On 3/12/2024 11:13 AM, immibis wrote:
> On 12/03/24 04:24, olcott wrote:
>> On 3/11/2024 9:41 PM, Richard Damon wrote:
>> There is no correct answer for this (program/input pair): (H/⟨Ĥ⟩ ⟨Ĥ⟩)
>
> Yes there is. If you show me the Turing machine description of Ĥ I will
> tell you whether it halts on its own input or not. As long as it doesn't
> check the Collatz conjecture.
>
> Once we understand that either YES or NO is the right answer, the whole
> rebuttal is tossed out as invalid and incorrect.

*This discussion has moved to my new post*
[Proving my 2004 claim that some decider/input pairs are incorrect
questions]

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/12/2024 11:14 AM, immibis wrote:
> On 12/03/24 04:37, olcott wrote:
>> On 3/11/2024 10:31 PM, Richard Damon wrote:
>>> On 3/11/24 7:52 PM, olcott wrote:
>>>> On 3/11/2024 9:32 PM, immibis wrote:
>>>>> On 12/03/24 03:24, olcott wrote:
>>> \
>>>>>> Troll detected.
>>>>>>
>>>>>
>>>>> Once we understand that either YES or NO is the right answer
>>>>
>>>> Not for this decider/input question: Ĥ.H / ⟨Ĥ⟩ ⟨Ĥ⟩
>>>> For that decider/input question both YES and NO are the wrong answer.
>>>
>>> The problem that you keeep on missing is that by the point we can ask
>>> this question, H and H^ are FULLY CODED, and thus we know their
>>> behavirs.
>>
>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy // Ĥ applied to ⟨Ĥ⟩ halts
>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>
>> Since you know that is false why lie?
>> ⊢* specifies an infinite set of encodings.
>>
>> Since you know that is false why lie?
>> ⊢* specifies an infinite set of encodings.
>>
>> Since you know that is false why lie?
>> ⊢* specifies an infinite set of encodings.
>>
>> Since you know that is false why lie?
>> ⊢* specifies an infinite set of encodings.
>>
>>
>
> Since you know that is false why lie?

*This discussion has moved to my new post*
[Proving my 2004 claim that some decider/input pairs are incorrect
questions]

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/11/24 9:01 PM, olcott wrote:
> On 3/11/2024 10:57 PM, Richard Damon wrote:
>> On 3/11/24 8:37 PM, olcott wrote:
>>> On 3/11/2024 10:31 PM, Richard Damon wrote:
>>>> On 3/11/24 7:52 PM, olcott wrote:
>>>>> On 3/11/2024 9:32 PM, immibis wrote:
>>>>>> On 12/03/24 03:24, olcott wrote:
>>>> \
>>>>>>> Troll detected.
>>>>>>>
>>>>>>
>>>>>> Once we understand that either YES or NO is the right answer
>>>>>
>>>>> Not for this decider/input question: Ĥ.H / ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>> For that decider/input question both YES and NO are the wrong answer.
>>>>
>>>> The problem that you keeep on missing is that by the point we can
>>>> ask this question, H and H^ are FULLY CODED, and thus we know their
>>>> behavirs.
>>>
>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy // Ĥ applied to ⟨Ĥ⟩ halts
>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>
>>> Since you know that is false why lie?
>>> ⊢* specifies an infinite set of encodings.
>>
>> Nope, read him again, not just skim and assume.
>>
>> Should Represents the ARBITRARY path that THIS H will do.
>>
>
> I have read it again and again since 2004, you are getting
> this incorrectly. I have two copies of the book.
>

Really, so how does he actually DEFINE that notation, his exact words.

I am sure he doesn't use the words "an infinite set of encodings", as he
will always be talking about a given (but arbitrary) Turing Machine at
any given time, as that is what you run.

My guess is that this is like everything you do, you never bothered to
learn the actual meaning of the words he is using (in the context he is
using them) so your zeroth principles (they are first principles, since
you don't have the actual basics of the field under your belt) give you
wrong meanings to what he is saying.

On 3/12/24 9:02 AM, olcott wrote:
> On 3/11/2024 10:57 PM, Richard Damon wrote:
>> On 3/11/24 8:37 PM, olcott wrote:
>>> On 3/11/2024 10:31 PM, Richard Damon wrote:
>>>> On 3/11/24 7:52 PM, olcott wrote:
>>>>> On 3/11/2024 9:32 PM, immibis wrote:
>>>>>> On 12/03/24 03:24, olcott wrote:
>>>> \
>>>>>>> Troll detected.
>>>>>>>
>>>>>>
>>>>>> Once we understand that either YES or NO is the right answer
>>>>>
>>>>> Not for this decider/input question: Ĥ.H / ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>> For that decider/input question both YES and NO are the wrong answer.
>>>>
>>>> The problem that you keeep on missing is that by the point we can
>>>> ask this question, H and H^ are FULLY CODED, and thus we know their
>>>> behavirs.
>>>
>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy // Ĥ applied to ⟨Ĥ⟩ halts
>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>
>>> Since you know that is false why lie?
>>> ⊢* specifies an infinite set of encodings.
>>
>> Nope, read him again, not just skim and assume.
>>
>
> *Here is the proof that I am correct*
> ∀ H ∈ Turing_Machine_Deciders
> ∃ TMD ∈ Turing_Machine_Descriptions  |
> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>
>

So, H, being an ELEMENT of Turing Machine Deciders, is a SINGLE INSTANCE
of it, it is NOT the set itself.

You just don't understand categorical logic.

Yes, you can do this for ANY element, but the following logic is done
one machine at a time.

On 3/12/2024 12:27 PM, Richard Damon wrote:
> On 3/11/24 8:24 PM, olcott wrote:
>> On 3/11/2024 9:41 PM, Richard Damon wrote:
>>> On 3/11/24 6:39 PM, olcott wrote:
>>>> On 3/11/2024 7:08 PM, Richard Damon wrote:
>>>>> On 3/11/24 4:00 PM, olcott wrote:
>>>>>> On 3/11/2024 12:13 PM, Richard Damon wrote:
>>>>>>> On 3/11/24 6:19 AM, olcott wrote:
>>>>>>>> On 3/11/2024 1:02 AM, Richard Damon wrote:
>>>>>>>>> On 3/10/24 10:44 PM, olcott wrote:
>>>>>>>>>
>>>>>>>>>> *Every implementation of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ gets the wrong answer*
>>>>>>>>>> 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
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Yes, you have rotely repeated that many times, not knowing what
>>>>>>>>> that implies, or doesn't imply.
>>>>>>>>>
>>>>>>>>
>>>>>>>>   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
>>>>>>>>
>>>>>>>>   *Every implementation of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ gets the wrong answer*
>>>>>>>>   *Every implementation of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ gets the wrong answer*
>>>>>>>>   *Every implementation of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ gets the wrong answer*
>>>>>>>
>>>>>>> Really?
>>>>>>>
>>>>>>> A "submachine" doesn't have a requirement except to act as the
>>>>>>> machine it is a copy of.
>>>>>>>
>>>>>>
>>>>>> There is no such thing as a sub-machine.
>>>>>
>>>>> OF course there is.
>>>>>
>>>>> What do you think H^.H is?
>>>>>
>>>>> You are just showing how stupid you are.
>>>>
>>>> An an abstract concept that humans can talk about that
>>>> cannot actually be implemented as any actual aspect of
>>>> any actual Turing machine.
>>>
>>> So, you admit you were wrong, and are just stupid.
>>>
>>> Why isn't H^.H the implementation in the Turing Machine H^ of a
>>> submachine that is a copy of H?
>>>
>>>>
>>>> The ghost of Bug Bunny exists as a fictional idea.
>>>
>>> So seems most of your ideas.
>>>
>>>>
>>>>>>
>>>>>>> So, what you are REALLY Saying is that:
>>>>>>>
>>>>>>> H (H^) (H^) gets the wrong answer for every implementation of H,
>>>>>>>
>>>>>>
>>>>>> Both answers of YES and NO are incorrect for any H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>> that is inconsistent with the behavior of Ĥ ⟨Ĥ⟩ when an
>>>>>> exact copy of this same H is embedded within Ĥ.
>>>>>
>>>>> No, there IS a 'Correct answer', it just isn't the one that that H
>>>>> gives.
>>>>>
>>>>
>>>> You are bullshitting yourself, yet not bullshitting me.
>>>> There is no correct answer for the H/⟨Ĥ⟩ ⟨Ĥ⟩ program/input pair.
>>>
>>> If H (H^) (H^) says Qn, as you normally say, then it is a FACT that
>>> H^ (H^) will go to Qn and Halt,
>>>
>>> And thus the CORRECT ANSWER is Qy.
>>>
>>> If you changed your mind, an now H (H^) (H^) says Qy, then it is a
>>> fact that H^ (H^) will also goto Qy and loop forever.
>>>
>>> And thus, the CORRECT ANSWER is Qn
>> There is no correct answer for this (program/input pair): (H/⟨Ĥ⟩ ⟨Ĥ⟩)
>>
>> That you continue to try to get away with the strawman deception
>> and change to any other (program/input pair) seems to prove that
>> you are not being honest and have rebuttal rather that truth as your
>> priority.
>>
>
> And what is wrong with my analysis I have posted seversal times, and to
> which you haen't shown an error.

*This discussion has moved to my new post*
[Proving my 2004 claim that some decider/input pairs are incorrect
questions]

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/12/24 10:46 AM, olcott wrote:
> On 3/12/2024 12:36 PM, Richard Damon wrote:
>> On 3/12/24 9:02 AM, olcott wrote:
>>> On 3/11/2024 10:57 PM, Richard Damon wrote:
>>>> On 3/11/24 8:37 PM, olcott wrote:
>>>>> On 3/11/2024 10:31 PM, Richard Damon wrote:
>>>>>> On 3/11/24 7:52 PM, olcott wrote:
>>>>>>> On 3/11/2024 9:32 PM, immibis wrote:
>>>>>>>> On 12/03/24 03:24, olcott wrote:
>>>>>> \
>>>>>>>>> Troll detected.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Once we understand that either YES or NO is the right answer
>>>>>>>
>>>>>>> Not for this decider/input question: Ĥ.H / ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>> For that decider/input question both YES and NO are the wrong
>>>>>>> answer.
>>>>>>
>>>>>> The problem that you keeep on missing is that by the point we can
>>>>>> ask this question, H and H^ are FULLY CODED, and thus we know
>>>>>> their behavirs.
>>>>>
>>>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy // Ĥ applied to ⟨Ĥ⟩ halts
>>>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>>
>>>>> Since you know that is false why lie?
>>>>> ⊢* specifies an infinite set of encodings.
>>>>
>>>> Nope, read him again, not just skim and assume.
>>>>
>>>
>>> *Here is the proof that I am correct*
>>> ∀ H ∈ Turing_Machine_Deciders
>>> ∃ TMD ∈ Turing_Machine_Descriptions  |
>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>
>>>
>>
>> So, H, being an ELEMENT of Turing Machine Deciders, is a SINGLE
>> INSTANCE of it, it is NOT the set itself.
>
> ∀ H ∈ Turing_Machine_Deciders *DOES NOT REFER TO A SINGLE INSTANCE*
> https://en.wikipedia.org/wiki/List_of_logic_symbols

Of COURSE "H" referes to just a single instance at a time.

H is not the set, it is an element of the set

You just don't understand the meaning of categorical logic.

>
> *This discussion has moved to my new post*
> [Proving my 2004 claim that some decider/input pairs are incorrect
> questions]
>
>>
>> You just don't understand categorical logic.
>>
>> Yes, you can do this for ANY element, but the following logic is done
>> one machine at a time.
>

On 3/12/2024 12:50 PM, Richard Damon wrote:
> On 3/12/24 10:46 AM, olcott wrote:
>> On 3/12/2024 12:36 PM, Richard Damon wrote:
>>> On 3/12/24 9:02 AM, olcott wrote:
>>>> On 3/11/2024 10:57 PM, Richard Damon wrote:
>>>>> On 3/11/24 8:37 PM, olcott wrote:
>>>>>> On 3/11/2024 10:31 PM, Richard Damon wrote:
>>>>>>> On 3/11/24 7:52 PM, olcott wrote:
>>>>>>>> On 3/11/2024 9:32 PM, immibis wrote:
>>>>>>>>> On 12/03/24 03:24, olcott wrote:
>>>>>>> \
>>>>>>>>>> Troll detected.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Once we understand that either YES or NO is the right answer
>>>>>>>>
>>>>>>>> Not for this decider/input question: Ĥ.H / ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>> For that decider/input question both YES and NO are the wrong
>>>>>>>> answer.
>>>>>>>
>>>>>>> The problem that you keeep on missing is that by the point we can
>>>>>>> ask this question, H and H^ are FULLY CODED, and thus we know
>>>>>>> their behavirs.
>>>>>>
>>>>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy // Ĥ applied to ⟨Ĥ⟩ halts
>>>>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>>>
>>>>>> Since you know that is false why lie?
>>>>>> ⊢* specifies an infinite set of encodings.
>>>>>
>>>>> Nope, read him again, not just skim and assume.
>>>>>
>>>>
>>>> *Here is the proof that I am correct*
>>>> ∀ H ∈ Turing_Machine_Deciders
>>>> ∃ TMD ∈ Turing_Machine_Descriptions  |
>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>
>>>>
>>>
>>> So, H, being an ELEMENT of Turing Machine Deciders, is a SINGLE
>>> INSTANCE of it, it is NOT the set itself.
>>
>> ∀ H ∈ Turing_Machine_Deciders *DOES NOT REFER TO A SINGLE INSTANCE*
>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>
> Of COURSE "H" referes to just a single instance at a time.
>

*You have updated your words to address my objection*

*This discussion has moved to my new post*
[Proving my 2004 claim that some decider/input pairs are incorrect
questions]

> H is not the set, it is an element of the set
>
> You just don't understand the meaning of categorical logic.
>
>>
>> *This discussion has moved to my new post*
>> [Proving my 2004 claim that some decider/input pairs are incorrect
>> questions]
>>
>>>
>>> You just don't understand categorical logic.
>>>
>>> Yes, you can do this for ANY element, but the following logic is done
>>> one machine at a time.
>>
>

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/11/24 8:56 AM, olcott wrote:
> On 3/11/2024 10:36 AM, immibis wrote:
>> On 11/03/24 04:33, olcott wrote:
>>> Then we are back to undecidability being incorrectly construed
>>> as an actual limit to computation.
>>
>> Proof that a certain thing cannot be computed is always a limit to
>> computation.
>>
> Yet in only the same way that the Liar Paradox
> "This sentence is not true."
> does not have a truth value that can be computed.
>
>> For example, you can't compute the colour of the number 4. That is an
>> actual limit to computation.
>>
>
> The inability to to the logically impossible is not any actual limit.
> If we say that the Halting Problem cannot be solved for the same sort
> of reason that Square Circles do not exist then this is not any actual
> limit.

But SHOWING that something is logically impossible reveals the
limitations that were already there.

Yes, the Halting Theorem doesn't MAKE the problem impossible, it shows
that it always was, and gives us knowledge of that.

But, you don't understand the nature of Truth and Knowledge, so that
won't make sense.

>
>> You can't compute the halting problem. That is an actual limit to
>> computation.
>

On 3/11/24 8:51 AM, olcott wrote:
> On 3/11/2024 10:34 AM, immibis wrote:
>> On 11/03/24 03:38, olcott wrote:
>>> If the only reason that a machine does not get a correct yes/no answer
>>> for this machine/input pair is that both yes and no are the wrong answer
>>> for this machine/input pair then this machine/input pair is a yes/no
>>> question that has no correct yes/no answer for this machine/input pair.
>>
>> This is bullshit, because the question has a correct yes/no answer,
>> and you know this, so stop lying.
>>
>
> When you ignore the context of {who is asked} then the halting
> problem question incorrectly seems to always have a correct answer.

And show me an actual Turing Machine that changes its behavior based on
who is looking at it.

Remember, H^ is a SPECIFIC implementation based on a SPECIFIC
implemetation of H, and thus doesn't change, if you try a "different H"
on it (which will be a different machine, and not the H that H^ was
built on)

>
> Alan Turing's Halting Problem is incorrectly formed (PART-TWO)  sci.logic
> On 6/20/2004 11:31 AM, Peter Olcott wrote:
> > PREMISES:
> > (1) The Halting Problem was specified in such a way that a solution
> > was defined to be impossible.
> >
> > (2) The set of questions that are defined to not have any possible
> > correct answer(s) forms a proper subset of all possible questions.
> > …
> > CONCLUSION:
> > Therefore the Halting Problem is an ill-formed question.
> >
> USENET Message-ID:
> <kZiBc.103407$Gx4.18142@bgtnsc04-news.ops.worldnet.att.net>
>
> *Direct Link to original message*
> http://al.howardknight.net/?STYPE=msgid&MSGI=%3CkZiBc.103407%24Gx4.18142%40bgtnsc04-news.ops.worldnet.att.net%3E+
>
>

On 3/12/2024 1:04 PM, Richard Damon wrote:
> On 3/11/24 8:56 AM, olcott wrote:
>> On 3/11/2024 10:36 AM, immibis wrote:
>>> On 11/03/24 04:33, olcott wrote:
>>>> Then we are back to undecidability being incorrectly construed
>>>> as an actual limit to computation.
>>>
>>> Proof that a certain thing cannot be computed is always a limit to
>>> computation.
>>>
>> Yet in only the same way that the Liar Paradox
>> "This sentence is not true."
>> does not have a truth value that can be computed.
>>
>>> For example, you can't compute the colour of the number 4. That is an
>>> actual limit to computation.
>>>
>>
>> The inability to to the logically impossible is not any actual limit.
>> If we say that the Halting Problem cannot be solved for the same sort
>> of reason that Square Circles do not exist then this is not any actual
>> limit.
>
> But SHOWING that something is logically impossible reveals the
> limitations that were already there.
>
> Yes, the Halting Theorem doesn't MAKE the problem impossible, it shows
> that it always was, and gives us knowledge of that.
>

The halting problem does not derive a limit to computation
any more than the inability of CAD systems to draw square
circles places a limit on computation.

> But, you don't understand the nature of Truth and Knowledge, so that
> won't make sense.
>
>>
>>> You can't compute the halting problem. That is an actual limit to
>>> computation.
>>
>

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/03/24 18:46, olcott wrote:
> On 3/12/2024 12:36 PM, Richard Damon wrote:
>> On 3/12/24 9:02 AM, olcott wrote:
>>> On 3/11/2024 10:57 PM, Richard Damon wrote:
>>>> On 3/11/24 8:37 PM, olcott wrote:
>>>>> On 3/11/2024 10:31 PM, Richard Damon wrote:
>>>>>> On 3/11/24 7:52 PM, olcott wrote:
>>>>>>> On 3/11/2024 9:32 PM, immibis wrote:
>>>>>>>> On 12/03/24 03:24, olcott wrote:
>>>>>> \
>>>>>>>>> Troll detected.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Once we understand that either YES or NO is the right answer
>>>>>>>
>>>>>>> Not for this decider/input question: Ĥ.H / ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>> For that decider/input question both YES and NO are the wrong
>>>>>>> answer.
>>>>>>
>>>>>> The problem that you keeep on missing is that by the point we can
>>>>>> ask this question, H and H^ are FULLY CODED, and thus we know
>>>>>> their behavirs.
>>>>>
>>>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy // Ĥ applied to ⟨Ĥ⟩ halts
>>>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>>
>>>>> Since you know that is false why lie?
>>>>> ⊢* specifies an infinite set of encodings.
>>>>
>>>> Nope, read him again, not just skim and assume.
>>>>
>>>
>>> *Here is the proof that I am correct*
>>> ∀ H ∈ Turing_Machine_Deciders
>>> ∃ TMD ∈ Turing_Machine_Descriptions  |
>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>
>>>
>>
>> So, H, being an ELEMENT of Turing Machine Deciders, is a SINGLE
>> INSTANCE of it, it is NOT the set itself.
>
> ∀ H ∈ Turing_Machine_Deciders *DOES NOT REFER TO A SINGLE INSTANCE*

Yes it does. It means that if H is a single instance, no matter which
one it is, the rest of the sentence is true.

On 3/11/24 1:56 PM, olcott wrote:
> On 3/11/2024 1:49 PM, Richard Damon wrote:
>> On 3/11/24 7:25 AM, olcott wrote:
>>> On 3/11/2024 1:17 AM, Richard Damon wrote:
>>>> On 3/10/24 10:40 PM, olcott wrote:
>>>>> On 3/11/2024 12:07 AM, Richard Damon wrote:
>>>>>> On 3/10/24 9:33 PM, olcott wrote:
>>>>>>> On 3/10/2024 10:07 PM, Richard Damon wrote:
>>>>>>>> On 3/10/24 7:47 PM, olcott wrote:
>>>>>>>>> On 3/10/2024 9:08 PM, Richard Damon wrote:
>>>>>>>>>> On 3/10/24 5:32 PM, olcott wrote:
>>>>>>>>>>> On 3/10/2024 2:16 PM, immibis wrote:
>>>>>>>>>>>> On 10/03/24 19:32, olcott wrote:
>>>>>>>>>>>>> On 3/10/2024 1:08 PM, immibis wrote:
>>>>>>>>>>>>>> On 10/03/24 18:17, olcott wrote:
>>>>>>>>>>>>>>> ZFC simply tossed out the Russell's Paradox question as
>>>>>>>>>>>>>>> unsound.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So you are saying that some Turing machines are not sound?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Both H ⟨Ĥ⟩ ⟨Ĥ⟩ and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ correctly decide that:
>>>>>>>>>>>>>>>>> (a) Their input halts H.qy
>>>>>>>>>>>>>>>>> (b) Their input fails to halt or has a pathological
>>>>>>>>>>>>>>>>> relationship to itself H.qn.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> But the "Pathological Relationship" is ALLOWED.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> ZFC simply tossed out the Russell's Paradox question as
>>>>>>>>>>>>>>> unsound
>>>>>>>>>>>>>>> expressly disallowing the "Pathological Relationship".
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So you are saying that some Turing machines are not real
>>>>>>>>>>>>>> Turing machines?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I am only claiming that both H and Ĥ.H correctly say YES
>>>>>>>>>>>>>>> when their input halts and correctly say NOT YES otherwise.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> well the halting problem requires them to correctly say
>>>>>>>>>>>>>> NO, so you haven't solved it
>>>>>>>>>>>>>
>>>>>>>>>>>>> All decision problem instances of program/input such that both
>>>>>>>>>>>>> yes and no are the wrong answer toss out the input as invalid.
>>>>>>>>>>>>
>>>>>>>>>>>> I noticed that you gave up on Olcott machines and now you
>>>>>>>>>>>> are back to your old bullshit ways of pretending that the
>>>>>>>>>>>> same machine can produce two different execution traces on
>>>>>>>>>>>> the same input. Why don't you show us an execution trace
>>>>>>>>>>>> where that happens? Both traces must show the first
>>>>>>>>>>>> instruction that is different in both traces and I recommend
>>>>>>>>>>>> showing 20 more instructions after that, but you can abort
>>>>>>>>>>>> one after that time, if it doesn't halt, to prevent the
>>>>>>>>>>>> trace getting infinitely long.
>>>>>>>>>>>
>>>>>>>>>>> Turing Machines and Olcott machines cannot properly implement
>>>>>>>>>>> H1(D,D) and H(D,D) that know their own machine address.
>>>>>>>>>>>
>>>>>>>>>>> My C code proves these two have different behavior:
>>>>>>>>>>> (a) H1(D,D) + H1_machine_address
>>>>>>>>>>> (b) H(D,D) + H_machine_address
>>>>>>>>>>>
>>>>>>>>>>> Because they are different computations they are
>>>>>>>>>>> not required to have the same behavior.
>>>>>>>>>>
>>>>>>>>>> Right, but it also means that since the dfference is because
>>>>>>>>>> of a "Hidden" input none of them qualify as a Halt Decider.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> The key input (the machines own address) is not hidden
>>>>>>>>> merely unavailable to Turing machine and Olcott machines.
>>>>>>>>
>>>>>>>> And if it isn't hidden, then the other copies that take use a
>>>>>>>> different address become different computations and can't claim
>>>>>>>> to fill in for THE H.
>>>>>>>>
>>>>>>>> You then prove each copy wrong by giving it the version of H^/D
>>>>>>>> that is built on it, which it will get wrong.
>>>>>>>>
>>>>>>>> All the other ones might get it right, showing that there IS a
>>>>>>>> correct answer.
>>>>>>>>
>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> H(D,D) immediately sees the first time it calls itself
>>>>>>>>>>> with its same inputs.
>>>>>>>>>>>
>>>>>>>>>>> H1(D,D) never sees it call itself with its same inputs.
>>>>>>>>>>>
>>>>>>>>>>> Full Execution trace of H1(D,D)
>>>>>>>>>>> (a) main() invokes H1(D,D)
>>>>>>>>>>> (b) H1(D,D) simulates D(D)
>>>>>>>>>>> (c) Simulated D(D) calls simulated H(D,D)
>>>>>>>>>>> (d) Simulated H(D,D) simulates another D(D)
>>>>>>>>>>> (e) Simulated H(D,D) aborts this D(D) when it would call itself
>>>>>>>>>>> (f) Simulated H(D,D) returns 0 to simulated caller D(D)
>>>>>>>>>>> (g) Simulated caller D(D) returns to H1(D,D)
>>>>>>>>>>> (h) H1(D,D) returns 1 to main()
>>>>>>>>>>>
>>>>>>>>>>> They cannot be implemented as Turing Machines or Olcott
>>>>>>>>>>> Machines. They can be implemented as RASP machines proven
>>>>>>>>>>> by the fact that they are implemented as C functions.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Right, which proves your C functions also were never the
>>>>>>>>>> required computation, as they has an extra "hidden" input. As
>>>>>>>>>> has been told to you many times in the past.
>>>>>>>>>
>>>>>>>>> When I specify that every machine can know its own machine address
>>>>>>>>> in x86 machines and (possibly augmented) RASP machines then it is
>>>>>>>>> not hidden and an explicitly part of the input to the computation.
>>>>>>>>
>>>>>>>> And if it isn't hidden, then the other copies that take use a
>>>>>>>> different address become different computations and can't claim
>>>>>>>> to fill in for THE H.
>>>>>>>>
>>>>>>>> You then prove each copy wrong by giving it the version of H^/D
>>>>>>>> that is built on it, which it will get wrong.
>>>>>>>>
>>>>>>>> All the other ones might get it right, showing that there IS a
>>>>>>>> correct answer.
>>>>>>>>
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> So, you just admitted that you hae just been lying for all
>>>>>>>>>> these years, and you are no closer to your fantasy goal then
>>>>>>>>>> you ever were.
>>>>>>>>>>
>>>>>>>>>> Sorry, you just don't know enough to do this problem.
>>>>>>>>>
>>>>>>>>> I just admitted that it took me about two years to translate my
>>>>>>>>> intuitions into words that address your objections.
>>>>>>>>>
>>>>>>>>> For these two years you and many other people claimed that H1(D,D)
>>>>>>>>> could not possibly do what it actually did actually do. This has
>>>>>>>>> always been the same thing as disagreeing with arithmetic.
>>>>>>>>>
>>>>>>>>
>>>>>>>> It can't do it and be the SAME COMPUTATION as H, which is what
>>>>>>>> you were claiming.
>>>>>>>>
>>>>>>>
>>>>>>> It did actually do exactly what I claimed and everyone wanted
>>>>>>> to stick to their opinion and deny the actual facts that it
>>>>>>> did actually do what I said.
>>>>>>
>>>>>> It might have done what you THOUGHT you were saying, but it
>>>>>> doesn't do what you ACTUALLY SAID.
>>>>>>
>>>>>
>>>>> I always claimed that H1(D,D) returns 1 and H(D,D) returns 0 and you
>>>>> always said it was impossible even though that is what actual code
>>>>> actually did. The code always discloses that H and H1 have their
>>>>> own address.
>>>>
>>>> No, we said it was impossible if they were the COMPUTATIONS you were
>>>> claiming them to be.
>>>>
>>>
>>> I never ever claimed that they were the same computation.
>>
>> yes you did. You problem don't remember because the word computation
>> doesn't seem to have a real meaning to you.
>>
>
> I have known the meaning of theory of computation meaning of computation
> for two years. It was very difficult to correctly adapt this to account
> for C functions. I finally did and had it checked over by quite a few
> people and for C functions to be computable functions they must be this
> notion of a pure function.
>
> https://en.wikipedia.org/wiki/Pure_function

On 3/12/2024 1:27 PM, immibis wrote:
> On 12/03/24 18:46, olcott wrote:
>> On 3/12/2024 12:36 PM, Richard Damon wrote:
>>> On 3/12/24 9:02 AM, olcott wrote:
>>>> On 3/11/2024 10:57 PM, Richard Damon wrote:
>>>>> On 3/11/24 8:37 PM, olcott wrote:
>>>>>> On 3/11/2024 10:31 PM, Richard Damon wrote:
>>>>>>> On 3/11/24 7:52 PM, olcott wrote:
>>>>>>>> On 3/11/2024 9:32 PM, immibis wrote:
>>>>>>>>> On 12/03/24 03:24, olcott wrote:
>>>>>>> \
>>>>>>>>>> Troll detected.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Once we understand that either YES or NO is the right answer
>>>>>>>>
>>>>>>>> Not for this decider/input question: Ĥ.H / ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>> For that decider/input question both YES and NO are the wrong
>>>>>>>> answer.
>>>>>>>
>>>>>>> The problem that you keeep on missing is that by the point we can
>>>>>>> ask this question, H and H^ are FULLY CODED, and thus we know
>>>>>>> their behavirs.
>>>>>>
>>>>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy // Ĥ applied to ⟨Ĥ⟩ halts
>>>>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>>>
>>>>>> Since you know that is false why lie?
>>>>>> ⊢* specifies an infinite set of encodings.
>>>>>
>>>>> Nope, read him again, not just skim and assume.
>>>>>
>>>>
>>>> *Here is the proof that I am correct*
>>>> ∀ H ∈ Turing_Machine_Deciders
>>>> ∃ TMD ∈ Turing_Machine_Descriptions  |
>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>
>>>>
>>>
>>> So, H, being an ELEMENT of Turing Machine Deciders, is a SINGLE
>>> INSTANCE of it, it is NOT the set itself.
>>
>> ∀ H ∈ Turing_Machine_Deciders *DOES NOT REFER TO A SINGLE INSTANCE*
>
> Yes it does. It means that if H is a single instance, no matter which
> one it is, the rest of the sentence is true.

*Richard updated his incorrect words*
On 3/12/2024 12:50 PM, Richard Damon wrote:
> Of COURSE "H" referes to just a single instance at a time.

More correctly
"H" refers to just a single instance at a time
of the elements of the infinite set specified by
∀ H ∈ Turing_Machine_Deciders

*This discussion has moved to my new post*
[Proving my 2004 claim that some decider/input pairs are incorrect
questions]

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/12/2024 2:08 PM, Ross Finlayson wrote:
> On 03/12/2024 08:52 AM, olcott wrote:
>
>> ∀ H ∈ Turing_Machine_Deciders
>> ∃ TMD ∈ Turing_Machine_Descriptions  |
>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>
>> There is some input TMD to every H such that
>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>
>> When we disallow decider/input pairs that are incorrect
>> questions where both YES and NO are the wrong answer
>> (the same way the ZFC disallowed self-referential sets) then
>> pathological inputs are not allowed to come into existence.
>>
>> Does the barber that shaves everyone that does not shave
>> themselves shave himself? is rejected as an incorrect question.
>> https://en.wikipedia.org/wiki/Barber_paradox#
>>
>
>
> People learn about ZFC when their mathematical curiousity
> brings them to questions of foundations.
>
> Then it's understood that it's an axiomatic theory,
> and that axioms are rules, and in an axiomatic theory,
> there result theorems derived from axioms, with axioms
> themselves being considered theorems, and that no theorems
> break any axioms.
>
> This is that axioms are somehow "true", and in the theory
> they're defined to be true, meaning they're never contradicted.
>
That is a great insight that you and Haskell Curry and
very few others agree on.
https://www.liarparadox.org/Haskell_Curry_45.pdf

> This is with the usual notion of contradiction and
> non-contradiction, about opposition and juxtaposition,
> where it's established usually that there is "true" or
> there is "false" and there is no middle ground, that
> a third case or tertium does not exist in the world,
> "tertium non datur", the laws of excluded middle, the
> principle of excluded middle, which in this axiomatic
> theory, is somehow always a theorem, as it results
> from the plain contemplation or consideration, that
> axioms are "true", in the theory, in what is almost
> always these days, a "meta-theory", that's undefined,
> except that axioms are true and none of their theorems
> contradict each other, saying "both true and false",
> which is tertium and non datur.
>
>
> So anyways ZFC is a theory where there's only one relation,
> it's "elt".  There's only one kind of object, it's "set".

I have no idea what "elt" means.

> For any given set P and any given set Q, either P elt Q
> or Q elt P, or neither, and, not both.  Then you might
> wonder, "well why not both?", and it's because, one of
> the axioms of ZFC is "not both".
>
> The axioms of ZFC either _expand_ comprehension, meaning,
> "no reason why not, so, it's so", or _restrict_ comprehension,
> meaning, "not: because this axiom is true in this theory,
> and says no".
>
> This introduces the concept of "independence" of axioms,
> that axioms that are independent say nothing about the
> theorems of otherwise independent axioms, and that axioms
> that are not independent, contradict each other, and that
> restriction is defined to always win, in any case of otherwise
> contradiction, when axioms aren't independent, in ZFC,
> that axioms of _restriction_ of comprehension aren't
> necessarily independent each other, or, the independent
> axioms of _expansion_ of comprehension.
>
>
>
> So, ZFC has various axioms of restriction of comprehension,
Yes, no set can be defined that contains itself.

> what boil down to the "Axiom of Regularity" also known as
> the "Axiom of Well-Foundedness" or "Axiom of Foundation",
Yes that one

> that for any two sets P elt Q or Q elt P, or neither,
> but not both.  This is where otherwise the axioms of
> expansion of comprehension, would otherwise result,
> "no reason why not", except that eventually certain
> theorems _desired_, of the theory, would either not be
> evident or would see contradictions.
>
>
> So, yeah, "ZFC solution to incorrect questions: reject them",
> is what's called "restriction of comprehension" and then
Great !!!

> what you do is get into all the various combinations of
> otherwise the expansion of comprehension, then get into
> why the models of the universe of the objects so related,
> is a wider theory where ZFC, or ZF, set theory, is variously
> considerable as either a fragment or an extension,
> the universe of the objects of ZF and ZFC set theories,
> in all theory in all comprehension according to what's, "true".
>
>
> Or, you know, "not false".
>
>
>
> So of course there are names for all these things and
> studies of all these things and criteria for all these
> things, what basically results for "Set Theory" what's
> called "Class/Set Distinction", a sort of, meta-theory,
NBG set theory
https://www.britannica.com/science/proper-class

> about set theory, where "elt" has a sort of complement
> "members" reflects "elt's sets are contained in sets"
> while "members' classes contain classes", that also the
> Class/Set distinction reflects objects as of the,
> "Inconsistent Multiplicities", of set theory, that
> one can relate to the, "Indeterminate Forms", of
> mathematics, that variously kind of do or don't have
> structure, "models" in the "model theory", where a
> theory has a model and a model has a theory is the meta-theory,
> helping explain why the wider world of theory knows that
> ZFC, or ZF, set theory, is a fragment of the universe of
> the objects of ZF set theory, which is its model in
> the wider model theory,
>
> Theory of ZF, of course, doesn't actually acknowledge,
> "a universe of objects of ZF, the domain of discourse"
> not so much as it's axiomatic "there is no universe of
> objects in ZF set theory", but that it's a theorem that's
> a consequence of restriction of comprehension, "foundational
> well-foundedness", which follows from otherwise a very
> useful result called "uncountability", .
>
> Now, "Regularity" means "the Rulial", it rules or defines
> a rule, so other theories otherwise about sets can have
> their own sorts rulial definitions, just saying that the
> theory where Well-Foundedness is rulial, just indicates
> that this is moreso "ZF's axiom that establishes ZF's
> main restriction of comprehension as ruliality, AoR
> the Axiom of Regularity, is particular to ZF, and it's
> called Well-Foundedness or Foundation, to reflect that
> theories without it are called Non-Well-Founded or
> sometimes Anti-Well-Founded, with regards to the regular
Yes I get that and have known about it for some years.

> or rulial the ruliality of what may be other theories,
> of sets, which are defined by one relation, elt".
>
>
>
> So anyways, there are others.

*Your knowledge of these things seem truly superb*
I had forgotten many of the details that you referenced.

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/12/24 11:16 AM, olcott wrote:
> On 3/12/2024 1:04 PM, Richard Damon wrote:

>> But SHOWING that something is logically impossible reveals the
>> limitations that were already there.
>>
>> Yes, the Halting Theorem doesn't MAKE the problem impossible, it shows
>> that it always was, and gives us knowledge of that.
>>
>
> The halting problem does not derive a limit to computation
> any more than the inability of CAD systems to draw square
> circles places a limit on computation.
>

But shows the limitation that already existed in compuations.

You don't seem to understand that.

Computation can only do what Computation do.

One of the LIMITS of Computations, is they can not determine is the
halting state us any and all algoritms + data.

They may be able to determine it for a subset of all possible,
but not for all possible.

That IS a limit of Computations REVEALED by the Halting Theorem.

On 03/12/2024 12:32 PM, olcott wrote:
> On 3/12/2024 2:08 PM, Ross Finlayson wrote:
>> On 03/12/2024 08:52 AM, olcott wrote:
>>
>>> ∀ H ∈ Turing_Machine_Deciders
>>> ∃ TMD ∈ Turing_Machine_Descriptions |
>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>
>>> There is some input TMD to every H such that
>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>
>>> When we disallow decider/input pairs that are incorrect
>>> questions where both YES and NO are the wrong answer
>>> (the same way the ZFC disallowed self-referential sets) then
>>> pathological inputs are not allowed to come into existence.
>>>
>>> Does the barber that shaves everyone that does not shave
>>> themselves shave himself? is rejected as an incorrect question.
>>> https://en.wikipedia.org/wiki/Barber_paradox#
>>>
>>
>>
>> People learn about ZFC when their mathematical curiousity
>> brings them to questions of foundations.
>>
>> Then it's understood that it's an axiomatic theory,
>> and that axioms are rules, and in an axiomatic theory,
>> there result theorems derived from axioms, with axioms
>> themselves being considered theorems, and that no theorems
>> break any axioms.
>>
>> This is that axioms are somehow "true", and in the theory
>> they're defined to be true, meaning they're never contradicted.
>>
> That is a great insight that you and Haskell Curry and
> very few others agree on.
> https://www.liarparadox.org/Haskell_Curry_45.pdf
>
>> This is with the usual notion of contradiction and
>> non-contradiction, about opposition and juxtaposition,
>> where it's established usually that there is "true" or
>> there is "false" and there is no middle ground, that
>> a third case or tertium does not exist in the world,
>> "tertium non datur", the laws of excluded middle, the
>> principle of excluded middle, which in this axiomatic
>> theory, is somehow always a theorem, as it results
>> from the plain contemplation or consideration, that
>> axioms are "true", in the theory, in what is almost
>> always these days, a "meta-theory", that's undefined,
>> except that axioms are true and none of their theorems
>> contradict each other, saying "both true and false",
>> which is tertium and non datur.
>>
>>
>> So anyways ZFC is a theory where there's only one relation,
>> it's "elt". There's only one kind of object, it's "set".
>
> I have no idea what "elt" means.
>
>> For any given set P and any given set Q, either P elt Q
>> or Q elt P, or neither, and, not both. Then you might
>> wonder, "well why not both?", and it's because, one of
>> the axioms of ZFC is "not both".
>>
>> The axioms of ZFC either _expand_ comprehension, meaning,
>> "no reason why not, so, it's so", or _restrict_ comprehension,
>> meaning, "not: because this axiom is true in this theory,
>> and says no".
>>
>> This introduces the concept of "independence" of axioms,
>> that axioms that are independent say nothing about the
>> theorems of otherwise independent axioms, and that axioms
>> that are not independent, contradict each other, and that
>> restriction is defined to always win, in any case of otherwise
>> contradiction, when axioms aren't independent, in ZFC,
>> that axioms of _restriction_ of comprehension aren't
>> necessarily independent each other, or, the independent
>> axioms of _expansion_ of comprehension.
>>
>>
>>
>> So, ZFC has various axioms of restriction of comprehension,
> Yes, no set can be defined that contains itself.
>
>> what boil down to the "Axiom of Regularity" also known as
>> the "Axiom of Well-Foundedness" or "Axiom of Foundation",
> Yes that one
>
>> that for any two sets P elt Q or Q elt P, or neither,
>> but not both. This is where otherwise the axioms of
>> expansion of comprehension, would otherwise result,
>> "no reason why not", except that eventually certain
>> theorems _desired_, of the theory, would either not be
>> evident or would see contradictions.
>>
>>
>> So, yeah, "ZFC solution to incorrect questions: reject them",
>> is what's called "restriction of comprehension" and then
> Great !!!
>
>> what you do is get into all the various combinations of
>> otherwise the expansion of comprehension, then get into
>> why the models of the universe of the objects so related,
>> is a wider theory where ZFC, or ZF, set theory, is variously
>> considerable as either a fragment or an extension,
>> the universe of the objects of ZF and ZFC set theories,
>> in all theory in all comprehension according to what's, "true".
>>
>>
>> Or, you know, "not false".
>>
>>
>>
>> So of course there are names for all these things and
>> studies of all these things and criteria for all these
>> things, what basically results for "Set Theory" what's
>> called "Class/Set Distinction", a sort of, meta-theory,
> NBG set theory
> https://www.britannica.com/science/proper-class
>
>> about set theory, where "elt" has a sort of complement
>> "members" reflects "elt's sets are contained in sets"
>> while "members' classes contain classes", that also the
>> Class/Set distinction reflects objects as of the,
>> "Inconsistent Multiplicities", of set theory, that
>> one can relate to the, "Indeterminate Forms", of
>> mathematics, that variously kind of do or don't have
>> structure, "models" in the "model theory", where a
>> theory has a model and a model has a theory is the meta-theory,
>> helping explain why the wider world of theory knows that
>> ZFC, or ZF, set theory, is a fragment of the universe of
>> the objects of ZF set theory, which is its model in
>> the wider model theory,
>>
>> Theory of ZF, of course, doesn't actually acknowledge,
>> "a universe of objects of ZF, the domain of discourse"
>> not so much as it's axiomatic "there is no universe of
>> objects in ZF set theory", but that it's a theorem that's
>> a consequence of restriction of comprehension, "foundational
>> well-foundedness", which follows from otherwise a very
>> useful result called "uncountability", .
>>
>> Now, "Regularity" means "the Rulial", it rules or defines
>> a rule, so other theories otherwise about sets can have
>> their own sorts rulial definitions, just saying that the
>> theory where Well-Foundedness is rulial, just indicates
>> that this is moreso "ZF's axiom that establishes ZF's
>> main restriction of comprehension as ruliality, AoR
>> the Axiom of Regularity, is particular to ZF, and it's
>> called Well-Foundedness or Foundation, to reflect that
>> theories without it are called Non-Well-Founded or
>> sometimes Anti-Well-Founded, with regards to the regular
> Yes I get that and have known about it for some years.
>
>> or rulial the ruliality of what may be other theories,
>> of sets, which are defined by one relation, elt".
>>
>>
>>
>> So anyways, there are others.
>
> *Your knowledge of these things seem truly superb*
> I had forgotten many of the details that you referenced.
>

Well, yeah, my mathematical curiousity brought me
to questions of foundations.

"Question" is a word, and it's kind of loaded. For
example, the German language has two different words
for "question-able", "fraglich", as, dubious, and,
"question-providing", "fragwuerdig", as, profound.

I.e., the profound, opens new questions, vis-a-vis
the interrogable, which may or may not.

I'm reading about this in Steiner on Heidegger as
of from old Roger Bacon. (I've sort of got a
trio of anti-Plato's in Wittgenstein, Nietzsche,
and Heidegger as various rejections of logical
positivism in the accommodation of logical positivism
after their compensation in search of teleology
after the breakwater of ontology, that of course
they're each strong Platonists in otherwise a
world of mundane, subjective, inauthentic,
Existentialists, the adrift logical positivists.
Of course that's for a strong logical positivism
overall, with re-attaching the silver thread, or cord.)

On 3/12/2024 2:59 PM, Ross Finlayson wrote:
> On 03/12/2024 12:32 PM, olcott wrote:
>> On 3/12/2024 2:08 PM, Ross Finlayson wrote:
>>> On 03/12/2024 08:52 AM, olcott wrote:
>>>
>>>> ∀ H ∈ Turing_Machine_Deciders
>>>> ∃ TMD ∈ Turing_Machine_Descriptions  |
>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>
>>>> There is some input TMD to every H such that
>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>
>>>> When we disallow decider/input pairs that are incorrect
>>>> questions where both YES and NO are the wrong answer
>>>> (the same way the ZFC disallowed self-referential sets) then
>>>> pathological inputs are not allowed to come into existence.
>>>>
>>>> Does the barber that shaves everyone that does not shave
>>>> themselves shave himself? is rejected as an incorrect question.
>>>> https://en.wikipedia.org/wiki/Barber_paradox#
>>>>
>>>
>>>
>>> People learn about ZFC when their mathematical curiousity
>>> brings them to questions of foundations.
>>>
>>> Then it's understood that it's an axiomatic theory,
>>> and that axioms are rules, and in an axiomatic theory,
>>> there result theorems derived from axioms, with axioms
>>> themselves being considered theorems, and that no theorems
>>> break any axioms.
>>>
>>> This is that axioms are somehow "true", and in the theory
>>> they're defined to be true, meaning they're never contradicted.
>>>
>> That is a great insight that you and Haskell Curry and
>> very few others agree on.
>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>
>>> This is with the usual notion of contradiction and
>>> non-contradiction, about opposition and juxtaposition,
>>> where it's established usually that there is "true" or
>>> there is "false" and there is no middle ground, that
>>> a third case or tertium does not exist in the world,
>>> "tertium non datur", the laws of excluded middle, the
>>> principle of excluded middle, which in this axiomatic
>>> theory, is somehow always a theorem, as it results
>>> from the plain contemplation or consideration, that
>>> axioms are "true", in the theory, in what is almost
>>> always these days, a "meta-theory", that's undefined,
>>> except that axioms are true and none of their theorems
>>> contradict each other, saying "both true and false",
>>> which is tertium and non datur.
>>>
>>>
>>> So anyways ZFC is a theory where there's only one relation,
>>> it's "elt".  There's only one kind of object, it's "set".
>>
>> I have no idea what "elt" means.
>>
>>> For any given set P and any given set Q, either P elt Q
>>> or Q elt P, or neither, and, not both.  Then you might
>>> wonder, "well why not both?", and it's because, one of
>>> the axioms of ZFC is "not both".
>>>
>>> The axioms of ZFC either _expand_ comprehension, meaning,
>>> "no reason why not, so, it's so", or _restrict_ comprehension,
>>> meaning, "not: because this axiom is true in this theory,
>>> and says no".
>>>
>>> This introduces the concept of "independence" of axioms,
>>> that axioms that are independent say nothing about the
>>> theorems of otherwise independent axioms, and that axioms
>>> that are not independent, contradict each other, and that
>>> restriction is defined to always win, in any case of otherwise
>>> contradiction, when axioms aren't independent, in ZFC,
>>> that axioms of _restriction_ of comprehension aren't
>>> necessarily independent each other, or, the independent
>>> axioms of _expansion_ of comprehension.
>>>
>>>
>>>
>>> So, ZFC has various axioms of restriction of comprehension,
>> Yes, no set can be defined that contains itself.
>>
>>> what boil down to the "Axiom of Regularity" also known as
>>> the "Axiom of Well-Foundedness" or "Axiom of Foundation",
>> Yes that one
>>
>>> that for any two sets P elt Q or Q elt P, or neither,
>>> but not both.  This is where otherwise the axioms of
>>> expansion of comprehension, would otherwise result,
>>> "no reason why not", except that eventually certain
>>> theorems _desired_, of the theory, would either not be
>>> evident or would see contradictions.
>>>
>>>
>>> So, yeah, "ZFC solution to incorrect questions: reject them",
>>> is what's called "restriction of comprehension" and then
>> Great !!!
>>
>>> what you do is get into all the various combinations of
>>> otherwise the expansion of comprehension, then get into
>>> why the models of the universe of the objects so related,
>>> is a wider theory where ZFC, or ZF, set theory, is variously
>>> considerable as either a fragment or an extension,
>>> the universe of the objects of ZF and ZFC set theories,
>>> in all theory in all comprehension according to what's, "true".
>>>
>>>
>>> Or, you know, "not false".
>>>
>>>
>>>
>>> So of course there are names for all these things and
>>> studies of all these things and criteria for all these
>>> things, what basically results for "Set Theory" what's
>>> called "Class/Set Distinction", a sort of, meta-theory,
>> NBG set theory
>> https://www.britannica.com/science/proper-class
>>
>>> about set theory, where "elt" has a sort of complement
>>> "members" reflects "elt's sets are contained in sets"
>>> while "members' classes contain classes", that also the
>>> Class/Set distinction reflects objects as of the,
>>> "Inconsistent Multiplicities", of set theory, that
>>> one can relate to the, "Indeterminate Forms", of
>>> mathematics, that variously kind of do or don't have
>>> structure, "models" in the "model theory", where a
>>> theory has a model and a model has a theory is the meta-theory,
>>> helping explain why the wider world of theory knows that
>>> ZFC, or ZF, set theory, is a fragment of the universe of
>>> the objects of ZF set theory, which is its model in
>>> the wider model theory,
>>>
>>> Theory of ZF, of course, doesn't actually acknowledge,
>>> "a universe of objects of ZF, the domain of discourse"
>>> not so much as it's axiomatic "there is no universe of
>>> objects in ZF set theory", but that it's a theorem that's
>>> a consequence of restriction of comprehension, "foundational
>>> well-foundedness", which follows from otherwise a very
>>> useful result called "uncountability", .
>>>
>>> Now, "Regularity" means "the Rulial", it rules or defines
>>> a rule, so other theories otherwise about sets can have
>>> their own sorts rulial definitions, just saying that the
>>> theory where Well-Foundedness is rulial, just indicates
>>> that this is moreso "ZF's axiom that establishes ZF's
>>> main restriction of comprehension as ruliality, AoR
>>> the Axiom of Regularity, is particular to ZF, and it's
>>> called Well-Foundedness or Foundation, to reflect that
>>> theories without it are called Non-Well-Founded or
>>> sometimes Anti-Well-Founded, with regards to the regular
>> Yes I get that and have known about it for some years.
>>
>>> or rulial the ruliality of what may be other theories,
>>> of sets, which are defined by one relation, elt".
>>>
>>>
>>>
>>> So anyways, there are others.
>>
>> *Your knowledge of these things seem truly superb*
>> I had forgotten many of the details that you referenced.
>>
>
> Well, yeah, my mathematical curiousity brought me
> to questions of foundations.
>
I love foundations because I noticed errors in the understanding
of the notion of true_on_the_basis_of_semantic_meaning(x) back
in 2004.

On 03/12/2024 01:28 PM, olcott wrote:
> On 3/12/2024 2:59 PM, Ross Finlayson wrote:
>> On 03/12/2024 12:32 PM, olcott wrote:
>>> On 3/12/2024 2:08 PM, Ross Finlayson wrote:
>>>> On 03/12/2024 08:52 AM, olcott wrote:
>>>>
>>>>> ∀ H ∈ Turing_Machine_Deciders
>>>>> ∃ TMD ∈ Turing_Machine_Descriptions |
>>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>>
>>>>> There is some input TMD to every H such that
>>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>>
>>>>> When we disallow decider/input pairs that are incorrect
>>>>> questions where both YES and NO are the wrong answer
>>>>> (the same way the ZFC disallowed self-referential sets) then
>>>>> pathological inputs are not allowed to come into existence.
>>>>>
>>>>> Does the barber that shaves everyone that does not shave
>>>>> themselves shave himself? is rejected as an incorrect question.
>>>>> https://en.wikipedia.org/wiki/Barber_paradox#
>>>>>
>>>>
>>>>
>>>> People learn about ZFC when their mathematical curiousity
>>>> brings them to questions of foundations.
>>>>
>>>> Then it's understood that it's an axiomatic theory,
>>>> and that axioms are rules, and in an axiomatic theory,
>>>> there result theorems derived from axioms, with axioms
>>>> themselves being considered theorems, and that no theorems
>>>> break any axioms.
>>>>
>>>> This is that axioms are somehow "true", and in the theory
>>>> they're defined to be true, meaning they're never contradicted.
>>>>
>>> That is a great insight that you and Haskell Curry and
>>> very few others agree on.
>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>
>>>> This is with the usual notion of contradiction and
>>>> non-contradiction, about opposition and juxtaposition,
>>>> where it's established usually that there is "true" or
>>>> there is "false" and there is no middle ground, that
>>>> a third case or tertium does not exist in the world,
>>>> "tertium non datur", the laws of excluded middle, the
>>>> principle of excluded middle, which in this axiomatic
>>>> theory, is somehow always a theorem, as it results
>>>> from the plain contemplation or consideration, that
>>>> axioms are "true", in the theory, in what is almost
>>>> always these days, a "meta-theory", that's undefined,
>>>> except that axioms are true and none of their theorems
>>>> contradict each other, saying "both true and false",
>>>> which is tertium and non datur.
>>>>
>>>>
>>>> So anyways ZFC is a theory where there's only one relation,
>>>> it's "elt". There's only one kind of object, it's "set".
>>>
>>> I have no idea what "elt" means.
>>>
>>>> For any given set P and any given set Q, either P elt Q
>>>> or Q elt P, or neither, and, not both. Then you might
>>>> wonder, "well why not both?", and it's because, one of
>>>> the axioms of ZFC is "not both".
>>>>
>>>> The axioms of ZFC either _expand_ comprehension, meaning,
>>>> "no reason why not, so, it's so", or _restrict_ comprehension,
>>>> meaning, "not: because this axiom is true in this theory,
>>>> and says no".
>>>>
>>>> This introduces the concept of "independence" of axioms,
>>>> that axioms that are independent say nothing about the
>>>> theorems of otherwise independent axioms, and that axioms
>>>> that are not independent, contradict each other, and that
>>>> restriction is defined to always win, in any case of otherwise
>>>> contradiction, when axioms aren't independent, in ZFC,
>>>> that axioms of _restriction_ of comprehension aren't
>>>> necessarily independent each other, or, the independent
>>>> axioms of _expansion_ of comprehension.
>>>>
>>>>
>>>>
>>>> So, ZFC has various axioms of restriction of comprehension,
>>> Yes, no set can be defined that contains itself.
>>>
>>>> what boil down to the "Axiom of Regularity" also known as
>>>> the "Axiom of Well-Foundedness" or "Axiom of Foundation",
>>> Yes that one
>>>
>>>> that for any two sets P elt Q or Q elt P, or neither,
>>>> but not both. This is where otherwise the axioms of
>>>> expansion of comprehension, would otherwise result,
>>>> "no reason why not", except that eventually certain
>>>> theorems _desired_, of the theory, would either not be
>>>> evident or would see contradictions.
>>>>
>>>>
>>>> So, yeah, "ZFC solution to incorrect questions: reject them",
>>>> is what's called "restriction of comprehension" and then
>>> Great !!!
>>>
>>>> what you do is get into all the various combinations of
>>>> otherwise the expansion of comprehension, then get into
>>>> why the models of the universe of the objects so related,
>>>> is a wider theory where ZFC, or ZF, set theory, is variously
>>>> considerable as either a fragment or an extension,
>>>> the universe of the objects of ZF and ZFC set theories,
>>>> in all theory in all comprehension according to what's, "true".
>>>>
>>>>
>>>> Or, you know, "not false".
>>>>
>>>>
>>>>
>>>> So of course there are names for all these things and
>>>> studies of all these things and criteria for all these
>>>> things, what basically results for "Set Theory" what's
>>>> called "Class/Set Distinction", a sort of, meta-theory,
>>> NBG set theory
>>> https://www.britannica.com/science/proper-class
>>>
>>>> about set theory, where "elt" has a sort of complement
>>>> "members" reflects "elt's sets are contained in sets"
>>>> while "members' classes contain classes", that also the
>>>> Class/Set distinction reflects objects as of the,
>>>> "Inconsistent Multiplicities", of set theory, that
>>>> one can relate to the, "Indeterminate Forms", of
>>>> mathematics, that variously kind of do or don't have
>>>> structure, "models" in the "model theory", where a
>>>> theory has a model and a model has a theory is the meta-theory,
>>>> helping explain why the wider world of theory knows that
>>>> ZFC, or ZF, set theory, is a fragment of the universe of
>>>> the objects of ZF set theory, which is its model in
>>>> the wider model theory,
>>>>
>>>> Theory of ZF, of course, doesn't actually acknowledge,
>>>> "a universe of objects of ZF, the domain of discourse"
>>>> not so much as it's axiomatic "there is no universe of
>>>> objects in ZF set theory", but that it's a theorem that's
>>>> a consequence of restriction of comprehension, "foundational
>>>> well-foundedness", which follows from otherwise a very
>>>> useful result called "uncountability", .
>>>>
>>>> Now, "Regularity" means "the Rulial", it rules or defines
>>>> a rule, so other theories otherwise about sets can have
>>>> their own sorts rulial definitions, just saying that the
>>>> theory where Well-Foundedness is rulial, just indicates
>>>> that this is moreso "ZF's axiom that establishes ZF's
>>>> main restriction of comprehension as ruliality, AoR
>>>> the Axiom of Regularity, is particular to ZF, and it's
>>>> called Well-Foundedness or Foundation, to reflect that
>>>> theories without it are called Non-Well-Founded or
>>>> sometimes Anti-Well-Founded, with regards to the regular
>>> Yes I get that and have known about it for some years.
>>>
>>>> or rulial the ruliality of what may be other theories,
>>>> of sets, which are defined by one relation, elt".
>>>>
>>>>
>>>>
>>>> So anyways, there are others.
>>>
>>> *Your knowledge of these things seem truly superb*
>>> I had forgotten many of the details that you referenced.
>>>
>>
>> Well, yeah, my mathematical curiousity brought me
>> to questions of foundations.
>>
> I love foundations because I noticed errors in the understanding
> of the notion of true_on_the_basis_of_semantic_meaning(x) back
> in 2004.
>
>> "Question" is a word, and it's kind of loaded. For
>> example, the German language has two different words
>> for "question-able", "fraglich", as, dubious, and,
>> "question-providing", "fragwuerdig", as, profound.
>>
>> I.e., the profound, opens new questions, vis-a-vis
>> the interrogable, which may or may not.
>>
>> I'm reading about this in Steiner on Heidegger as
>> of from old Roger Bacon. (I've sort of got a
>> trio of anti-Plato's in Wittgenstein, Nietzsche,
>> and Heidegger as various rejections of logical
>> positivism in the accommodation of logical positivism
> The coherent notion of true_on_the_basis_of_semantic_meaning(x)
> seems to affirm logical positivism over Gödel.
>
>> after their compensation in search of teleology
>> after the breakwater of ontology, that of course
>> they're each strong Platonists in otherwise a
>> world of mundane, subjective, inauthentic,
>> Existentialists, the adrift logical positivists.
>> Of course that's for a strong logical positivism
>> overall, with re-attaching the silver thread, or cord.)
>>
>>
>>
>> The universe of logical and mathematical objects
>> is its own, intuitively structured, thing. All
>
> Yes, hence true_on_the_basis_of_semantic_meaning(x) does
> not apply to reality only mental models of reality.
>
>> matters of relation are assumed to exist in it,
>> both the concrete as realizable mathematically,
>> and of course all suchly matters of mathematical
>> or logical consistency, and inconsistency, so effable,
>> or ineffable.
>>
> Perhaps with true_on_the_basis_of_semantic_meaning(x)
> it becomes effable.
>
>> Then, humans or objectively thinkers, or course have
>> limited or finite means, and, communication has its
>> own finite yet open means.
>>
> Yet with Montague semantics can be formalized to eliminate
> all ambiguity.
>
>>
>>
>> I thank you for your compliments, affinity,
>> then would suggest that you look to the fuller
>> complements, complementarity, as what such
>> notions of the fuller dialectic, arrive largely
>> as fundamentally from "complementary duals",
>> that not only is something filled, also filling.
>>
> I can only understand those aspects of my ideas that you
> directly referenced that I acknowledged that I understood.
> This was much more tan I expected to understand. I had
> forgotten some of the key details that you referenced.
>
>> I.e., "is there an axiom?" "Inverse".
>>
>> Or, you know, yes and no.
>>
>>
>>
>> You can find some hundred hours or readings
>> and lectures on my youtube channel as of
>> like https youtube /@rossfinlayson .
>>
>> Or, you know, the 10,000's posts to sci.math.
>