Re: The philosophy of computation reformulates existing ideas on a new basis --- INFALLIBLY CORRECT REASONING

Am Fri, 08 Nov 2024 09:01:47 -0600 schrieb olcott:

On 11/8/2024 4:54 AM, joes wrote:

Am Thu, 07 Nov 2024 21:54:05 -0600 schrieb olcott:

On 11/7/2024 9:10 PM, Richard Damon wrote:

On 11/7/24 11:39 AM, olcott wrote:

On 11/7/2024 3:56 AM, Mikko wrote:

On 2024-11-06 15:26:06 +0000, olcott said:

On 11/6/2024 8:39 AM, Mikko wrote:

On 2024-11-05 13:18:43 +0000, olcott said:

On 11/5/2024 3:01 AM, Mikko wrote:

On 2024-11-03 15:13:56 +0000, olcott said:

On 11/3/2024 7:04 AM, Mikko wrote:

On 2024-11-02 12:24:29 +0000, olcott said:

It should be noted that the problem STARTS with a program, which gets
represented with a finite string,

No that it incorrect. It never starts with a program. A TM cannot
handle another TM as its input. It starts with an encoding that has
associated semantics.

Silly distinction that buys you nothing.

It has always only been about the behavior that the INPUT Specifies.
NON-INPUTS HAVE ALWAYS BEEN OFF THE TABLE.

What non-input do you have in mind? The TM the encoding of which we’re
feeding to HHH to simulate?

and that string might be different for different deciders, as the
problem doesn't define a specific encoding method.
Your insistance that the problem starts with a finite-string just
shows your ignorance.

It is much dumber to think that a TM takes another actual TM as input.
It is common knowledge that this is not the case.

It is common knowledge that nobody is giving actual(?) TMs as input.

Whatever those are.

DDD specifies a non-halting computation to HHH because DDD calls HHH
in recursive simulation.

No, because the HHH that DDD calls is programmed to break that
recursive simulation, and thus make the results finite.

Now you are back to stupidly saying that DDD emulated by HHH reaches
its final halt state because it is aborted.

You are confusing your simulation levels here.
Not because itself is aborted, but because the HHH that it calls
aborts.

DDD emulated by HHH never reaches its own final state EVEN IF GOD
COMMANDS IT!!!

No, I mean the DDD that the outermost

If God commands it then God is INCORRECT.

Yes, you are incorrect.

You know that DDD emulated by HHH cannot possibly reach its own final
state (whether HHH ever aborts or not) and seem to believe that this
is irrelevant.

When HHH aborts, it halts and returns.

int main()
{
   HHH(DDD); // When HHH aborts its emulated DDD
             // this emulated DDD does not return

Maybe it would have, but ok.

   DDD();    // When DDD calls HHH(DDD)
             // this emulated DDD never returns
}

What about this DDD though?

If you change HHH to not abort, then DDD does become non-halting, but

The infinite set of each HHH that emulates DDD (that aborts at some
point or not) is not above your educational or intellectual capacity.

The selfreference of HHH seems to be above your intellectual capacity.

Surprising relationship, considering your own pathology.

HHH doesn't give the right answer. That is a DIFFERENT HHH, and thus
a DIFFERENT DDD (as DDD to be a program includes ALL the code it
uses, so it includes the code of HHH, which you changed)

*We are not even talking about HHH giving the right answer yet*

No, we are talking about HHH halting either way.

(a) DDD emulated by every HHH that aborts at some point
      or not never reaches its final state.

You mean, if DDD called a fixed simulator that didn’t change along with
the one simulating DDD.

For N = 0 to  ∞
each instance of HHH that emulate DDD N number of times DDD fails to
reach its final state and halts.

Only if DDD actually calls the strict simulator HHH1 instead of the
aborting HHH.

(b) This means that the right answer would be that DDD emulated
      by HHH does not halt.

This means that HHH aborts, halts and returns "DDD doesn’t halt". Then
DDD, which calls HHH, also halts, making HHH wrong.

DDD emulated by HHH never halts as a matter of actual fact.
The directly executed DDD does halt conclusively proves that it is not
the same instance of DDD.

Nobody cares about non-inputs.

Termination analyzers report on the behavior that their input specifies.
They never have been allowed to report on anything else.

Such as programs suddenly calling different simulators than they are
simulated by.

(c) If HHH rejects DDD as non halting then HHH is correct.
(d) Can any HHH compute the mapping from its input DDD to
      the actual behavior that DDD specifies as a pure function of its
      inputs *IS THE ONLY ACTUAL REMAINING UNRESOLVED ISSUE*

Why shouldn’t it?

--
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.