Re: Proof that H(D,D) meets its abort criteria --self-evident truth--

On 3/16/24 9:59 PM, olcott wrote:

On 3/16/2024 11:56 PM, Richard Damon wrote:

On 3/16/24 9:44 PM, olcott wrote:

On 3/16/2024 11:33 PM, Richard Damon wrote:

On 3/16/24 9:26 PM, olcott wrote:

On 3/16/2024 11:21 PM, Richard Damon wrote:

On 3/16/24 9:14 PM, olcott wrote:

On 3/16/2024 11:12 PM, Richard Damon wrote:

On 3/16/24 9:08 PM, olcott wrote:

On 3/16/2024 10:50 PM, Richard Damon wrote:

On 3/16/24 7:54 PM, olcott wrote:

On 3/16/2024 9:50 PM, Richard Damon wrote:

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So, are you admitting that you "Halt Deciders" are

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Not being discussed. We are only looking at this:
[Proof that H(D,D) meets its abort criteria]
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Then why do you call them Halt Deciders?

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In this thread we must focus on the single point
[Proof that H(D,D) meets its abort criteria]
Or we will never ever get closure on this single point.
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So, is this criteria supposed to be a Halt Deciding criteria?
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H is an algorithm that simulates its input and correctly
determines whether or not it needs to abort this simulation.
That is all that this thread's H does.
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And what defines "Need"?
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Note, if H is an algorithm, we can't talk of "changing" it, or it looses its identity.
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It is the set of every implementation of its spec:

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But it was an algorithm, not a set. Make up your mind.
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(a) H(D,D) Simulate input.
(b) Determine if it needs to stop simulating its input to prevent
the simulated D(D) from never halting.

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And how do you determine NEED.
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Determine if it needs to stop simulating its input
*to prevent the simulated D(D) from never halting*
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But H already does what it does.
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We never validated that it is definitely correct.
 

How do we know?
Your "algorithm" included a non-algorithmic step, so how do you intend to perform that step?
Best you can do is try all possiblities are remove those that fail.
Which removes them all.
You need to define how to determine NEED as an algorithm.
That mean the decision is based just on what it knows already.
Then the results can be compared to the specification to determine it is correct.
You can't just "assume" a given algorithm meets a specificaiton, unless the specification is itself an algorithm, which this isnt.
As you said, we can't ask H to look into the future, so it can't base its actions on what WILL (or will not) happen in the future.
We also can't imagine CHANGING H, as it is what it is, we can imagine something else acting in its stead (but that doesn't affect the definition of H) and H can't act on the imagining, we can only use that to show if it was correct or not.