Re: The philosophy of computation reformulates existing ideas on a new basis --- getting somewhere

Am Sun, 03 Nov 2024 12:33:44 -0600 schrieb olcott:

On 11/3/2024 12:20 PM, Richard Damon wrote:

On 11/3/24 9:39 AM, olcott wrote:

The finite string input to HHH specifies that HHH MUST EMULATE ITSELF
emulating DDD.

Right, and it must CORRECTLY determine what an unbounded emulation of
that input would do, even if its own programming only lets it emulate a
part of that.

Yes this is exactly correct. I don't understand why you keep disagreeing
with your own self this.

You understood it wrong previously.

The finite string input to HHH1 specifies that HHH1 MUST NOT EMULATE
ITSELF emulating DDD.

But the semantics of the string haven't changed, as the string needs to
contain all the details of how the machine it is looking at will work.

DDD emulated by HHH specifies that HHH will emulate itself emulating
DDD.
DDD emulated by HHH1 specifies that HHH1 will NOT emulate itself
emulating DDD.

And here we have you cardinal mistake: this case requires DDD to call
its own emulator. We are interested in that program which is constructed
from it; it doesn't exist on its own but depends on HHH/HHH1.
Usually a program is specified by its code, including everything that
it calls. But even HHH1 cannot simulate EEE(){HHH1(EEE);}.

Unless HHH rejects its input DDD as non halting the executed DDD never
stops running. This itself proves that HHH is correct and that DDD is
not the same instance as the one that HHH rejected.

You have cause and effect backwards.

--
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.