On Sunday, April 10, 2022 at 11:57:10 PM UTC-4, olcott wrote:
> On 4/10/2022 10:32 PM, Dennis Bush wrote:
> > On Sunday, April 10, 2022 at 11:29:34 PM UTC-4, olcott wrote:
> >> On 4/10/2022 10:22 PM, Dennis Bush wrote:
> >>> On Sunday, April 10, 2022 at 11:19:51 PM UTC-4, olcott wrote:
> >>>> On 4/10/2022 10:14 PM, Dennis Bush wrote:
> >>>>> On Sunday, April 10, 2022 at 11:06:31 PM UTC-4, olcott wrote:
> >>>>>> On 4/10/2022 10:00 PM, Dennis Bush wrote:
> >>>>>>> On Sunday, April 10, 2022 at 10:53:38 PM UTC-4, olcott wrote:
> >>>>>> I know that you are not so bobble headed that you would forget this:
> >>>>>> A simulating halt decider must continue to simulate its input until it
> >>>>>> has proof that this simulation would never end.
> >>>>>>> You don't seem to agree with that, which would mean that your claim that "the actual behavior of the actual simulated input is the ULTIMATE MEASURE of the correctness of any halt decider" doesn't make sense.
> >>>>>> No it would be that you are playing head games and ignoring this criteria:
> >>>>>> A simulating halt decider must continue to simulate its input until it
> >>>>>> has proof that this simulation would never end.
> >>>>>> I may ignore what you say after this.
> >>>>>
> >>>>> Since Ha3 is defined to simulate for exactly 3 steps, it can't really be "changed".
> >>>> The change is that you acknowledge that you already know how
> >>>> ridiculously lame and condescending your Ha3 example is.
> >>>>
> >>>
> >>> If we defined another simulating halt decider called Ha7 which simulates for 7 steps before aborting, and we give it <N><5> as input, we can see that it simulates its input to a final state of <N.qy> and reports halting.
> >>>
> >>> Would you then agree that Ha7 accepting <N><5> after simulating that input to its final state of <N.qy> is proof that Ha3 was incorrect to reject <N><5>?
> >> OTHERWISE ITS WRONG
> >> A simulating halt decider must continue to simulate its input until it
> >> has proof that this simulation would never end.
> >
> > Then you would agree that
> If it isn't in this category I am not discussing it:
> A simulating halt decider must continue to simulate its input until it
> has proof that this simulation would never end.

Which would mean that Ha7 accepting <N><5> after simulating that input to its final state of <N.qy> is proof that Ha3 was incorrect to reject <N><5>.

Agreed?

On Monday, 11 April 2022 at 12:01:53 UTC+1, richar...@gmail.com wrote:
> On 4/11/22 12:32 AM, olcott wrote:
> > On 4/10/2022 11:26 PM, André G. Isaak wrote:
> >> On 2022-04-10 22:15, olcott wrote:
> >>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
> >>>> On 2022-04-10 21:01, olcott wrote:
> >>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
> >>>>>> On 2022-04-10 20:38, olcott wrote:
> >>>>>>
> >>>>>>> That is too far off topic. I have been talking circles with Ben
> >>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
> >>>>>>> trimmed off of the decision tree.
> >>>>>>>
> >>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
> >>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
> >>>>>>
> >>>>>> And we're back to the meaningless notation again.
> >>>>>>
> >>>>>> You are truly incapable of learning anything.
> >>>>>>
> >>>>>> André
> >>>>>>
> >>>>>
> >>>>> You can't remember the details between posts? Everyone else can.
> >>>>
> >>>> I can remember. But that doesn't change the fact that the notation
> >>>> you write above is meaningless without a condition specified.
> >>>>
> >>>> You claim you want to know how to present your ideas so you will be
> >>>> taken seriously. I'm trying to help with that. When someone points
> >>>> out an error in your notation, why insist on continuing to use the
> >>>> broken notation?
> >>>>
> >>>> André
> >>>
> >>> I have a single primary goal that supersedes and overrides all other
> >>> goals, get mutual agreement on my current stage of progress.
> >>
> >> I thought your goal was to eventually publish, which requires learning
> >> to use notation properly so you don't look like an illiterate crank.
> >>
> >>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
> >>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach
> >>> its own final state.
> >>>
> >>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
> >>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
> >>> reach its own final state.
> >>>
> >>> embedded_H correctly rejects its input.
> >>
> >> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
> >
> > The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded in Ĥ
> > is the only thing that is being examined.
> And the CORRECT simulation of <H^> <H^> will HALT if the copy of H that
> is embedded in H^ aborts its simulation and goes to H.Qn.
>
> Thus
> >
> > It is self-evident that the actual behavior of the actual simulated
> > input is the ULTIMATE MEASURE of the correctness of any halt decider.
> Right, and Halting is not the Non-Halting that an H that goes to H.Qn is
> claiming.
> >
> > In epistemology (theory of knowledge), a self-evident proposition is a
> > proposition that is known to be true by understanding its meaning
> > without proof... https://en.wikipedia.org/wiki/Self-evidence
> >
> >
> Right, it is self-evident that H is wrong, since the input doesn't do
> what it said it does.
>
> Note, self-evident can be tricky or you can persuade yourself that
> something that is wrong is actually true. That gives rise to the errors
> like the self-evident truth the Achilles can't pass the Tortoise that
> Zeno was able to show 'self-evidently'.
>
Except that Zeno was fully aware that Achilles would overtake the tortoise.
The Greeks staged regular athletics competitions, and he must have
observed a faster runner overhaul a slower one.

On Monday, April 11, 2022 at 12:33:06 AM UTC-4, olcott wrote:
> On 4/10/2022 11:26 PM, André G. Isaak wrote:
> > On 2022-04-10 22:15, olcott wrote:
> >> On 4/10/2022 11:11 PM, André G. Isaak wrote:
> >>> On 2022-04-10 21:01, olcott wrote:
> >>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
> >>>>> On 2022-04-10 20:38, olcott wrote:
> >>>>>
> >>>>>> That is too far off topic. I have been talking circles with Ben
> >>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
> >>>>>> trimmed off of the decision tree.
> >>>>>>
> >>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
> >>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
> >>>>>
> >>>>> And we're back to the meaningless notation again.
> >>>>>
> >>>>> You are truly incapable of learning anything.
> >>>>>
> >>>>> André
> >>>>>
> >>>>
> >>>> You can't remember the details between posts? Everyone else can.
> >>>
> >>> I can remember. But that doesn't change the fact that the notation
> >>> you write above is meaningless without a condition specified.
> >>>
> >>> You claim you want to know how to present your ideas so you will be
> >>> taken seriously. I'm trying to help with that. When someone points
> >>> out an error in your notation, why insist on continuing to use the
> >>> broken notation?
> >>>
> >>> André
> >>
> >> I have a single primary goal that supersedes and overrides all other
> >> goals, get mutual agreement on my current stage of progress.
> >
> > I thought your goal was to eventually publish, which requires learning
> > to use notation properly so you don't look like an illiterate crank.
> >
> >> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
> >> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach its
> >> own final state.
> >>
> >> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
> >> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
> >> reach its own final state.
> >>
> >> embedded_H correctly rejects its input.
> >
> > No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded in Ĥ
> is the only thing that is being examined.
> It is self-evident that the actual behavior of the actual simulated
> input is the ULTIMATE MEASURE of the correctness of any halt decider.

We've already established that that criteria is invalid because it concludes that Ha3 is correct to reject <N><5> because "the actual behavior of the actual simulated input" is non-halting by this criteria.

You came up with a better one:

A simulating halt decider must continue to simulate its input until it
has proof that this simulation would never end.

Put another way:

If one simulating halt decider reports that an input is non-halting but a second simulating halt decider simulates that same input to completion and reports halting, then the first was not correct to report non-halting.

Which would mean that Ha7 accepting <N><5> after simulating that input to its final state of <N.qy> is proof that Ha3 was incorrect to reject <N><5>.

Agreed?

On 4/11/22 7:48 AM, Malcolm McLean wrote:
> On Monday, 11 April 2022 at 12:01:53 UTC+1, richar...@gmail.com wrote:
>> On 4/11/22 12:32 AM, olcott wrote:
>>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
>>>> On 2022-04-10 22:15, olcott wrote:
>>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
>>>>>> On 2022-04-10 21:01, olcott wrote:
>>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
>>>>>>>> On 2022-04-10 20:38, olcott wrote:
>>>>>>>>
>>>>>>>>> That is too far off topic. I have been talking circles with Ben
>>>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
>>>>>>>>> trimmed off of the decision tree.
>>>>>>>>>
>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
>>>>>>>>
>>>>>>>> And we're back to the meaningless notation again.
>>>>>>>>
>>>>>>>> You are truly incapable of learning anything.
>>>>>>>>
>>>>>>>> André
>>>>>>>>
>>>>>>>
>>>>>>> You can't remember the details between posts? Everyone else can.
>>>>>>
>>>>>> I can remember. But that doesn't change the fact that the notation
>>>>>> you write above is meaningless without a condition specified.
>>>>>>
>>>>>> You claim you want to know how to present your ideas so you will be
>>>>>> taken seriously. I'm trying to help with that. When someone points
>>>>>> out an error in your notation, why insist on continuing to use the
>>>>>> broken notation?
>>>>>>
>>>>>> André
>>>>>
>>>>> I have a single primary goal that supersedes and overrides all other
>>>>> goals, get mutual agreement on my current stage of progress.
>>>>
>>>> I thought your goal was to eventually publish, which requires learning
>>>> to use notation properly so you don't look like an illiterate crank.
>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach
>>>>> its own final state.
>>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
>>>>> reach its own final state.
>>>>>
>>>>> embedded_H correctly rejects its input.
>>>>
>>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
>>>
>>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded in Ĥ
>>> is the only thing that is being examined.
>> And the CORRECT simulation of <H^> <H^> will HALT if the copy of H that
>> is embedded in H^ aborts its simulation and goes to H.Qn.
>>
>> Thus
>>>
>>> It is self-evident that the actual behavior of the actual simulated
>>> input is the ULTIMATE MEASURE of the correctness of any halt decider.
>> Right, and Halting is not the Non-Halting that an H that goes to H.Qn is
>> claiming.
>>>
>>> In epistemology (theory of knowledge), a self-evident proposition is a
>>> proposition that is known to be true by understanding its meaning
>>> without proof... https://en.wikipedia.org/wiki/Self-evidence
>>>
>>>
>> Right, it is self-evident that H is wrong, since the input doesn't do
>> what it said it does.
>>
>> Note, self-evident can be tricky or you can persuade yourself that
>> something that is wrong is actually true. That gives rise to the errors
>> like the self-evident truth the Achilles can't pass the Tortoise that
>> Zeno was able to show 'self-evidently'.
>>
> Except that Zeno was fully aware that Achilles would overtake the tortoise.
> The Greeks staged regular athletics competitions, and he must have
> observed a faster runner overhaul a slower one.

Yes, he saw 'reality' but he also saw the 'self-evident' proof that this
couldn't happen!

Thus PROVING that 'self-evident' isn't actually a valid form of argument.

It also shows that PO doesn't actually understand what epistemology
means with that statement, which isn't strange since he doesn't
understand a lot of things that are clearly stated because he filters
reality through his POOP colored glasses.

On 4/11/22 7:50 AM, Dennis Bush wrote:
> On Monday, April 11, 2022 at 12:33:06 AM UTC-4, olcott wrote:
>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
>>> On 2022-04-10 22:15, olcott wrote:
>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
>>>>> On 2022-04-10 21:01, olcott wrote:
>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
>>>>>>> On 2022-04-10 20:38, olcott wrote:
>>>>>>>
>>>>>>>> That is too far off topic. I have been talking circles with Ben
>>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
>>>>>>>> trimmed off of the decision tree.
>>>>>>>>
>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
>>>>>>>
>>>>>>> And we're back to the meaningless notation again.
>>>>>>>
>>>>>>> You are truly incapable of learning anything.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> You can't remember the details between posts? Everyone else can.
>>>>>
>>>>> I can remember. But that doesn't change the fact that the notation
>>>>> you write above is meaningless without a condition specified.
>>>>>
>>>>> You claim you want to know how to present your ideas so you will be
>>>>> taken seriously. I'm trying to help with that. When someone points
>>>>> out an error in your notation, why insist on continuing to use the
>>>>> broken notation?
>>>>>
>>>>> André
>>>>
>>>> I have a single primary goal that supersedes and overrides all other
>>>> goals, get mutual agreement on my current stage of progress.
>>>
>>> I thought your goal was to eventually publish, which requires learning
>>> to use notation properly so you don't look like an illiterate crank.
>>>
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach its
>>>> own final state.
>>>>
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
>>>> reach its own final state.
>>>>
>>>> embedded_H correctly rejects its input.
>>>
>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded in Ĥ
>> is the only thing that is being examined.
>> It is self-evident that the actual behavior of the actual simulated
>> input is the ULTIMATE MEASURE of the correctness of any halt decider.
>
> We've already established that that criteria is invalid because it concludes that Ha3 is correct to reject <N><5> because "the actual behavior of the actual simulated input" is non-halting by this criteria.

Actually, PO's statement CAN be true, when using the right definition of
all the words. This is one of his standard practices. Make a statement
that can be correct when correctly interpret, then change (slightly) the
meaning of parts of it to make it show his falsehood. Then when you
object, he goes back and shows a trivial case that fits in the overlap
to 'prove' that his reasoning is correct.

The 'ACTUAL BEHAVIOR' of the input, is by definition the behavior of the
machine it represents (H^ applied to <H^> in this case), and that
behavior CAN be determined by a simulation (with a UTM)

The problem is that H can't actually determine the right answer that way
as it takes 'too long' as the time to determine becomes unbounded when
it needs to answer in finite time.

PO has a number of blind spots in his ability to think, and one of them
is not understanding the nature of non-finite quantities, thinking they
act just like finite values.

>
> You came up with a better one:
>
> A simulating halt decider must continue to simulate its input until it
> has proof that this simulation would never end.
>
> Put another way:
>
> If one simulating halt decider reports that an input is non-halting but a second simulating halt decider simulates that same input to completion and reports halting, then the first was not correct to report non-halting.
>
> Which would mean that Ha7 accepting <N><5> after simulating that input to its final state of <N.qy> is proof that Ha3 was incorrect to reject <N><5>.
>
> Agreed?

On Monday, 11 April 2022 at 12:59:41 UTC+1, richar...@gmail.com wrote:
> On 4/11/22 7:48 AM, Malcolm McLean wrote:
> > On Monday, 11 April 2022 at 12:01:53 UTC+1, richar...@gmail.com wrote:
> >> On 4/11/22 12:32 AM, olcott wrote:
> >>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
> >>>> On 2022-04-10 22:15, olcott wrote:
> >>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
> >>>>>> On 2022-04-10 21:01, olcott wrote:
> >>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
> >>>>>>>> On 2022-04-10 20:38, olcott wrote:
> >>>>>>>>
> >>>>>>>>> That is too far off topic. I have been talking circles with Ben
> >>>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
> >>>>>>>>> trimmed off of the decision tree.
> >>>>>>>>>
> >>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
> >>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
> >>>>>>>>
> >>>>>>>> And we're back to the meaningless notation again.
> >>>>>>>>
> >>>>>>>> You are truly incapable of learning anything.
> >>>>>>>>
> >>>>>>>> André
> >>>>>>>>
> >>>>>>>
> >>>>>>> You can't remember the details between posts? Everyone else can.
> >>>>>>
> >>>>>> I can remember. But that doesn't change the fact that the notation
> >>>>>> you write above is meaningless without a condition specified.
> >>>>>>
> >>>>>> You claim you want to know how to present your ideas so you will be
> >>>>>> taken seriously. I'm trying to help with that. When someone points
> >>>>>> out an error in your notation, why insist on continuing to use the
> >>>>>> broken notation?
> >>>>>>
> >>>>>> André
> >>>>>
> >>>>> I have a single primary goal that supersedes and overrides all other
> >>>>> goals, get mutual agreement on my current stage of progress.
> >>>>
> >>>> I thought your goal was to eventually publish, which requires learning
> >>>> to use notation properly so you don't look like an illiterate crank.
> >>>>
> >>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
> >>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach
> >>>>> its own final state.
> >>>>>
> >>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
> >>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
> >>>>> reach its own final state.
> >>>>>
> >>>>> embedded_H correctly rejects its input.
> >>>>
> >>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
> >>>
> >>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded in Ĥ
> >>> is the only thing that is being examined.
> >> And the CORRECT simulation of <H^> <H^> will HALT if the copy of H that
> >> is embedded in H^ aborts its simulation and goes to H.Qn.
> >>
> >> Thus
> >>>
> >>> It is self-evident that the actual behavior of the actual simulated
> >>> input is the ULTIMATE MEASURE of the correctness of any halt decider.
> >> Right, and Halting is not the Non-Halting that an H that goes to H.Qn is
> >> claiming.
> >>>
> >>> In epistemology (theory of knowledge), a self-evident proposition is a
> >>> proposition that is known to be true by understanding its meaning
> >>> without proof... https://en.wikipedia.org/wiki/Self-evidence
> >>>
> >>>
> >> Right, it is self-evident that H is wrong, since the input doesn't do
> >> what it said it does.
> >>
> >> Note, self-evident can be tricky or you can persuade yourself that
> >> something that is wrong is actually true. That gives rise to the errors
> >> like the self-evident truth the Achilles can't pass the Tortoise that
> >> Zeno was able to show 'self-evidently'.
> >>
> > Except that Zeno was fully aware that Achilles would overtake the tortoise.
> > The Greeks staged regular athletics competitions, and he must have
> > observed a faster runner overhaul a slower one.
> Yes, he saw 'reality' but he also saw the 'self-evident' proof that this
> couldn't happen!
>
> Thus PROVING that 'self-evident' isn't actually a valid form of argument.
>
> It also shows that PO doesn't actually understand what epistemology
> means with that statement, which isn't strange since he doesn't
> understand a lot of things that are clearly stated because he filters
> reality through his POOP colored glasses.
>
Whilst I don't know much about Zeno's thought except the basics, he
was probably trying to work out the nature of a mathematical proof.
The Greeks had started to develop mathematical proofs, but they didn't
fully understand what they were. So a "proof" of a manifest absurdity
was of interest.

It's actually harder than it first appears to say what constitutes a proof.
So whilst individual proofs are taught at high school level, children
are not usually taught how to set out a proof formally. And of course they
are not expected to develop their own proofs. That's why someone
without a maths degree can struggle.

On 2022-04-11 12:14:11 +0000, Malcolm McLean said:

> Whilst I don't know much about Zeno's thought except the basics, he
> was probably trying to work out the nature of a mathematical proof.
> The Greeks had started to develop mathematical proofs, but they didn't
> fully understand what they were. So a "proof" of a manifest absurdity
> was of interest.

At the time many considered self-evident that one cannot do what requires
that an infinite number of other things are done before. Zeno proved
that Achilles must do an infinte number of other things before he can
catch the tortoise. As this contradicts what is observed, the conclusion
is that either a proven claim or an observed fact can be false. Many
philosophers considered proofs so convincing that they concluded that
observations must be false, and e.g. that there is no motion. Aristotle
disagreed: time is infinitely divisible, so Achilles can first do an
infinite number of other things and then catch the tortoise.

Mikko

On 4/11/2022 7:14 AM, Malcolm McLean wrote:
> On Monday, 11 April 2022 at 12:59:41 UTC+1, richar...@gmail.com wrote:
>> On 4/11/22 7:48 AM, Malcolm McLean wrote:
>>> On Monday, 11 April 2022 at 12:01:53 UTC+1, richar...@gmail.com wrote:
>>>> On 4/11/22 12:32 AM, olcott wrote:
>>>>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
>>>>>> On 2022-04-10 22:15, olcott wrote:
>>>>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
>>>>>>>> On 2022-04-10 21:01, olcott wrote:
>>>>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
>>>>>>>>>> On 2022-04-10 20:38, olcott wrote:
>>>>>>>>>>
>>>>>>>>>>> That is too far off topic. I have been talking circles with Ben
>>>>>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
>>>>>>>>>>> trimmed off of the decision tree.
>>>>>>>>>>>
>>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
>>>>>>>>>>
>>>>>>>>>> And we're back to the meaningless notation again.
>>>>>>>>>>
>>>>>>>>>> You are truly incapable of learning anything.
>>>>>>>>>>
>>>>>>>>>> André
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You can't remember the details between posts? Everyone else can.
>>>>>>>>
>>>>>>>> I can remember. But that doesn't change the fact that the notation
>>>>>>>> you write above is meaningless without a condition specified.
>>>>>>>>
>>>>>>>> You claim you want to know how to present your ideas so you will be
>>>>>>>> taken seriously. I'm trying to help with that. When someone points
>>>>>>>> out an error in your notation, why insist on continuing to use the
>>>>>>>> broken notation?
>>>>>>>>
>>>>>>>> André
>>>>>>>
>>>>>>> I have a single primary goal that supersedes and overrides all other
>>>>>>> goals, get mutual agreement on my current stage of progress.
>>>>>>
>>>>>> I thought your goal was to eventually publish, which requires learning
>>>>>> to use notation properly so you don't look like an illiterate crank.
>>>>>>
>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach
>>>>>>> its own final state.
>>>>>>>
>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
>>>>>>> reach its own final state.
>>>>>>>
>>>>>>> embedded_H correctly rejects its input.
>>>>>>
>>>>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
>>>>>
>>>>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded in Ĥ
>>>>> is the only thing that is being examined.
>>>> And the CORRECT simulation of <H^> <H^> will HALT if the copy of H that
>>>> is embedded in H^ aborts its simulation and goes to H.Qn.
>>>>
>>>> Thus
>>>>>
>>>>> It is self-evident that the actual behavior of the actual simulated
>>>>> input is the ULTIMATE MEASURE of the correctness of any halt decider.
>>>> Right, and Halting is not the Non-Halting that an H that goes to H.Qn is
>>>> claiming.
>>>>>
>>>>> In epistemology (theory of knowledge), a self-evident proposition is a
>>>>> proposition that is known to be true by understanding its meaning
>>>>> without proof... https://en.wikipedia.org/wiki/Self-evidence
>>>>>
>>>>>
>>>> Right, it is self-evident that H is wrong, since the input doesn't do
>>>> what it said it does.
>>>>
>>>> Note, self-evident can be tricky or you can persuade yourself that
>>>> something that is wrong is actually true. That gives rise to the errors
>>>> like the self-evident truth the Achilles can't pass the Tortoise that
>>>> Zeno was able to show 'self-evidently'.
>>>>
>>> Except that Zeno was fully aware that Achilles would overtake the tortoise.
>>> The Greeks staged regular athletics competitions, and he must have
>>> observed a faster runner overhaul a slower one.
>> Yes, he saw 'reality' but he also saw the 'self-evident' proof that this
>> couldn't happen!
>>
>> Thus PROVING that 'self-evident' isn't actually a valid form of argument.
>>
>> It also shows that PO doesn't actually understand what epistemology
>> means with that statement, which isn't strange since he doesn't
>> understand a lot of things that are clearly stated because he filters
>> reality through his POOP colored glasses.
>>
> Whilst I don't know much about Zeno's thought except the basics, he
> was probably trying to work out the nature of a mathematical proof.
> The Greeks had started to develop mathematical proofs, but they didn't
> fully understand what they were. So a "proof" of a manifest absurdity
> was of interest.
>
> It's actually harder than it first appears to say what constitutes a proof.
> So whilst individual proofs are taught at high school level, children
> are not usually taught how to set out a proof formally. And of course they
> are not expected to develop their own proofs. That's why someone
> without a maths degree can struggle.

A proof is merely the set of necessary consequences derived from true
premises.

--
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 4/11/2022 6:50 AM, Dennis Bush wrote:
> On Monday, April 11, 2022 at 12:33:06 AM UTC-4, olcott wrote:
>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
>>> On 2022-04-10 22:15, olcott wrote:
>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
>>>>> On 2022-04-10 21:01, olcott wrote:
>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
>>>>>>> On 2022-04-10 20:38, olcott wrote:
>>>>>>>
>>>>>>>> That is too far off topic. I have been talking circles with Ben
>>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
>>>>>>>> trimmed off of the decision tree.
>>>>>>>>
>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
>>>>>>>
>>>>>>> And we're back to the meaningless notation again.
>>>>>>>
>>>>>>> You are truly incapable of learning anything.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> You can't remember the details between posts? Everyone else can.
>>>>>
>>>>> I can remember. But that doesn't change the fact that the notation
>>>>> you write above is meaningless without a condition specified.
>>>>>
>>>>> You claim you want to know how to present your ideas so you will be
>>>>> taken seriously. I'm trying to help with that. When someone points
>>>>> out an error in your notation, why insist on continuing to use the
>>>>> broken notation?
>>>>>
>>>>> André
>>>>
>>>> I have a single primary goal that supersedes and overrides all other
>>>> goals, get mutual agreement on my current stage of progress.
>>>
>>> I thought your goal was to eventually publish, which requires learning
>>> to use notation properly so you don't look like an illiterate crank.
>>>
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach its
>>>> own final state.
>>>>
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
>>>> reach its own final state.
>>>>
>>>> embedded_H correctly rejects its input.
>>>
>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.

>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded in Ĥ

correct simulation
correct simulation
correct simulation
correct simulation
correct simulation

>> is the only thing that is being examined.
>> It is self-evident that the actual behavior of the actual simulated
>> input is the ULTIMATE MEASURE of the correctness of any halt decider.
>
> We've already established that that criteria is invalid because

Dennis is to stupid to pay attention that a "correct simulation"
is required thus provides his moronically stupid rebuttal using an
incorrect simulation.

> it concludes that Ha3 is correct to reject <N><5> because "the actual behavior of the actual simulated input" is non-halting by this criteria.
>
> You came up with a better one:
>
> A simulating halt decider must continue to simulate its input until it
> has proof that this simulation would never end.
>
> Put another way:
>
> If one simulating halt decider reports that an input is non-halting but a second simulating halt decider simulates that same input to completion and reports halting, then the first was not correct to report non-halting.
>
> Which would mean that Ha7 accepting <N><5> after simulating that input to its final state of <N.qy> is proof that Ha3 was incorrect to reject <N><5>.
>
> Agreed?

--
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 4/11/2022 6:45 AM, Dennis Bush wrote:
> On Sunday, April 10, 2022 at 11:57:10 PM UTC-4, olcott wrote:
>> On 4/10/2022 10:32 PM, Dennis Bush wrote:
>>> On Sunday, April 10, 2022 at 11:29:34 PM UTC-4, olcott wrote:
>>>> On 4/10/2022 10:22 PM, Dennis Bush wrote:
>>>>> On Sunday, April 10, 2022 at 11:19:51 PM UTC-4, olcott wrote:
>>>>>> On 4/10/2022 10:14 PM, Dennis Bush wrote:
>>>>>>> On Sunday, April 10, 2022 at 11:06:31 PM UTC-4, olcott wrote:
>>>>>>>> On 4/10/2022 10:00 PM, Dennis Bush wrote:
>>>>>>>>> On Sunday, April 10, 2022 at 10:53:38 PM UTC-4, olcott wrote:
>>>>>>>> I know that you are not so bobble headed that you would forget this:
>>>>>>>> A simulating halt decider must continue to simulate its input until it
>>>>>>>> has proof that this simulation would never end.
>>>>>>>>> You don't seem to agree with that, which would mean that your claim that "the actual behavior of the actual simulated input is the ULTIMATE MEASURE of the correctness of any halt decider" doesn't make sense.
>>>>>>>> No it would be that you are playing head games and ignoring this criteria:
>>>>>>>> A simulating halt decider must continue to simulate its input until it
>>>>>>>> has proof that this simulation would never end.
>>>>>>>> I may ignore what you say after this.
>>>>>>>
>>>>>>> Since Ha3 is defined to simulate for exactly 3 steps, it can't really be "changed".
>>>>>> The change is that you acknowledge that you already know how
>>>>>> ridiculously lame and condescending your Ha3 example is.
>>>>>>
>>>>>
>>>>> If we defined another simulating halt decider called Ha7 which simulates for 7 steps before aborting, and we give it <N><5> as input, we can see that it simulates its input to a final state of <N.qy> and reports halting.
>>>>>
>>>>> Would you then agree that Ha7 accepting <N><5> after simulating that input to its final state of <N.qy> is proof that Ha3 was incorrect to reject <N><5>?
>>>> OTHERWISE ITS WRONG
>>>> A simulating halt decider must continue to simulate its input until it
>>>> has proof that this simulation would never end.
>>>
>>> Then you would agree that
>> If it isn't in this category I am not discussing it:
>> A simulating halt decider must continue to simulate its input until it
>> has proof that this simulation would never end.
>
> Which would mean that Ha7

is something that you should STFU about

--
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 4/11/2022 2:50 AM, Mikko wrote:
> On 2022-04-10 21:56:38 +0000, olcott said:
>
>> THE NOTATION IS A STIPULATIVE DEFINITION THUS DISAGREEMENT IS INCORRECT.
>
> That is not quite true. Whenever somenthing is claimed there is a
> possibility of disagreement. Every definition contains a claim: it
> claims that something is defined. But sometimes there is a mistake
> in a definition so that in reality nothing is defined.
>
> Mikko
>

In BASIC let X = 5,
one is not free to disagree that X has the value of 5.

--
Copyright 2022 Pete Olcott

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

Demented LIAR Peter Olcott wrote:
> On 4/11/2022 2:50 AM, Mikko wrote:
>> On 2022-04-10 21:56:38 +0000, olcott said:
>>
>>> THE NOTATION IS A STIPULATIVE DEFINITION THUS DISAGREEMENT IS INCORRECT.
>>
>> That is not quite true. Whenever somenthing is claimed there is a
>> possibility of disagreement. Every definition contains a claim: it
>> claims that something is defined. But sometimes there is a mistake
>> in a definition so that in reality nothing is defined.
>>
>> Mikko
>>
>
> In BASIC let X = 5,
> one is not free to disagree that X has the value of 5.

This is not what you are doing.

What you are doing is similar to claim "Let p be the greatest
prime number" and then claim that one is not free to disagree
that p exists.

On 4/11/2022 9:56 AM, Python wrote:
> Demented LIAR Peter Olcott wrote:
>> On 4/11/2022 2:50 AM, Mikko wrote:
>>> On 2022-04-10 21:56:38 +0000, olcott said:
>>>
>>>> THE NOTATION IS A STIPULATIVE DEFINITION THUS DISAGREEMENT IS
>>>> INCORRECT.
>>>
>>> That is not quite true. Whenever somenthing is claimed there is a
>>> possibility of disagreement. Every definition contains a claim: it
>>> claims that something is defined. But sometimes there is a mistake
>>> in a definition so that in reality nothing is defined.
>>>
>>> Mikko
>>>
>>
>> In BASIC let X = 5,
>> one is not free to disagree that X has the value of 5.
>
> This is not what you are doing.
>
> What you are doing is similar to claim "Let p be the greatest
> prime number" and then claim that one is not free to disagree
> that p exists.
>

It is self-evident that the actual behavior of the actual simulated
input is the ULTIMATE MEASURE of the correctness of any halt decider.

--
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 Monday, 11 April 2022 at 15:15:01 UTC+1, olcott wrote:
> On 4/11/2022 7:14 AM, Malcolm McLean wrote:
> > On Monday, 11 April 2022 at 12:59:41 UTC+1, richar...@gmail.com wrote:
> >> On 4/11/22 7:48 AM, Malcolm McLean wrote:
> >>> On Monday, 11 April 2022 at 12:01:53 UTC+1, richar...@gmail.com wrote:
> >>>> On 4/11/22 12:32 AM, olcott wrote:
> >>>>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
> >>>>>> On 2022-04-10 22:15, olcott wrote:
> >>>>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
> >>>>>>>> On 2022-04-10 21:01, olcott wrote:
> >>>>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
> >>>>>>>>>> On 2022-04-10 20:38, olcott wrote:
> >>>>>>>>>>
> >>>>>>>>>>> That is too far off topic. I have been talking circles with Ben
> >>>>>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
> >>>>>>>>>>> trimmed off of the decision tree.
> >>>>>>>>>>>
> >>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
> >>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
> >>>>>>>>>>
> >>>>>>>>>> And we're back to the meaningless notation again.
> >>>>>>>>>>
> >>>>>>>>>> You are truly incapable of learning anything.
> >>>>>>>>>>
> >>>>>>>>>> André
> >>>>>>>>>>
> >>>>>>>>>
> >>>>>>>>> You can't remember the details between posts? Everyone else can..
> >>>>>>>>
> >>>>>>>> I can remember. But that doesn't change the fact that the notation
> >>>>>>>> you write above is meaningless without a condition specified.
> >>>>>>>>
> >>>>>>>> You claim you want to know how to present your ideas so you will be
> >>>>>>>> taken seriously. I'm trying to help with that. When someone points
> >>>>>>>> out an error in your notation, why insist on continuing to use the
> >>>>>>>> broken notation?
> >>>>>>>>
> >>>>>>>> André
> >>>>>>>
> >>>>>>> I have a single primary goal that supersedes and overrides all other
> >>>>>>> goals, get mutual agreement on my current stage of progress.
> >>>>>>
> >>>>>> I thought your goal was to eventually publish, which requires learning
> >>>>>> to use notation properly so you don't look like an illiterate crank.
> >>>>>>
> >>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
> >>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach
> >>>>>>> its own final state.
> >>>>>>>
> >>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
> >>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
> >>>>>>> reach its own final state.
> >>>>>>>
> >>>>>>> embedded_H correctly rejects its input.
> >>>>>>
> >>>>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
> >>>>>
> >>>>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded in Ĥ
> >>>>> is the only thing that is being examined.
> >>>> And the CORRECT simulation of <H^> <H^> will HALT if the copy of H that
> >>>> is embedded in H^ aborts its simulation and goes to H.Qn.
> >>>>
> >>>> Thus
> >>>>>
> >>>>> It is self-evident that the actual behavior of the actual simulated
> >>>>> input is the ULTIMATE MEASURE of the correctness of any halt decider.
> >>>> Right, and Halting is not the Non-Halting that an H that goes to H.Qn is
> >>>> claiming.
> >>>>>
> >>>>> In epistemology (theory of knowledge), a self-evident proposition is a
> >>>>> proposition that is known to be true by understanding its meaning
> >>>>> without proof... https://en.wikipedia.org/wiki/Self-evidence
> >>>>>
> >>>>>
> >>>> Right, it is self-evident that H is wrong, since the input doesn't do
> >>>> what it said it does.
> >>>>
> >>>> Note, self-evident can be tricky or you can persuade yourself that
> >>>> something that is wrong is actually true. That gives rise to the errors
> >>>> like the self-evident truth the Achilles can't pass the Tortoise that
> >>>> Zeno was able to show 'self-evidently'.
> >>>>
> >>> Except that Zeno was fully aware that Achilles would overtake the tortoise.
> >>> The Greeks staged regular athletics competitions, and he must have
> >>> observed a faster runner overhaul a slower one.
> >> Yes, he saw 'reality' but he also saw the 'self-evident' proof that this
> >> couldn't happen!
> >>
> >> Thus PROVING that 'self-evident' isn't actually a valid form of argument.
> >>
> >> It also shows that PO doesn't actually understand what epistemology
> >> means with that statement, which isn't strange since he doesn't
> >> understand a lot of things that are clearly stated because he filters
> >> reality through his POOP colored glasses.
> >>
> > Whilst I don't know much about Zeno's thought except the basics, he
> > was probably trying to work out the nature of a mathematical proof.
> > The Greeks had started to develop mathematical proofs, but they didn't
> > fully understand what they were. So a "proof" of a manifest absurdity
> > was of interest.
> >
> > It's actually harder than it first appears to say what constitutes a proof.
> > So whilst individual proofs are taught at high school level, children
> > are not usually taught how to set out a proof formally. And of course they
> > are not expected to develop their own proofs. That's why someone
> > without a maths degree can struggle.
> A proof is merely the set of necessary consequences derived from true
> premises.
>
Zeno created something that looks like a proof that Achilles cannot overtake
the tortoise. But of course, Achilles overtakes the tortoise.

It's not quite as simple as you are implying.

You should be the first to agree with this. since you claim to have found a flaw in
what you call the Linz proof. However whilst it's possible to produce something
that looks like a proof but isn't, it doesn't follow that any specific proof is
fallacious.

On 4/11/2022 11:01 AM, Malcolm McLean wrote:
> On Monday, 11 April 2022 at 15:15:01 UTC+1, olcott wrote:
>> On 4/11/2022 7:14 AM, Malcolm McLean wrote:
>>> On Monday, 11 April 2022 at 12:59:41 UTC+1, richar...@gmail.com wrote:
>>>> On 4/11/22 7:48 AM, Malcolm McLean wrote:
>>>>> On Monday, 11 April 2022 at 12:01:53 UTC+1, richar...@gmail.com wrote:
>>>>>> On 4/11/22 12:32 AM, olcott wrote:
>>>>>>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
>>>>>>>> On 2022-04-10 22:15, olcott wrote:
>>>>>>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
>>>>>>>>>> On 2022-04-10 21:01, olcott wrote:
>>>>>>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
>>>>>>>>>>>> On 2022-04-10 20:38, olcott wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> That is too far off topic. I have been talking circles with Ben
>>>>>>>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
>>>>>>>>>>>>> trimmed off of the decision tree.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
>>>>>>>>>>>>
>>>>>>>>>>>> And we're back to the meaningless notation again.
>>>>>>>>>>>>
>>>>>>>>>>>> You are truly incapable of learning anything.
>>>>>>>>>>>>
>>>>>>>>>>>> André
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> You can't remember the details between posts? Everyone else can.
>>>>>>>>>>
>>>>>>>>>> I can remember. But that doesn't change the fact that the notation
>>>>>>>>>> you write above is meaningless without a condition specified.
>>>>>>>>>>
>>>>>>>>>> You claim you want to know how to present your ideas so you will be
>>>>>>>>>> taken seriously. I'm trying to help with that. When someone points
>>>>>>>>>> out an error in your notation, why insist on continuing to use the
>>>>>>>>>> broken notation?
>>>>>>>>>>
>>>>>>>>>> André
>>>>>>>>>
>>>>>>>>> I have a single primary goal that supersedes and overrides all other
>>>>>>>>> goals, get mutual agreement on my current stage of progress.
>>>>>>>>
>>>>>>>> I thought your goal was to eventually publish, which requires learning
>>>>>>>> to use notation properly so you don't look like an illiterate crank.
>>>>>>>>
>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>>>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach
>>>>>>>>> its own final state.
>>>>>>>>>
>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>>>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
>>>>>>>>> reach its own final state.
>>>>>>>>>
>>>>>>>>> embedded_H correctly rejects its input.
>>>>>>>>
>>>>>>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
>>>>>>>
>>>>>>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded in Ĥ
>>>>>>> is the only thing that is being examined.
>>>>>> And the CORRECT simulation of <H^> <H^> will HALT if the copy of H that
>>>>>> is embedded in H^ aborts its simulation and goes to H.Qn.
>>>>>>
>>>>>> Thus
>>>>>>>
>>>>>>> It is self-evident that the actual behavior of the actual simulated
>>>>>>> input is the ULTIMATE MEASURE of the correctness of any halt decider.
>>>>>> Right, and Halting is not the Non-Halting that an H that goes to H.Qn is
>>>>>> claiming.
>>>>>>>
>>>>>>> In epistemology (theory of knowledge), a self-evident proposition is a
>>>>>>> proposition that is known to be true by understanding its meaning
>>>>>>> without proof... https://en.wikipedia.org/wiki/Self-evidence
>>>>>>>
>>>>>>>
>>>>>> Right, it is self-evident that H is wrong, since the input doesn't do
>>>>>> what it said it does.
>>>>>>
>>>>>> Note, self-evident can be tricky or you can persuade yourself that
>>>>>> something that is wrong is actually true. That gives rise to the errors
>>>>>> like the self-evident truth the Achilles can't pass the Tortoise that
>>>>>> Zeno was able to show 'self-evidently'.
>>>>>>
>>>>> Except that Zeno was fully aware that Achilles would overtake the tortoise.
>>>>> The Greeks staged regular athletics competitions, and he must have
>>>>> observed a faster runner overhaul a slower one.
>>>> Yes, he saw 'reality' but he also saw the 'self-evident' proof that this
>>>> couldn't happen!
>>>>
>>>> Thus PROVING that 'self-evident' isn't actually a valid form of argument.
>>>>
>>>> It also shows that PO doesn't actually understand what epistemology
>>>> means with that statement, which isn't strange since he doesn't
>>>> understand a lot of things that are clearly stated because he filters
>>>> reality through his POOP colored glasses.
>>>>
>>> Whilst I don't know much about Zeno's thought except the basics, he
>>> was probably trying to work out the nature of a mathematical proof.
>>> The Greeks had started to develop mathematical proofs, but they didn't
>>> fully understand what they were. So a "proof" of a manifest absurdity
>>> was of interest.
>>>
>>> It's actually harder than it first appears to say what constitutes a proof.
>>> So whilst individual proofs are taught at high school level, children
>>> are not usually taught how to set out a proof formally. And of course they
>>> are not expected to develop their own proofs. That's why someone
>>> without a maths degree can struggle.
>> A proof is merely the set of necessary consequences derived from true
>> premises.
>>
> Zeno created something that looks like a proof that Achilles cannot overtake
> the tortoise. But of course, Achilles overtakes the tortoise.
>
> It's not quite as simple as you are implying.
>
> You should be the first to agree with this. since you claim to have found a flaw in
> what you call the Linz proof. However whilst it's possible to produce something
> that looks like a proof but isn't, it doesn't follow that any specific proof is
> fallacious.

Every proof is correct that is a necessary consequence of a set of true
premises.

--
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 2022-04-10 22:32, olcott wrote:
> On 4/10/2022 11:26 PM, André G. Isaak wrote:
>> On 2022-04-10 22:15, olcott wrote:
>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
>>>> On 2022-04-10 21:01, olcott wrote:
>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
>>>>>> On 2022-04-10 20:38, olcott wrote:
>>>>>>
>>>>>>> That is too far off topic. I have been talking circles with Ben
>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
>>>>>>> trimmed off of the decision tree.
>>>>>>>
>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
>>>>>>
>>>>>> And we're back to the meaningless notation again.
>>>>>>
>>>>>> You are truly incapable of learning anything.
>>>>>>
>>>>>> André
>>>>>>
>>>>>
>>>>> You can't remember the details between posts? Everyone else can.
>>>>
>>>> I can remember. But that doesn't change the fact that the notation
>>>> you write above is meaningless without a condition specified.
>>>>
>>>> You claim you want to know how to present your ideas so you will be
>>>> taken seriously. I'm trying to help with that. When someone points
>>>> out an error in your notation, why insist on continuing to use the
>>>> broken notation?
>>>>
>>>> André
>>>
>>> I have a single primary goal that supersedes and overrides all other
>>> goals, get mutual agreement on my current stage of progress.
>>
>> I thought your goal was to eventually publish, which requires learning
>> to use notation properly so you don't look like an illiterate crank.
>>
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach
>>> its own final state.
>>>
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
>>> reach its own final state.
>>>
>>> embedded_H correctly rejects its input.
>>
>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
>
> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded in Ĥ
> is the only thing that is being examined.

There is no "correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is
embedded in Ĥ"

H is not a simulator. It is a halt decider.

> It is self-evident that the actual behavior of the actual simulated
> input is the ULTIMATE MEASURE of the correctness of any halt decider.

The "ultimate measure" is whether the computation represented by the
input is finite. That's the definition of the halting problem. Any other
metric is invalid unless it can be shown to be equivalent to this, and
since you acknowledge that Ĥ applied to ⟨Ĥ⟩ does halt, your metric is
NOT equivalent. So you are working on the wrong problem.

> In epistemology (theory of knowledge), a self-evident proposition is a
> proposition that is known to be true by understanding its meaning
> without proof... https://en.wikipedia.org/wiki/Self-evidence

And from the very article you cite: "Some epistemologists [many, in
fact] deny that any proposition can be self-evident." So just claiming
that something is 'self-evident' isn't a sufficient basis for an
argument -- you'd need to first establish that such propositions are
even possible.

More importantly, we're not talking about epistemology. We're talking
about the halting problem. "self-evident propositions" play no role in
formal systems or the theory of computation.

Generally, it's not a good idea to import notions from one field into
another unless you can actually justify their applicability to that field.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

On 4/11/2022 12:57 PM, André G. Isaak wrote:
> On 2022-04-10 22:32, olcott wrote:
>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
>>> On 2022-04-10 22:15, olcott wrote:
>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
>>>>> On 2022-04-10 21:01, olcott wrote:
>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
>>>>>>> On 2022-04-10 20:38, olcott wrote:
>>>>>>>
>>>>>>>> That is too far off topic. I have been talking circles with Ben
>>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
>>>>>>>> trimmed off of the decision tree.
>>>>>>>>
>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
>>>>>>>
>>>>>>> And we're back to the meaningless notation again.
>>>>>>>
>>>>>>> You are truly incapable of learning anything.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> You can't remember the details between posts? Everyone else can.
>>>>>
>>>>> I can remember. But that doesn't change the fact that the notation
>>>>> you write above is meaningless without a condition specified.
>>>>>
>>>>> You claim you want to know how to present your ideas so you will be
>>>>> taken seriously. I'm trying to help with that. When someone points
>>>>> out an error in your notation, why insist on continuing to use the
>>>>> broken notation?
>>>>>
>>>>> André
>>>>
>>>> I have a single primary goal that supersedes and overrides all other
>>>> goals, get mutual agreement on my current stage of progress.
>>>
>>> I thought your goal was to eventually publish, which requires
>>> learning to use notation properly so you don't look like an
>>> illiterate crank.
>>>
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach
>>>> its own final state.
>>>>
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
>>>> reach its own final state.
>>>>
>>>> embedded_H correctly rejects its input.
>>>
>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
>>
>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded in
>> Ĥ is the only thing that is being examined.
>
> There is no "correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is
> embedded in Ĥ"
>
> H is not a simulator. It is a halt decider.

That is a quite stupid thing to say.

Every simulating halt decider (SHD) contains a fully functional UTM that
it uses to continue to simulate its input until this SHD has proof that
this simulation would never end.

>
>> It is self-evident that the actual behavior of the actual simulated
>> input is the ULTIMATE MEASURE of the correctness of any halt decider.
>
> The "ultimate measure" is whether the computation represented by the
> input is finite. That's the definition of the halting problem. Any other
> metric is invalid unless it can be shown to be equivalent to this, and
> since you acknowledge that Ĥ applied to ⟨Ĥ⟩ does halt, your metric is
> NOT equivalent. So you are working on the wrong problem.
>

The ultimate measure of the behavior of the input is the actual freaking
behavior of the actual freaking input.

>> In epistemology (theory of knowledge), a self-evident proposition is a
>> proposition that is known to be true by understanding its meaning
>> without proof... https://en.wikipedia.org/wiki/Self-evidence
>
> And from the very article you cite: "Some epistemologists [many, in
> fact] deny that any proposition can be self-evident." So just claiming
> that something is 'self-evident' isn't a sufficient basis for an
> argument -- you'd need to first establish that such propositions are
> even possible.

self-evident is stipulated to mean any expression of language that can
be verified as completely true entirely on the basis of its meaning.

>
> More importantly, we're not talking about epistemology. We're talking
> about the halting problem. "self-evident propositions" play no role in
> formal systems or the theory of computation.
>
> Generally, it's not a good idea to import notions from one field into
> another unless you can actually justify their applicability to that field.
>
> André
>

The meaning of words is ultimately anchored in epistemology.

--
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 2022-04-11 12:17, olcott wrote:
> On 4/11/2022 12:57 PM, André G. Isaak wrote:
>> On 2022-04-10 22:32, olcott wrote:
>>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
>>>> On 2022-04-10 22:15, olcott wrote:
>>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
>>>>>> On 2022-04-10 21:01, olcott wrote:
>>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
>>>>>>>> On 2022-04-10 20:38, olcott wrote:
>>>>>>>>
>>>>>>>>> That is too far off topic. I have been talking circles with Ben
>>>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
>>>>>>>>> trimmed off of the decision tree.
>>>>>>>>>
>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
>>>>>>>>
>>>>>>>> And we're back to the meaningless notation again.
>>>>>>>>
>>>>>>>> You are truly incapable of learning anything.
>>>>>>>>
>>>>>>>> André
>>>>>>>>
>>>>>>>
>>>>>>> You can't remember the details between posts? Everyone else can.
>>>>>>
>>>>>> I can remember. But that doesn't change the fact that the notation
>>>>>> you write above is meaningless without a condition specified.
>>>>>>
>>>>>> You claim you want to know how to present your ideas so you will
>>>>>> be taken seriously. I'm trying to help with that. When someone
>>>>>> points out an error in your notation, why insist on continuing to
>>>>>> use the broken notation?
>>>>>>
>>>>>> André
>>>>>
>>>>> I have a single primary goal that supersedes and overrides all
>>>>> other goals, get mutual agreement on my current stage of progress.
>>>>
>>>> I thought your goal was to eventually publish, which requires
>>>> learning to use notation properly so you don't look like an
>>>> illiterate crank.
>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach
>>>>> its own final state.
>>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
>>>>> reach its own final state.
>>>>>
>>>>> embedded_H correctly rejects its input.
>>>>
>>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
>>>
>>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded
>>> in Ĥ is the only thing that is being examined.
>>
>> There is no "correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is
>> embedded in Ĥ"
>>
>> H is not a simulator. It is a halt decider.
>
> That is a quite stupid thing to say.
>
> Every simulating halt decider (SHD) contains a fully functional UTM that
> it uses to continue to simulate its input until this SHD has proof that
> this simulation would never end.

This claim is simply nonsense.

A UTM is *defined* as a Turing Machine which takes as its input the
description of a computation and computes what the result of that
computation would be. While this is normally done via something which
might be described as 'simulation', that isn't part of the definition of
a UTM. UTMs are defined in terms of the *result* which they compute.

If you have some TM which takes a string and prints an infinite number
of copies of that string to the tape (obviously, this is a non-halting
computation), then a UTM must also print and infinite number of copies
of that string to the tape. Would your SHD print an infinite number of
copies of string X when given a description of this TM and X as its
input? Unless the answer is 'yes', you're not dealing with a UTM.

And since a UTM is defined by what it does rather than by the steps it
takes to do that, saying something acts as a UTM "until X" is entirely
meaningless.

>>
>>> It is self-evident that the actual behavior of the actual simulated
>>> input is the ULTIMATE MEASURE of the correctness of any halt decider.
>>
>> The "ultimate measure" is whether the computation represented by the
>> input is finite. That's the definition of the halting problem. Any
>> other metric is invalid unless it can be shown to be equivalent to
>> this, and since you acknowledge that Ĥ applied to ⟨Ĥ⟩ does halt, your
>> metric is NOT equivalent. So you are working on the wrong problem.
>>
>
> The ultimate measure of the behavior of the input is the actual freaking
> behavior of the actual freaking input.

That's not how the halting problem is defined. A halt decider, by
definition, is a TM which solves the halting problem.

>>> In epistemology (theory of knowledge), a self-evident proposition is
>>> a proposition that is known to be true by understanding its meaning
>>> without proof... https://en.wikipedia.org/wiki/Self-evidence
>>
>> And from the very article you cite: "Some epistemologists [many, in
>> fact] deny that any proposition can be self-evident." So just claiming
>> that something is 'self-evident' isn't a sufficient basis for an
>> argument -- you'd need to first establish that such propositions are
>> even possible.
>
> self-evident is stipulated to mean any expression of language that can
> be verified as completely true entirely on the basis of its meaning.

That's not the normal definition. And the proposition you claimed to be
'self-evident' certainly isn't true on this basis.

>>
>> More importantly, we're not talking about epistemology. We're talking
>> about the halting problem. "self-evident propositions" play no role in
>> formal systems or the theory of computation.
>>
>> Generally, it's not a good idea to import notions from one field into
>> another unless you can actually justify their applicability to that
>> field.
>>
>> André
>>
>
> The meaning of words is ultimately anchored in epistemology.

Add 'epistemology' to the list of words you don't know. Epistemology is
concerned with our knowledge of the world, not with the meanings of words.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

On 4/11/2022 1:39 PM, André G. Isaak wrote:
> On 2022-04-11 12:17, olcott wrote:
>> On 4/11/2022 12:57 PM, André G. Isaak wrote:
>>> On 2022-04-10 22:32, olcott wrote:
>>>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
>>>>> On 2022-04-10 22:15, olcott wrote:
>>>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
>>>>>>> On 2022-04-10 21:01, olcott wrote:
>>>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
>>>>>>>>> On 2022-04-10 20:38, olcott wrote:
>>>>>>>>>
>>>>>>>>>> That is too far off topic. I have been talking circles with
>>>>>>>>>> Ben for 17 years. We now must talk in hierarchies, cyclic
>>>>>>>>>> paths are trimmed off of the decision tree.
>>>>>>>>>>
>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
>>>>>>>>>
>>>>>>>>> And we're back to the meaningless notation again.
>>>>>>>>>
>>>>>>>>> You are truly incapable of learning anything.
>>>>>>>>>
>>>>>>>>> André
>>>>>>>>>
>>>>>>>>
>>>>>>>> You can't remember the details between posts? Everyone else can.
>>>>>>>
>>>>>>> I can remember. But that doesn't change the fact that the
>>>>>>> notation you write above is meaningless without a condition
>>>>>>> specified.
>>>>>>>
>>>>>>> You claim you want to know how to present your ideas so you will
>>>>>>> be taken seriously. I'm trying to help with that. When someone
>>>>>>> points out an error in your notation, why insist on continuing to
>>>>>>> use the broken notation?
>>>>>>>
>>>>>>> André
>>>>>>
>>>>>> I have a single primary goal that supersedes and overrides all
>>>>>> other goals, get mutual agreement on my current stage of progress.
>>>>>
>>>>> I thought your goal was to eventually publish, which requires
>>>>> learning to use notation properly so you don't look like an
>>>>> illiterate crank.
>>>>>
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach
>>>>>> its own final state.
>>>>>>
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
>>>>>> reach its own final state.
>>>>>>
>>>>>> embedded_H correctly rejects its input.
>>>>>
>>>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
>>>>
>>>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded
>>>> in Ĥ is the only thing that is being examined.
>>>
>>> There is no "correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is
>>> embedded in Ĥ"
>>>
>>> H is not a simulator. It is a halt decider.
>>
>> That is a quite stupid thing to say.
>>
>> Every simulating halt decider (SHD) contains a fully functional UTM
>> that it uses to continue to simulate its input until this SHD has
>> proof that this simulation would never end.
>
> This claim is simply nonsense.
>

No you are simply a jack ass.

In computer science, a universal Turing machine (UTM) is a Turing
machine that simulates an arbitrary Turing machine on arbitrary input.
The universal machine essentially achieves this by reading both the
description of the machine to be simulated as well as the input to that
machine from its own tape.
https://en.wikipedia.org/wiki/Universal_Turing_machine

> A UTM is *defined* as a Turing Machine which takes as its input the
> description of a computation and computes what the result of that
> computation would be. While this is normally done via something which
> might be described as 'simulation', that isn't part of the definition of
> a UTM. UTMs are defined in terms of the *result* which they compute.
>
> If you have some TM which takes a string and prints an infinite number
> of copies of that string to the tape (obviously, this is a non-halting
> computation), then a UTM must also print and infinite number of copies
> of that string to the tape. Would your SHD print an infinite number of
> copies of string X when given a description of this TM and X as its
> input? Unless the answer is 'yes', you're not dealing with a UTM.
>
> And since a UTM is defined by what it does rather than by the steps it
> takes to do that, saying something acts as a UTM "until X" is entirely
> meaningless.
>
>>>
>>>> It is self-evident that the actual behavior of the actual simulated
>>>> input is the ULTIMATE MEASURE of the correctness of any halt decider.
>>>
>>> The "ultimate measure" is whether the computation represented by the
>>> input is finite. That's the definition of the halting problem. Any
>>> other metric is invalid unless it can be shown to be equivalent to
>>> this, and since you acknowledge that Ĥ applied to ⟨Ĥ⟩ does halt, your
>>> metric is NOT equivalent. So you are working on the wrong problem.
>>>
>>
>> The ultimate measure of the behavior of the input is the actual
>> freaking behavior of the actual freaking input.
>
> That's not how the halting problem is defined. A halt decider, by
> definition, is a TM which solves the halting problem.
>

You are such a complete jack ass. I am stopping here.

--
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 4/10/2022 11:26 PM, André G. Isaak wrote:
> On 2022-04-10 22:15, olcott wrote:
>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
>>> On 2022-04-10 21:01, olcott wrote:
>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
>>>>> On 2022-04-10 20:38, olcott wrote:
>>>>>
>>>>>> That is too far off topic. I have been talking circles with Ben
>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
>>>>>> trimmed off of the decision tree.
>>>>>>
>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
>>>>>
>>>>> And we're back to the meaningless notation again.
>>>>>
>>>>> You are truly incapable of learning anything.
>>>>>
>>>>> André
>>>>>
>>>>
>>>> You can't remember the details between posts? Everyone else can.
>>>
>>> I can remember. But that doesn't change the fact that the notation
>>> you write above is meaningless without a condition specified.
>>>
>>> You claim you want to know how to present your ideas so you will be
>>> taken seriously. I'm trying to help with that. When someone points
>>> out an error in your notation, why insist on continuing to use the
>>> broken notation?
>>>
>>> André
>>
>> I have a single primary goal that supersedes and overrides all other
>> goals, get mutual agreement on my current stage of progress.
>
> I thought your goal was to eventually publish,

My goal is to be understood to be essentially correct every other goal
has 100,000-fold less priority.

It is self-evident that the actual behavior of the actual simulated
input is the ULTIMATE MEASURE of the correctness of any halt decider.

By this measure embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn is correct
and H(P,P) correctly returns false.

--
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 Monday, 11 April 2022 at 19:39:44 UTC+1, André G. Isaak wrote:
> On 2022-04-11 12:17, olcott wrote:
> > On 4/11/2022 12:57 PM, André G. Isaak wrote:
> >> On 2022-04-10 22:32, olcott wrote:
> >>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
> >>>> On 2022-04-10 22:15, olcott wrote:
> >>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
> >>>>>> On 2022-04-10 21:01, olcott wrote:
> >>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
> >>>>>>>> On 2022-04-10 20:38, olcott wrote:
> >>>>>>>>
> >>>>>>>>> That is too far off topic. I have been talking circles with Ben
> >>>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
> >>>>>>>>> trimmed off of the decision tree.
> >>>>>>>>>
> >>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
> >>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
> >>>>>>>>
> >>>>>>>> And we're back to the meaningless notation again.
> >>>>>>>>
> >>>>>>>> You are truly incapable of learning anything.
> >>>>>>>>
> >>>>>>>> André
> >>>>>>>>
> >>>>>>>
> >>>>>>> You can't remember the details between posts? Everyone else can.
> >>>>>>
> >>>>>> I can remember. But that doesn't change the fact that the notation
> >>>>>> you write above is meaningless without a condition specified.
> >>>>>>
> >>>>>> You claim you want to know how to present your ideas so you will
> >>>>>> be taken seriously. I'm trying to help with that. When someone
> >>>>>> points out an error in your notation, why insist on continuing to
> >>>>>> use the broken notation?
> >>>>>>
> >>>>>> André
> >>>>>
> >>>>> I have a single primary goal that supersedes and overrides all
> >>>>> other goals, get mutual agreement on my current stage of progress.
> >>>>
> >>>> I thought your goal was to eventually publish, which requires
> >>>> learning to use notation properly so you don't look like an
> >>>> illiterate crank.
> >>>>
> >>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
> >>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach
> >>>>> its own final state.
> >>>>>
> >>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
> >>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
> >>>>> reach its own final state.
> >>>>>
> >>>>> embedded_H correctly rejects its input.
> >>>>
> >>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
> >>>
> >>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded
> >>> in Ĥ is the only thing that is being examined.
> >>
> >> There is no "correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is
> >> embedded in Ĥ"
> >>
> >> H is not a simulator. It is a halt decider.
> >
> > That is a quite stupid thing to say.
> >
> > Every simulating halt decider (SHD) contains a fully functional UTM that
> > it uses to continue to simulate its input until this SHD has proof that
> > this simulation would never end.
> This claim is simply nonsense.
>
> A UTM is *defined* as a Turing Machine which takes as its input the
> description of a computation and computes what the result of that
> computation would be. While this is normally done via something which
> might be described as 'simulation', that isn't part of the definition of
> a UTM. UTMs are defined in terms of the *result* which they compute.
>
> If you have some TM which takes a string and prints an infinite number
> of copies of that string to the tape (obviously, this is a non-halting
> computation), then a UTM must also print and infinite number of copies
> of that string to the tape. Would your SHD print an infinite number of
> copies of string X when given a description of this TM and X as its
> input? Unless the answer is 'yes', you're not dealing with a UTM.
>
> And since a UTM is defined by what it does rather than by the steps it
> takes to do that, saying something acts as a UTM "until X" is entirely
> meaningless.
>
Not really. PO's idea is to have a simulator with an infinite cycle detector.
You would achieve this by modifying a UTM, so describing it as a "modified
UTM", or "acts like a UTM until it detects an infinite cycle", is reasonable.
And such a machine is a fairly powerful halt decider. Even if the infinite cycle
detector isn't very sophisticated, it will still catch a large subset of non-
halting machines. But it won't catch all non-halting machines, and it can't
be scaled up by adding features until it is perfect. And Linz's H_Hat construct
will always defeat it, which PO refuses to accept.

On 4/11/2022 3:19 PM, Malcolm McLean wrote:
> On Monday, 11 April 2022 at 19:39:44 UTC+1, André G. Isaak wrote:
>> On 2022-04-11 12:17, olcott wrote:
>>> On 4/11/2022 12:57 PM, André G. Isaak wrote:
>>>> On 2022-04-10 22:32, olcott wrote:
>>>>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
>>>>>> On 2022-04-10 22:15, olcott wrote:
>>>>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
>>>>>>>> On 2022-04-10 21:01, olcott wrote:
>>>>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
>>>>>>>>>> On 2022-04-10 20:38, olcott wrote:
>>>>>>>>>>
>>>>>>>>>>> That is too far off topic. I have been talking circles with Ben
>>>>>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
>>>>>>>>>>> trimmed off of the decision tree.
>>>>>>>>>>>
>>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
>>>>>>>>>>
>>>>>>>>>> And we're back to the meaningless notation again.
>>>>>>>>>>
>>>>>>>>>> You are truly incapable of learning anything.
>>>>>>>>>>
>>>>>>>>>> André
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You can't remember the details between posts? Everyone else can.
>>>>>>>>
>>>>>>>> I can remember. But that doesn't change the fact that the notation
>>>>>>>> you write above is meaningless without a condition specified.
>>>>>>>>
>>>>>>>> You claim you want to know how to present your ideas so you will
>>>>>>>> be taken seriously. I'm trying to help with that. When someone
>>>>>>>> points out an error in your notation, why insist on continuing to
>>>>>>>> use the broken notation?
>>>>>>>>
>>>>>>>> André
>>>>>>>
>>>>>>> I have a single primary goal that supersedes and overrides all
>>>>>>> other goals, get mutual agreement on my current stage of progress.
>>>>>>
>>>>>> I thought your goal was to eventually publish, which requires
>>>>>> learning to use notation properly so you don't look like an
>>>>>> illiterate crank.
>>>>>>
>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach
>>>>>>> its own final state.
>>>>>>>
>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
>>>>>>> reach its own final state.
>>>>>>>
>>>>>>> embedded_H correctly rejects its input.
>>>>>>
>>>>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
>>>>>
>>>>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded
>>>>> in Ĥ is the only thing that is being examined.
>>>>
>>>> There is no "correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is
>>>> embedded in Ĥ"
>>>>
>>>> H is not a simulator. It is a halt decider.
>>>
>>> That is a quite stupid thing to say.
>>>
>>> Every simulating halt decider (SHD) contains a fully functional UTM that
>>> it uses to continue to simulate its input until this SHD has proof that
>>> this simulation would never end.
>> This claim is simply nonsense.
>>
>> A UTM is *defined* as a Turing Machine which takes as its input the
>> description of a computation and computes what the result of that
>> computation would be. While this is normally done via something which
>> might be described as 'simulation', that isn't part of the definition of
>> a UTM. UTMs are defined in terms of the *result* which they compute.
>>
>> If you have some TM which takes a string and prints an infinite number
>> of copies of that string to the tape (obviously, this is a non-halting
>> computation), then a UTM must also print and infinite number of copies
>> of that string to the tape. Would your SHD print an infinite number of
>> copies of string X when given a description of this TM and X as its
>> input? Unless the answer is 'yes', you're not dealing with a UTM.
>>
>> And since a UTM is defined by what it does rather than by the steps it
>> takes to do that, saying something acts as a UTM "until X" is entirely
>> meaningless.
>>
> Not really. PO's idea is to have a simulator with an infinite cycle detector.
> You would achieve this by modifying a UTM, so describing it as a "modified
> UTM", or "acts like a UTM until it detects an infinite cycle", is reasonable.
> And such a machine is a fairly powerful halt decider. Even if the infinite cycle
> detector isn't very sophisticated, it will still catch a large subset of non-
> halting machines. But it won't catch all non-halting machines, and it can't
> be scaled up by adding features until it is perfect. And Linz's H_Hat construct
> will always defeat it, which PO refuses to accept.
>

It is self-evident that the actual behavior of the actual simulated
input is the ULTIMATE MEASURE of the correctness of any halt decider.

By this measure embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn is correct
and H(P,P) correctly returns false.

--
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 4/11/22 10:14 AM, olcott wrote:
> On 4/11/2022 7:14 AM, Malcolm McLean wrote:
>> On Monday, 11 April 2022 at 12:59:41 UTC+1, richar...@gmail.com wrote:
>>> On 4/11/22 7:48 AM, Malcolm McLean wrote:
>>>> On Monday, 11 April 2022 at 12:01:53 UTC+1, richar...@gmail.com wrote:
>>>>> On 4/11/22 12:32 AM, olcott wrote:
>>>>>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
>>>>>>> On 2022-04-10 22:15, olcott wrote:
>>>>>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
>>>>>>>>> On 2022-04-10 21:01, olcott wrote:
>>>>>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
>>>>>>>>>>> On 2022-04-10 20:38, olcott wrote:
>>>>>>>>>>>
>>>>>>>>>>>> That is too far off topic. I have been talking circles with Ben
>>>>>>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
>>>>>>>>>>>> trimmed off of the decision tree.
>>>>>>>>>>>>
>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
>>>>>>>>>>>
>>>>>>>>>>> And we're back to the meaningless notation again.
>>>>>>>>>>>
>>>>>>>>>>> You are truly incapable of learning anything.
>>>>>>>>>>>
>>>>>>>>>>> André
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> You can't remember the details between posts? Everyone else can.
>>>>>>>>>
>>>>>>>>> I can remember. But that doesn't change the fact that the notation
>>>>>>>>> you write above is meaningless without a condition specified.
>>>>>>>>>
>>>>>>>>> You claim you want to know how to present your ideas so you
>>>>>>>>> will be
>>>>>>>>> taken seriously. I'm trying to help with that. When someone points
>>>>>>>>> out an error in your notation, why insist on continuing to use the
>>>>>>>>> broken notation?
>>>>>>>>>
>>>>>>>>> André
>>>>>>>>
>>>>>>>> I have a single primary goal that supersedes and overrides all
>>>>>>>> other
>>>>>>>> goals, get mutual agreement on my current stage of progress.
>>>>>>>
>>>>>>> I thought your goal was to eventually publish, which requires
>>>>>>> learning
>>>>>>> to use notation properly so you don't look like an illiterate crank.
>>>>>>>
>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach
>>>>>>>> its own final state.
>>>>>>>>
>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
>>>>>>>> reach its own final state.
>>>>>>>>
>>>>>>>> embedded_H correctly rejects its input.
>>>>>>>
>>>>>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
>>>>>>
>>>>>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is
>>>>>> embedded in Ĥ
>>>>>> is the only thing that is being examined.
>>>>> And the CORRECT simulation of <H^> <H^> will HALT if the copy of H
>>>>> that
>>>>> is embedded in H^ aborts its simulation and goes to H.Qn.
>>>>>
>>>>> Thus
>>>>>>
>>>>>> It is self-evident that the actual behavior of the actual simulated
>>>>>> input is the ULTIMATE MEASURE of the correctness of any halt decider.
>>>>> Right, and Halting is not the Non-Halting that an H that goes to
>>>>> H.Qn is
>>>>> claiming.
>>>>>>
>>>>>> In epistemology (theory of knowledge), a self-evident proposition
>>>>>> is a
>>>>>> proposition that is known to be true by understanding its meaning
>>>>>> without proof... https://en.wikipedia.org/wiki/Self-evidence
>>>>>>
>>>>>>
>>>>> Right, it is self-evident that H is wrong, since the input doesn't do
>>>>> what it said it does.
>>>>>
>>>>> Note, self-evident can be tricky or you can persuade yourself that
>>>>> something that is wrong is actually true. That gives rise to the
>>>>> errors
>>>>> like the self-evident truth the Achilles can't pass the Tortoise that
>>>>> Zeno was able to show 'self-evidently'.
>>>>>
>>>> Except that Zeno was fully aware that Achilles would overtake the
>>>> tortoise.
>>>> The Greeks staged regular athletics competitions, and he must have
>>>> observed a faster runner overhaul a slower one.
>>> Yes, he saw 'reality' but he also saw the 'self-evident' proof that this
>>> couldn't happen!
>>>
>>> Thus PROVING that 'self-evident' isn't actually a valid form of
>>> argument.
>>>
>>> It also shows that PO doesn't actually understand what epistemology
>>> means with that statement, which isn't strange since he doesn't
>>> understand a lot of things that are clearly stated because he filters
>>> reality through his POOP colored glasses.
>>>
>> Whilst I don't know much about Zeno's thought except the basics, he
>> was probably trying to work out the nature of a mathematical proof.
>> The Greeks had started to develop mathematical proofs, but they didn't
>> fully understand what they were. So a "proof" of a manifest absurdity
>> was of interest.
>>
>> It's actually harder than it first appears to say what constitutes a
>> proof.
>> So whilst individual proofs are taught at high school level, children
>> are not usually taught how to set out a proof formally. And of course
>> they
>> are not expected to develop their own proofs. That's why someone
>> without a maths degree can struggle.
>
> A proof is merely the set of necessary consequences derived from true
> premises.
>

Right, and in a FORMAL Logic, like Mathematics, the ONLY things that can
be taken as 'True Premises' are the defined AXIOMS and DEFINITIONS, and
those things that can be proven from them.

'Self Evident' is NOT a source of 'Truth'.

Note also, this also means your whole 'proof' fails to meet your
definition as you start from a FALSE premise, your definition of halting
(as you interpret it).

So, you fail by your own admission.

On 4/11/22 10:19 AM, olcott wrote:
> On 4/11/2022 6:50 AM, Dennis Bush wrote:
>> On Monday, April 11, 2022 at 12:33:06 AM UTC-4, olcott wrote:
>>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
>>>> On 2022-04-10 22:15, olcott wrote:
>>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
>>>>>> On 2022-04-10 21:01, olcott wrote:
>>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
>>>>>>>> On 2022-04-10 20:38, olcott wrote:
>>>>>>>>
>>>>>>>>> That is too far off topic. I have been talking circles with Ben
>>>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths are
>>>>>>>>> trimmed off of the decision tree.
>>>>>>>>>
>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
>>>>>>>>
>>>>>>>> And we're back to the meaningless notation again.
>>>>>>>>
>>>>>>>> You are truly incapable of learning anything.
>>>>>>>>
>>>>>>>> André
>>>>>>>>
>>>>>>>
>>>>>>> You can't remember the details between posts? Everyone else can.
>>>>>>
>>>>>> I can remember. But that doesn't change the fact that the notation
>>>>>> you write above is meaningless without a condition specified.
>>>>>>
>>>>>> You claim you want to know how to present your ideas so you will be
>>>>>> taken seriously. I'm trying to help with that. When someone points
>>>>>> out an error in your notation, why insist on continuing to use the
>>>>>> broken notation?
>>>>>>
>>>>>> André
>>>>>
>>>>> I have a single primary goal that supersedes and overrides all other
>>>>> goals, get mutual agreement on my current stage of progress.
>>>>
>>>> I thought your goal was to eventually publish, which requires learning
>>>> to use notation properly so you don't look like an illiterate crank.
>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach its
>>>>> own final state.
>>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
>>>>> reach its own final state.
>>>>>
>>>>> embedded_H correctly rejects its input.
>>>>
>>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
>
>>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is embedded in Ĥ
>
> correct simulation
> correct simulation
> correct simulation
> correct simulation
> correct simulation

And you have a definition of 'Correct Simulation' that disagrees with
the simulation by a UTM?

>
>>> is the only thing that is being examined.
>>> It is self-evident that the actual behavior of the actual simulated
>>> input is the ULTIMATE MEASURE of the correctness of any halt decider.
>>
>> We've already established that that criteria is invalid because
>
> Dennis is to stupid to pay attention that a "correct simulation"
> is required thus provides his moronically stupid rebuttal using an
> incorrect simulation.

As do you.

You think H / embedded_H does a correct simulation when it aborts its
simulation. This is EXACTLY the error you claim Dennis is making.

So, by your own words, YOUR idea is disproven.

FAIL.

>
>> it concludes that Ha3 is correct to reject <N><5> because "the actual
>> behavior of the actual simulated input" is non-halting by this criteria.
>>
>> You came up with a better one:
>>
>> A simulating halt decider must continue to simulate its input until it
>> has proof that this simulation would never end.
>>
>> Put another way:
>>
>> If one simulating halt decider reports that an input is non-halting
>> but a second simulating halt decider simulates that same input to
>> completion and reports halting, then the first was not correct to
>> report non-halting.
>>
>> Which would mean that Ha7 accepting <N><5> after simulating that input
>> to its final state of <N.qy> is proof that Ha3 was incorrect to reject
>> <N><5>.
>>
>> Agreed?
>
>

On 4/11/2022 6:14 PM, Richard Damon wrote:
> On 4/11/22 10:14 AM, olcott wrote:
>> On 4/11/2022 7:14 AM, Malcolm McLean wrote:
>>> On Monday, 11 April 2022 at 12:59:41 UTC+1, richar...@gmail.com wrote:
>>>> On 4/11/22 7:48 AM, Malcolm McLean wrote:
>>>>> On Monday, 11 April 2022 at 12:01:53 UTC+1, richar...@gmail.com wrote:
>>>>>> On 4/11/22 12:32 AM, olcott wrote:
>>>>>>> On 4/10/2022 11:26 PM, André G. Isaak wrote:
>>>>>>>> On 2022-04-10 22:15, olcott wrote:
>>>>>>>>> On 4/10/2022 11:11 PM, André G. Isaak wrote:
>>>>>>>>>> On 2022-04-10 21:01, olcott wrote:
>>>>>>>>>>> On 4/10/2022 9:57 PM, André G. Isaak wrote:
>>>>>>>>>>>> On 2022-04-10 20:38, olcott wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> That is too far off topic. I have been talking circles with
>>>>>>>>>>>>> Ben
>>>>>>>>>>>>> for 17 years. We now must talk in hierarchies, cyclic paths
>>>>>>>>>>>>> are
>>>>>>>>>>>>> trimmed off of the decision tree.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qy
>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ0⟩ ⊢* H ⟨Ĥ0⟩ ⟨Ĥ1⟩ ⊢* H.qn
>>>>>>>>>>>>
>>>>>>>>>>>> And we're back to the meaningless notation again.
>>>>>>>>>>>>
>>>>>>>>>>>> You are truly incapable of learning anything.
>>>>>>>>>>>>
>>>>>>>>>>>> André
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> You can't remember the details between posts? Everyone else can.
>>>>>>>>>>
>>>>>>>>>> I can remember. But that doesn't change the fact that the
>>>>>>>>>> notation
>>>>>>>>>> you write above is meaningless without a condition specified.
>>>>>>>>>>
>>>>>>>>>> You claim you want to know how to present your ideas so you
>>>>>>>>>> will be
>>>>>>>>>> taken seriously. I'm trying to help with that. When someone
>>>>>>>>>> points
>>>>>>>>>> out an error in your notation, why insist on continuing to use
>>>>>>>>>> the
>>>>>>>>>> broken notation?
>>>>>>>>>>
>>>>>>>>>> André
>>>>>>>>>
>>>>>>>>> I have a single primary goal that supersedes and overrides all
>>>>>>>>> other
>>>>>>>>> goals, get mutual agreement on my current stage of progress.
>>>>>>>>
>>>>>>>> I thought your goal was to eventually publish, which requires
>>>>>>>> learning
>>>>>>>> to use notation properly so you don't look like an illiterate
>>>>>>>> crank.
>>>>>>>>
>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
>>>>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would reach
>>>>>>>>> its own final state.
>>>>>>>>>
>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
>>>>>>>>> If the correctly simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never
>>>>>>>>> reach its own final state.
>>>>>>>>>
>>>>>>>>> embedded_H correctly rejects its input.
>>>>>>>>
>>>>>>>> No, it doesn't, because a correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ halts.
>>>>>>>
>>>>>>> The correct simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by the copy of H that is
>>>>>>> embedded in Ĥ
>>>>>>> is the only thing that is being examined.
>>>>>> And the CORRECT simulation of <H^> <H^> will HALT if the copy of H
>>>>>> that
>>>>>> is embedded in H^ aborts its simulation and goes to H.Qn.
>>>>>>
>>>>>> Thus
>>>>>>>
>>>>>>> It is self-evident that the actual behavior of the actual simulated
>>>>>>> input is the ULTIMATE MEASURE of the correctness of any halt
>>>>>>> decider.
>>>>>> Right, and Halting is not the Non-Halting that an H that goes to
>>>>>> H.Qn is
>>>>>> claiming.
>>>>>>>
>>>>>>> In epistemology (theory of knowledge), a self-evident proposition
>>>>>>> is a
>>>>>>> proposition that is known to be true by understanding its meaning
>>>>>>> without proof... https://en.wikipedia.org/wiki/Self-evidence
>>>>>>>
>>>>>>>
>>>>>> Right, it is self-evident that H is wrong, since the input doesn't do
>>>>>> what it said it does.
>>>>>>
>>>>>> Note, self-evident can be tricky or you can persuade yourself that
>>>>>> something that is wrong is actually true. That gives rise to the
>>>>>> errors
>>>>>> like the self-evident truth the Achilles can't pass the Tortoise that
>>>>>> Zeno was able to show 'self-evidently'.
>>>>>>
>>>>> Except that Zeno was fully aware that Achilles would overtake the
>>>>> tortoise.
>>>>> The Greeks staged regular athletics competitions, and he must have
>>>>> observed a faster runner overhaul a slower one.
>>>> Yes, he saw 'reality' but he also saw the 'self-evident' proof that
>>>> this
>>>> couldn't happen!
>>>>
>>>> Thus PROVING that 'self-evident' isn't actually a valid form of
>>>> argument.
>>>>
>>>> It also shows that PO doesn't actually understand what epistemology
>>>> means with that statement, which isn't strange since he doesn't
>>>> understand a lot of things that are clearly stated because he filters
>>>> reality through his POOP colored glasses.
>>>>
>>> Whilst I don't know much about Zeno's thought except the basics, he
>>> was probably trying to work out the nature of a mathematical proof.
>>> The Greeks had started to develop mathematical proofs, but they didn't
>>> fully understand what they were. So a "proof" of a manifest absurdity
>>> was of interest.
>>>
>>> It's actually harder than it first appears to say what constitutes a
>>> proof.
>>> So whilst individual proofs are taught at high school level, children
>>> are not usually taught how to set out a proof formally. And of course
>>> they
>>> are not expected to develop their own proofs. That's why someone
>>> without a maths degree can struggle.
>>
>> A proof is merely the set of necessary consequences derived from true
>> premises.
>>
>
> Right, and in a FORMAL Logic, like Mathematics, the ONLY things that can
> be taken as 'True Premises' are the defined AXIOMS and DEFINITIONS, and
> those things that can be proven from them.
>

Yes and it is the same situation when we formalize natural language
semantics.

--
Copyright 2022 Pete Olcott

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