Re: Proof that H(D,D) meets its abort criteria --incorrect question instance--

On 3/20/2024 2:57 PM, Richard Damon wrote:

On 3/20/24 2:07 PM, olcott wrote:

<snip>

Since I defined the term "incorrect question" and I defined the
term "incorrect question instance" I cannot possibly have defined
them incorrectly. These are stipulative definitions.
https://en.wikipedia.org/wiki/Stipulative_definition

 And by stipulating your definition, you havve disconnected it from any other use in the theory, in prticular, just because some question turns out to be an Olcott-Incorrect Question doesn't me it is an improper question to put to a decider to see if it meets its defintion.
 

Every Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ says Ĥ ⟨Ĥ⟩ halts and fails to halt.
Every Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   says Ĥ ⟨Ĥ⟩ does not halt and then halts.
Every Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ that answers YES is wrong.
Every Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ that answers  NO is wrong.
Therefore:
Does Ĥ ⟨Ĥ⟩ halt? is an incorrect question instance when posed to Ĥ.H.
It is logically impossible for Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ to provide a correct answer
because every answer that Ĥ.H provides is contradicted.
If the inability to do the logically impossible was any actual
limitation then humans would be limited in that they cannot
correctly answer this question: What time is is (yes or no)?

This seems to be something you don't understand about Stipulating your definitions.
 

>
An {incorrect question} is any question that has no correct answer.
What time is it (yes or no)? is an incorrect question.
>

So, by YOUR definitoin, the "Halting Question", namely the question, "Does the Computation described by this input Halt?" is not an {incorrect question}, as EVERY specific computation will either Halt or Not.
 

Once the incorrect question instances are tossed out then it is
a correct question.

 

An {incorrect question instance} is any question that has no
correct answer from the one that this question was posed to.

 And, if the "one" that question was posed to, by reason of the "definition" of that "one" just doesn't give the correct answer, are you saying that is enough to make that question instance invalid?
 

When the only reason that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ fails to provide a correct
answer is that every answer is contradicted then these incorrect
question instances must be tossed out.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer