Re: How the requirements that Professor Sipser agreed to are exactly met

On 5/12/25 10:01 PM, olcott wrote:

 If the Goldbach conjecture is true (and there is
no short-cut) this requires testing against every
element of the set of natural numbers an infinite
computation.
 *That had nothing to do with this point*
  >> Exactly what actual reasoning shows that this
 >> is superior to reporting on the behavior that
 >> its input actual specifies?

Well, since the behavior of the input for a halt decider is DEFINED to be the behavior of the program that it describes.
That means that *YOU* are the one advocating to answer about something other than that.
I don't know where the comment about the Goldbach conjecture came from on this thread, but the other discussion on that just illustrte that you don't understand the nature of Turth.
If the only path that establishes a statement is a infinite series of deductive steps, then that statement is still true. It is just unprovable.
The fact that you try to argue otherwise just points out how out of touch you are with the basics of logic.
Yes, there are some logic field that don't let an infinte chain of actions, that don't have a finite chain do that to, make a statement true, but those do that by not having any such statements, as everything can either be estabished, refuted, or shown to be not a truth-bearer with a finite chain of steps as the logci system is limited.
But none of the theory you try to talk about are about such limited fields, as they require, in effect, the ability to have the properties of the infintie set of Natural Numbers, which is part of the power that gives us this "problem" of incompleteness and undeciability.
Logic system over finite fields don't have that sort of problem, but are very limited in their usefulness.