hb/Px is OK, it is difficult to understand.
>>> Since a simulating halt decider that simulates its input to a final state while remaining in UTM mode is necessarily correct, this proves that Hb(P,P) == true is correct and that H(P,P) == false is incorrect, and that H(P,P) does *not* in fact perform a correct simulation of its input because it aborts too soon.
>>>
>> It is very easy to verify the fact that the simulated input to H(P,P)
>> would never stop unless aborted. It is pretty psychotic that many of my
>> reviewers deny easily verified facts.
>
> There is no "unless". The fixed algorithm of H, which will henceforth be referred to as Ha and similarly P will be referred to as Pa, *does* abort.
Which is *NOT* halting. A halting input must reach its own final state.
> Because of this, Hb(Pa,Pa) explicitly shows that the simulated input to Ha(Pa,Pa) *does* stop. The fact that Pn(Pn) does not halt and that Hn(Pn,Pn) does not halt is irrelevant.
It it not Hb(Pa,Pa) it is Hb(Px,Px). That P calls H makes it an entirely
different input than Px that does not call Hb.
>>> You've been asked several times what input must be given to H to determine if P(P) halts. It turns out that the input (P,P) can be given to Hb to determine exactly that, so the fact that H can't give the same result for the same input just shows that it is wrong and that the halting problem is unsolvable as the existing proofs show.
>>>
>> It is ridiculously stupid to assume that an input having pathological
>> self-reference to its decider would have the same behavior as an input
>> NOT having pathological to its decider.
>
> Which is another way of saying that Ha can't give a correct answer for (Pa,Pa).
That P calls H makes it an entirely different input than Px that does
not call Hb.
>
>> and that deciders only compute the mapping from their inputs.
>
> And all halt deciders must compute the same mapping from the same input. Ha(Pa,Pa) and Hb(Pa,Pa) do not perform the same mapping from the same input so one must be wrong.
>
That P calls H makes it an entirely different input than Px that does
not call Hb.
> Since a simulating halt decider that simulates its input to a final state while remaining in UTM mode is necessarily correct, this proves that Hb(Pa,Pa) == true is correct and that Ha(Pa,Pa) == false is incorrect
That P calls H makes it an entirely different input than Px that does
not call Hb.
>
>>>> That several people here deny easily
>>>> verified facts is a little psychotic on their part.
>>>
>>> You're projecting. Again. In fact you're *so* good a projecting that if you opened a movie theater I'll bet the picture quality would be second to none.
>> Anyone that denies easily verified facts has (by definition) a break
>> from reality.
>
> I can't *wait* to see your movie theater. Such a expert at projection must have a great picture.
>
No I can't understand what you mean.
I think that I see it now, I had forgotten the notation.
An input having a pathological self-reference relationship to its
decider H would necessarily derive a different halt status than an input
not having a pathological self-reference relationship to its decider Hb.
The P having a pathological self-reference relationship to H is not the
same as the Px NOT having a pathological self-reference relationship to
Hb. Because P.H calls itself and Px.Hb does not call itself P is not the
same input as Px.
>
>>> Because H and Hb and both simulating halt deciders and are given the same input, they are deciding on the same sequence of configurations (namely starting with the first instruction of P). Because one answers false and one answers true, one must be wrong.
>>>
>> It is ridiculously stupid to assume that an input having pathological
>> self-reference to its decider would have the same behavior as an input
>> NOT having pathological to its decider.
>
>
Different computations must give different answers.
That you don't fully understand all of the nuances of how this applies
to H/P and Hb/Px is OK, it is difficult to understand.
>>> Since a simulating halt decider that simulates its input to a final state while remaining in UTM mode is necessarily correct, this proves that Hb(P,P) == true is correct and that H(P,P) == false is incorrect, and that H(P,P) does *not* in fact perform a correct simulation of its input because it aborts too soon.
>>>
>> It is very easy to verify the fact that the simulated input to H(P,P)
>> would never stop unless aborted. It is pretty psychotic that many of my
>> reviewers deny easily verified facts.
>
Which is *NOT* halting. A halting input must reach its own final state.
> Because of this, Hb(Pa,Pa) explicitly shows that the simulated input to Ha(Pa,Pa) *does* stop. The fact that Pn(Pn) does not halt and that Hn(Pn,Pn) does not halt is irrelevant.
It it not Hb(Pa,Pa) it is Hb(Px,Px). That P calls H makes it an entirely
different input than Px that does not call Hb.
>>> You've been asked several times what input must be given to H to determine if P(P) halts. It turns out that the input (P,P) can be given to Hb to determine exactly that, so the fact that H can't give the same result for the same input just shows that it is wrong and that the halting problem is unsolvable as the existing proofs show.
>>>
>> It is ridiculously stupid to assume that an input having pathological
>> self-reference to its decider would have the same behavior as an input
>> NOT having pathological to its decider.
>
>
>>
>> It is an easily verified fact that H does correctly reject its input
>
> Ha does not correctly reject its input as easily verified by Hb.
>>
>> It is an easily verified fact that H does correctly reject its input
>
That P calls H makes it an entirely different input than Px that does
not call Hb.
>
>> and that deciders only compute the mapping from their inputs.
>
>
That P calls H makes it an entirely different input than Px that does
not call Hb.
> Since a simulating halt decider that simulates its input to a final state while remaining in UTM mode is necessarily correct, this proves that Hb(Pa,Pa) == true is correct and that Ha(Pa,Pa) == false is incorrect
That P calls H makes it an entirely different input than Px that does
not call Hb.
>
>>>> That several people here deny easily
>>>> verified facts is a little psychotic on their part.
>>>
>>> You're projecting. Again. In fact you're *so* good a projecting that if you opened a movie theater I'll bet the picture quality would be second to none.
>> Anyone that denies easily verified facts has (by definition) a break
>> from reality.
>
olcott
May 3, 2022, 2:06:28 PM5/3/22
to
On 5/3/2022 12:17 PM, Mikko wrote:
> On 2022-05-03 14:38:57 +0000, olcott said:
>
>> On 5/3/2022 4:36 AM, Mikko wrote:
>>> On 2022-05-02 16:18:36 +0000, olcott said:
>>>
>>>> It seems to me that all infinitely recursive definitions are invalid
>>>> and I am having an excellent dialogue with some Prolog folks about
>>>> this in comp.lang.prolog.
>>>
>>> One of the rules that define Prolog language is
>>>
>>> arguments ::= argument | argument "," arguments
>>>
>>> which is infinitely recursive. Is it invalid? Is Prolog invalid because
>>> of this and other infinitely recursive rules?
>>>
>>> Mikko
>>>
>>
>> If would have to be invalid because it can never be resolved.
>
> What would be invalid? Prolog? Definition of Prolog?
> Why "would be" and not "is"?
>
> Mikko
>
Expressions that cannot be resolved in Prolog that fail the
unify_with_occurs_check test proves that these expressions are
semantically incorrect.
It is generally the case that every expression of any natural of formal
language that cannot be derived by applying truth preserving operations
(such as Prolog rules) to expressions known to be true (such as Prolog
facts) cannot possibly be correctly construed as true.
Dogs are animals (purely analytic)
There is a small dog in my living room right now (Empirical).
This is true for the entire body of analytic knowledge which only
excludes expressions of language that rely on sense data from the sense
organs to verify truth.
The proof that this is correct is that no counter-examples exist.
When G is considered true and unprovable there is some way the "true" is
derived, it is not merely a wild guess.
Just like Prolog databases True is limited to a specific formal system,
one formal system is the entire body of analytic knowledge: EBAK. This
is an entirely different formal system than PA.
unprovable in PA and true in EBAC is not the same thing as true and
unprovable. unprovable in PA means not true in PA, and true in EBAC
means provable in EBAC.
> On 2022-05-03 14:38:57 +0000, olcott said:
>
>> On 5/3/2022 4:36 AM, Mikko wrote:
>>> On 2022-05-02 16:18:36 +0000, olcott said:
>>>
>>>> It seems to me that all infinitely recursive definitions are invalid
>>>> and I am having an excellent dialogue with some Prolog folks about
>>>> this in comp.lang.prolog.
>>>
>>> One of the rules that define Prolog language is
>>>
>>> arguments ::= argument | argument "," arguments
>>>
>>> which is infinitely recursive. Is it invalid? Is Prolog invalid because
>>> of this and other infinitely recursive rules?
>>>
>>> Mikko
>>>
>>
>> If would have to be invalid because it can never be resolved.
>
> What would be invalid? Prolog? Definition of Prolog?
> Why "would be" and not "is"?
>
> Mikko
>
Expressions that cannot be resolved in Prolog that fail the
unify_with_occurs_check test proves that these expressions are
semantically incorrect.
It is generally the case that every expression of any natural of formal
language that cannot be derived by applying truth preserving operations
(such as Prolog rules) to expressions known to be true (such as Prolog
facts) cannot possibly be correctly construed as true.
Dogs are animals (purely analytic)
There is a small dog in my living room right now (Empirical).
This is true for the entire body of analytic knowledge which only
excludes expressions of language that rely on sense data from the sense
organs to verify truth.
The proof that this is correct is that no counter-examples exist.
When G is considered true and unprovable there is some way the "true" is
derived, it is not merely a wild guess.
Just like Prolog databases True is limited to a specific formal system,
one formal system is the entire body of analytic knowledge: EBAK. This
is an entirely different formal system than PA.
unprovable in PA and true in EBAC is not the same thing as true and
unprovable. unprovable in PA means not true in PA, and true in EBAC
means provable in EBAC.
olcott
May 3, 2022, 2:13:09 PM5/3/22
to
On 5/3/2022 12:27 PM, Mikko wrote:
> On 2022-05-03 14:42:32 +0000, olcott said:
>
>> On 5/3/2022 4:31 AM, Mikko wrote:
>>> recursion
>>> stops at the category error.
>>>
>>> Mikko
>>>
>>
>> The category error is that an expression of language X is construed as
>> a logic sentence / truth bearer that is true or false. It is because
>> of the infinitely recursive definition that X is neither of these.
>
> Only if the recursive expression is used as if it were a truth bearer.
> Definitions usually don't use expression that way.
>
> Mikko
>
Expressions of language can only be correctly construed as true:
(a) if they are defined to be true
(b) have no contradictory elements in (a)
(c) are derived by applying true preserving operations to (a) or (c)
> On 2022-05-03 14:42:32 +0000, olcott said:
>
>> On 5/3/2022 4:31 AM, Mikko wrote:
>>> On 2022-05-02 15:47:32 +0000, Mr Flibble said:
>>>
>>>> Not all infinitely recursive definitions are invalid however infinitely
>>>> recursive definitions that arise out of a category error (as is the
>>>> case with the halting problem) are invalid.
>>>
>>> An infinite recursion cannot arise out of a category error as the
>>>
>>>> Not all infinitely recursive definitions are invalid however infinitely
>>>> recursive definitions that arise out of a category error (as is the
>>>> case with the halting problem) are invalid.
>>>
>>> recursion
>>> stops at the category error.
>>>
>>> Mikko
>>>
>>
>> The category error is that an expression of language X is construed as
>> a logic sentence / truth bearer that is true or false. It is because
>> of the infinitely recursive definition that X is neither of these.
>
> Only if the recursive expression is used as if it were a truth bearer.
> Definitions usually don't use expression that way.
>
> Mikko
>
Expressions of language can only be correctly construed as true:
(a) if they are defined to be true
(b) have no contradictory elements in (a)
(c) are derived by applying true preserving operations to (a) or (c)
olcott
May 3, 2022, 6:08:32 PM5/3/22
to
On 5/3/2022 4:49 PM, Dennis Bush wrote:
> The P we're talking about is a *specific* P, namely Pa which is built from Ha, and Ha is a *specific* H. So Pa and Px are the *same*.
Not at all because H(P,P) has itself as part of its input and Hb(P,P)
does not have itself as part of its input.
>
> So just because Pa contains an embedded copy of Ha but not an embedded copy of Hb doesn't means that it's not the same.
>
Sure it does. The correctly simulated input to H(P,P) specifies
infinitely nested simulation where as correctly simulated input to
Hb(P,P) DOES NOT specify infinitely nested simulation.
How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.
> Ha(Pa,Pa) and Hb(Pa,Pa) have the *exact* same input.
>
The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested
simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT
specify infinitely nested simulation.
How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.
> Just because it appears from a glance that Ha is starting its simulation of Pa "in the middle" doesn't mean that's what's actually happening. That's just how the incorrect simulation is manifesting itself. It's kind of like undefined behavior in a C program.
You only have to do a correct execution trace of Ha(Pa,Pa) and Hb(Pa,Pa)
to see that:
The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested
simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT
specify infinitely nested simulation.
How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.
>>>
>>>>> Because H and Hb and both simulating halt deciders and are given the same input, they are deciding on the same sequence of configurations (namely starting with the first instruction of P). Because one answers false and one answers true, one must be wrong.
>>>>>
>>>> It is ridiculously stupid to assume that an input having pathological
>>>> self-reference to its decider would have the same behavior as an input
>>>> NOT having pathological to its decider.
>>>
>>> Which is another way of saying that H can't give a correct answer for (P,P).
>>>
>> Different computations must give different answers.
>> That you don't fully understand all of the nuances of how this applies
>> to H/P and Hb/Px is OK, it is difficult to understand.
>
> Just because Pa contains an embedded copy of Ha but not an embedded copy of Hb doesn't means that it's not the same.
You only have to do a correct execution trace of Ha(Pa,Pa) and Hb(Pa,Pa)
to see that:
The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested
simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT
specify infinitely nested simulation.
How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.
>>>>> Since a simulating halt decider that simulates its input to a final state while remaining in UTM mode is necessarily correct, this proves that Hb(P,P) == true is correct and that H(P,P) == false is incorrect, and that H(P,P) does *not* in fact perform a correct simulation of its input because it aborts too soon.
>>>>>
>>>> It is very easy to verify the fact that the simulated input to H(P,P)
>>>> would never stop unless aborted. It is pretty psychotic that many of my
>>>> reviewers deny easily verified facts.
>>>
>>> There is no "unless". The fixed algorithm of H, which will henceforth be referred to as Ha and similarly P will be referred to as Pa, *does* abort.
>> Which is *NOT* halting. A halting input must reach its own final state.
>>> Because of this, Hb(Pa,Pa) explicitly shows that the simulated input to Ha(Pa,Pa) *does* stop. The fact that Pn(Pn) does not halt and that Hn(Pn,Pn) does not halt is irrelevant.
>> It it not Hb(Pa,Pa) it is Hb(Px,Px). That P calls H makes it an entirely
>> different input than Px that does not call Hb.
>
> No it is *exactly* Hb(Pa,Pa). The same encoding passed to Ha is passed to Hb.
You only have to do a correct execution trace of Ha(Pa,Pa) and Hb(Pa,Pa)
to see that:
The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested
simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT
specify infinitely nested simulation.
How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.
Trimmed extraneous / redundant material to stay focused on the most
essential point.
Not at all because H(P,P) has itself as part of its input and Hb(P,P)
does not have itself as part of its input.
>
> So just because Pa contains an embedded copy of Ha but not an embedded copy of Hb doesn't means that it's not the same.
>
Sure it does. The correctly simulated input to H(P,P) specifies
infinitely nested simulation where as correctly simulated input to
Hb(P,P) DOES NOT specify infinitely nested simulation.
How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.
> Ha(Pa,Pa) and Hb(Pa,Pa) have the *exact* same input.
>
The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested
simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT
specify infinitely nested simulation.
How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.
> Just because it appears from a glance that Ha is starting its simulation of Pa "in the middle" doesn't mean that's what's actually happening. That's just how the incorrect simulation is manifesting itself. It's kind of like undefined behavior in a C program.
You only have to do a correct execution trace of Ha(Pa,Pa) and Hb(Pa,Pa)
to see that:
The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested
simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT
specify infinitely nested simulation.
How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.
>>>
>>>>> Because H and Hb and both simulating halt deciders and are given the same input, they are deciding on the same sequence of configurations (namely starting with the first instruction of P). Because one answers false and one answers true, one must be wrong.
>>>>>
>>>> It is ridiculously stupid to assume that an input having pathological
>>>> self-reference to its decider would have the same behavior as an input
>>>> NOT having pathological to its decider.
>>>
>>> Which is another way of saying that H can't give a correct answer for (P,P).
>>>
>> Different computations must give different answers.
>> That you don't fully understand all of the nuances of how this applies
>> to H/P and Hb/Px is OK, it is difficult to understand.
>
You only have to do a correct execution trace of Ha(Pa,Pa) and Hb(Pa,Pa)
to see that:
The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested
simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT
specify infinitely nested simulation.
How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.
>>>>> Since a simulating halt decider that simulates its input to a final state while remaining in UTM mode is necessarily correct, this proves that Hb(P,P) == true is correct and that H(P,P) == false is incorrect, and that H(P,P) does *not* in fact perform a correct simulation of its input because it aborts too soon.
>>>>>
>>>> It is very easy to verify the fact that the simulated input to H(P,P)
>>>> would never stop unless aborted. It is pretty psychotic that many of my
>>>> reviewers deny easily verified facts.
>>>
>>> There is no "unless". The fixed algorithm of H, which will henceforth be referred to as Ha and similarly P will be referred to as Pa, *does* abort.
>> Which is *NOT* halting. A halting input must reach its own final state.
>>> Because of this, Hb(Pa,Pa) explicitly shows that the simulated input to Ha(Pa,Pa) *does* stop. The fact that Pn(Pn) does not halt and that Hn(Pn,Pn) does not halt is irrelevant.
>> It it not Hb(Pa,Pa) it is Hb(Px,Px). That P calls H makes it an entirely
>> different input than Px that does not call Hb.
>
You only have to do a correct execution trace of Ha(Pa,Pa) and Hb(Pa,Pa)
to see that:
The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested
simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT
specify infinitely nested simulation.
How much longer are you going to continue the verified facts?
This does make you look quite foolish or dishonest.
Trimmed extraneous / redundant material to stay focused on the most
essential point.
olcott
May 3, 2022, 7:48:07 PM5/3/22
to
On 5/3/2022 6:05 PM, Python wrote:
> Peter Olcott wrote:
>> On 5/3/2022 5:46 PM, Python wrote:
>>> Peter Olcott wrote:
>>>> On 5/3/2022 5:21 PM, Python wrote:
>>>>> Peter Olcott wrote:
>>>>>> On 5/3/2022 1:59 PM, Mr Flibble wrote:
>>>>>>> On Tue, 3 May 2022 11:57:39 -0500
>>>>>>> olcott <polc...@gmail.com> wrote:
>>>>> ...
>>>>>>>> I don't buy into the whole imaginary numbers game.
>>>>>>>> We could imagine that 2 + 3 = 17 and call that an imaginary sum.
>>>>> ...
>>>>>>
>>>>>> Nice to know, thanks. Thus your rebuttal seems complete it is not
>>>>>> an infinite anything. Imagining the square root of a negative
>>>>>> number or that parallel lines meet seems a little nuts to me.
>>>>>
>>>>> Before jumping to such outrageously uninformed conclusions you may
>>>>> want
>>>>> to learn how complex numbers are actually defined nowadays.
>>>>>
>>>>
>>>> They are defined to directly contradict the verified facts.
>>>> I really hate anything that directly contradicts the verified facts
>>>> because this can result in:
>>>> (a) Climate change making humans extinct quite soon,
>>>>
>>>> (b) Nazi "big lie" propaganda about election fraud is making very
>>>> significant inroads to transforming Democracy ion the USA to Fascism.
>>>>
>>>> (c) It directly resulted in many covid-19 deaths
>>>
>>> You should definitely call a doctor and ask for help, your mental
>>> state is utterly ill. What the f* are complex numbers related to
>>> your rants on politics?
>>>
>>>>> It is true that, at first, it was used without any proper definition
>>>>> better than "let's assume we can deal with sqrt(-1) as usual". The
>>>>> surprising point at that time is it works pretty well.
>>>>>
>>>>
>>>> We can see what happens when we hypothesize (against the facts) that
>>>> square roots of negative numbers and parallel lines that meet exist
>>>> simply to see where this leads. I am sure that this is the intent.
>>>
>>>
>>> Not quite you're wrong. The intent was to find *real* roots of degree 3
>>> polynomials even if square root of negative quantities appears at
>>> intermediary steps.
>>>
>>
>> None-the-less as I just said this whole think relies on accepting a
>> known false premise.
>
> Let me guess, you are some kind of "information engineer" and consider
> yourself also as "one of the greatest logicians Humanity ever had",
> right? There is a demented guy of this kind on sci.physics.relativity,
> his name is Maciej Wozniak. You guys should definitely mate (NOT).
>
I consider myself to have made significant unique advancements on the
single subject on the philosophical foundation of the notion of logical
truth.
One of my key breakthroughs is redefining the analytic / synthetic
distinction such that analytic means (the same as it did) any expression
of formal or natural language that can be verified as true entirely on
the basis of its meaning. "Dogs are animals"
The somewhat vaguely defined synthetic is renamed as empirical and it is
the same sort of thing as analytic that additionally requires sense data
from the sense organs as an aspect of the truth verification process.
"There is a dog in my living room right now."
This is the most important paper on the subject
Two Dogmas of Empiricism by Willard Van Orman Quine
(Harvard University Press, 1953; second, revised, edition 1961)
https://www.theologie.uzh.ch/dam/jcr:ffffffff-fbd6-1538-0000-000070cf64bc/Quine51.pdf
Quine didn't seem to understand that bachelors are necessarily unmarried.
Meaning Postulates by RUDOLF CARNAP
https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf
conclusively proved the complete basis of how we know that bachelors are
necessarily unmarried. Quine didn't want to hear this because it
contradicted his paper.
>>> You know *nothing* about history of Science, Peter. Guessing is quite
>>> absurd when it comes to History.
>>>
>>>>> *Then*, in the XIXth Century, Gallois showed how to define complex
>>>>> numbers rigorously.
>>>>>
>>>>> You've never heard of that, Peter, really?
>>>>>
>>>>> [for the record: C is the set of equivalence classes of polynomials
>>>>> on R by the relation p ~ q iff p - q = 0 [mod x^2+1], compatibility
>>>>> of + and * on R and C can be proven easily, R is naturally injected
>>>>> into C as a set of constant polynomials, i is the equivalence class of
>>>>> the polynomial x]
>>>
>>> No reaction? Well... Not a big surprise, your eyes cancel out any
>>> sensible arguments proving you wrong, as usual.
>>>
>>> Die in Hell, idiotic annoying crank. You deserve it.
>
> (bis)
> Peter Olcott wrote:
>> On 5/3/2022 5:46 PM, Python wrote:
>>> Peter Olcott wrote:
>>>> On 5/3/2022 5:21 PM, Python wrote:
>>>>> Peter Olcott wrote:
>>>>>> On 5/3/2022 1:59 PM, Mr Flibble wrote:
>>>>>>> On Tue, 3 May 2022 11:57:39 -0500
>>>>>>> olcott <polc...@gmail.com> wrote:
>>>>> ...
>>>>>>>> I don't buy into the whole imaginary numbers game.
>>>>>>>> We could imagine that 2 + 3 = 17 and call that an imaginary sum.
>>>>> ...
>>>>>>
>>>>>> Nice to know, thanks. Thus your rebuttal seems complete it is not
>>>>>> an infinite anything. Imagining the square root of a negative
>>>>>> number or that parallel lines meet seems a little nuts to me.
>>>>>
>>>>> Before jumping to such outrageously uninformed conclusions you may
>>>>> want
>>>>> to learn how complex numbers are actually defined nowadays.
>>>>>
>>>>
>>>> They are defined to directly contradict the verified facts.
>>>> I really hate anything that directly contradicts the verified facts
>>>> because this can result in:
>>>> (a) Climate change making humans extinct quite soon,
>>>>
>>>> (b) Nazi "big lie" propaganda about election fraud is making very
>>>> significant inroads to transforming Democracy ion the USA to Fascism.
>>>>
>>>> (c) It directly resulted in many covid-19 deaths
>>>
>>> You should definitely call a doctor and ask for help, your mental
>>> state is utterly ill. What the f* are complex numbers related to
>>> your rants on politics?
>>>
>>>>> It is true that, at first, it was used without any proper definition
>>>>> better than "let's assume we can deal with sqrt(-1) as usual". The
>>>>> surprising point at that time is it works pretty well.
>>>>>
>>>>
>>>> We can see what happens when we hypothesize (against the facts) that
>>>> square roots of negative numbers and parallel lines that meet exist
>>>> simply to see where this leads. I am sure that this is the intent.
>>>
>>>
>>> Not quite you're wrong. The intent was to find *real* roots of degree 3
>>> polynomials even if square root of negative quantities appears at
>>> intermediary steps.
>>>
>>
>> None-the-less as I just said this whole think relies on accepting a
>> known false premise.
>
> Let me guess, you are some kind of "information engineer" and consider
> yourself also as "one of the greatest logicians Humanity ever had",
> right? There is a demented guy of this kind on sci.physics.relativity,
> his name is Maciej Wozniak. You guys should definitely mate (NOT).
>
I consider myself to have made significant unique advancements on the
single subject on the philosophical foundation of the notion of logical
truth.
One of my key breakthroughs is redefining the analytic / synthetic
distinction such that analytic means (the same as it did) any expression
of formal or natural language that can be verified as true entirely on
the basis of its meaning. "Dogs are animals"
The somewhat vaguely defined synthetic is renamed as empirical and it is
the same sort of thing as analytic that additionally requires sense data
from the sense organs as an aspect of the truth verification process.
"There is a dog in my living room right now."
This is the most important paper on the subject
Two Dogmas of Empiricism by Willard Van Orman Quine
(Harvard University Press, 1953; second, revised, edition 1961)
https://www.theologie.uzh.ch/dam/jcr:ffffffff-fbd6-1538-0000-000070cf64bc/Quine51.pdf
Quine didn't seem to understand that bachelors are necessarily unmarried.
Meaning Postulates by RUDOLF CARNAP
https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf
conclusively proved the complete basis of how we know that bachelors are
necessarily unmarried. Quine didn't want to hear this because it
contradicted his paper.
>>> You know *nothing* about history of Science, Peter. Guessing is quite
>>> absurd when it comes to History.
>>>
>>>>> *Then*, in the XIXth Century, Gallois showed how to define complex
>>>>> numbers rigorously.
>>>>>
>>>>> You've never heard of that, Peter, really?
>>>>>
>>>>> [for the record: C is the set of equivalence classes of polynomials
>>>>> on R by the relation p ~ q iff p - q = 0 [mod x^2+1], compatibility
>>>>> of + and * on R and C can be proven easily, R is naturally injected
>>>>> into C as a set of constant polynomials, i is the equivalence class of
>>>>> the polynomial x]
>>>
>>> No reaction? Well... Not a big surprise, your eyes cancel out any
>>> sensible arguments proving you wrong, as usual.
>>>
>>> Die in Hell, idiotic annoying crank. You deserve it.
>
> (bis)
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