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

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:
 

HHH does compute the mapping from its input DDD
to the actual behavior that DDD specifies and this
DOES INCLUDE HHH emulating itself emulating DDD.

 Yes but not the particular mapping required by the halting problem.

 Yes it is the particular mapping required by the halting problem.
The exact same process occurs in the Linz proof.

The halting probelm requires that every halt decider terminates.
If HHH(DDD) terminates so does DDD. The halting problmen requires
that if DDD terminates then HHH(DDD) accepts as halting.
If HHH(DDD) rejects as non-halting then HHH is not a halt decider.
If HHH(DDD) does not terminate then HHH is not a halt deider.
It is easy to construct a decider that accpets DDD but that decider
is not HHH.
--
Mikko