XPost: comp.theory, sci.logic
On 10/21/2021 9:21 PM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:
On 10/21/2021 5:38 PM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:
q0 ⟨Ĥ⟩ ⊢* Ĥq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥqn
We can tell that Ĥq0 correctly determines the halt status of ⟨Ĥ⟩ ⟨Ĥ⟩
entirely on the basis of the meaning of the words.
We can tell, based entirely on how Ĥ is defined, that no such Ĥ can
exit.
You can only "tell" this by making sure to dismiss what I say
out-of-hand without carefully evaluating it point-by-point.
Everyone (except you) can tell it by reading the proof given in Linz. Everything Linz says applies to what you consider your very special "simulating halt deciders".
The halt decider must only correctly decide whether or not its input
halts on its input. As long as this decision is correct then it is
impossible for anything else to show that the halt decider is incorrect.
The halt decider must only correctly decide whether or not its input
halts on its input. As long as this decision is correct then it is
impossible for anything else to show that the halt decider is incorrect.
The halt decider must only correctly decide whether or not its input
halts on its input. As long as this decision is correct then it is
impossible for anything else to show that the halt decider is incorrect.
The halt decider must only correctly decide whether or not its input
halts on its input. As long as this decision is correct then it is
impossible for anything else to show that the halt decider is incorrect.
The halt decider must only correctly decide whether or not its input
halts on its input. As long as this decision is correct then it is
impossible for anything else to show that the halt decider is incorrect.
--
Copyright 2021 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
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