Re: DDD simulated by HHH cannot possibly halt (Halting Problem) --- mindless robots

Am Mon, 14 Apr 2025 06:46:20 -0500 schrieb olcott:

On 4/13/2025 9:12 PM, dbush wrote:

On 4/13/2025 10:09 PM, olcott wrote:

On 4/13/2025 6:51 PM, dbush wrote:

On 4/13/2025 7:32 PM, olcott wrote:

On 4/13/2025 4:03 PM, dbush wrote:

On 4/13/2025 5:00 PM, olcott wrote:

On 4/13/2025 3:00 PM, dbush wrote:

On 4/13/2025 3:59 PM, olcott wrote:

On 4/13/2025 3:54 AM, joes wrote:

Am Fri, 11 Apr 2025 10:56:32 -0500 schrieb olcott:

On 4/11/2025 3:24 AM, Richard Heathfield wrote:

On 11/04/2025 08:57, Mikko wrote:

>

No proof of this principle has been shown so its use is not
valid.

>
No proof of Peano's axioms or Euclid's fifth postulate has
been shown.
That doesn't mean we can't use them.
Mr Olcott can have his principle if he likes, but only by
EITHER proving it (which, as you say, he has not yet done) OR
by taking it as axiomatic, leaving the world of mainstream
computer science behind him,
constructing his own computational 'geometry' so to speak,
and abandoning any claim to having overturned the Halting
Problem. Navel contemplation beckons.
Axioms are all very well, and he's free to invent as many as
he wishes,
but nobody else is obliged to accept them.
>

*Simulating termination analyzer Principle*
It is always correct for any simulating termination analyzer
to stop simulating and reject any input that would otherwise
prevent its own termination.

Sure. Why doesn’t the STA simulate itself rejecting its input?
>

Because that is a STUPID idea and categorically impossible
because the outermost HHH sees its needs to stop simulating
before any inner HHH can possibly see this.
>

In other words, you agree that Linz and others are correct that
no H exists that satisfies these requirements:
Given any algorithm (i.e. a fixed immutable sequence of
instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes
the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed
directly (<X>,Y) maps to 0 if and only if X(Y) does not halt when
executed directly
>
>

No stupid! Those freaking requirements are wrong

>
In other words, you have no interest in something that would make
all truth provable.
>

It will remain forever impossible to prove that five minutes ago
ever existed. This is empirical truth mislabeled as synthetic truth.
Semantic truth poorly labeled as analytic truth is the only truth
that is either provable else untrue. It is {provable}
on the basis of semantic connections to expressions that are
stipulated as true.
>

So you do want something that would make all truth provable.  An H
that meets the following requirements would do that, therefore these
requirements are not "wrong":
>

*Ignorance on your part about this*
https://philosophy.stackexchange.com/questions/43748/how-do-we-know-
the--wasnt-created-5-minutes-ago#:~:text=Ask%20Question,non-
falsifiable%20and%20all).

 
None-the-less an H that meets the requirements below would make all
formal systems complete.  That makes such an H *very* useful, and
therefore the requirements are not "wrong".
 

Given any algorithm (i.e. a fixed immutable sequence of instructions)
X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the
following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
directly
>

Such an HHH works fine when the input DD is not attempting to do the
opposite of whatever this HHH reports. This is not a problem though. DD
merely changes its own behavior through the pathological self-reference
that it implements.

DD doesn’t change anything. It is completeley determined by the return
value of HHH. Either it halts or it doesn’t, and HHH returns the wrong
result.

Then HHH simply reports on this changed behavior. HHH need not even know
that DD is calling itself. It only need to know that the behavior of DD
would prevent its own termination.

If HHH reports on what DD *would* do *if* HHH returned the other value,
that’s changing the input. (HHH doesn’t „know” anything at all.)

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.