On 4/11/22 8:17 PM, olcott wrote:
> On 4/11/2022 7:14 PM, Richard Damon wrote:
>> On 4/11/22 7:18 PM, olcott wrote:
>>> 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.
>>>
>>>
>>
>> And thus your 'from the meaning of the words' are not true, as the
>> MEANING of the words 'halting' are ONLY based on the behavior of the
>> machine the input represents,
>
> In this you are flatly incorrect.
>
> 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 the ACTUAL BEHAVIOR of the ACTUAL SIMULATED INPUT is BY
DEFINITON the results of applying an ACTUAL UTM to that input which
matches the behavior of the machine it represents.

DEFINITION.

If you mean ANYTHING ELSE, you are just a LIAR, as that is the DEFINED
meaning of the words.

From this if H rejects <H^> <H^> we have shown that H^ applied to <H^>
will halt, and thus UTM <H^> <H^> will halt and thus by the proper
definiton, the behavior of the actual simulated input is to Halt.

You have confused ACTUAL CORRECT SIMULATION with the junk that H does.

FAIL.

Have fun playing with this for your stay in eternal torent trying to
figure out haw it can actually work.