Re: Refutation of Turing’s 1936 Halting Problem Proof Based on Self-Referential Conflation as a Category (Type) Error

On 4/25/2025 11:54 AM, Richard Damon wrote:

On 4/25/25 12:31 PM, olcott wrote:

Once we understand that Turing computable functions are only allowed
to derived their outputs by applying finite string operations to their
inputs then my claim about the behavior of DD that HHH must report on
is completely proven.
>

Youy have your words wrong. They are only ABLE to use finite algorithms
of finite string operations. The problem they need to solve do not need
to be based on that, but on just general mappings of finite strings to
finite strings that might not be described by a finite algorithm.
The mapping is computable, *IF* we can find a finite algorith of
transformation steps to make that mapping.
 

There are no finite string operations that can be applied to the input
to HHH(DD) that derive the behavior of of the directly executed DD thus
DD is forbidden from reporting on this behavior.