XPost: sci.logic

On 16/03/24 19:19, olcott wrote:

On 3/16/2024 12:30 PM, immibis wrote:

On 16/03/24 16:28, olcott wrote:

The original halt status criteria has the impossible requirement
that H(D,D) must report on behavior that it does not actually see.
Requiring H to be clairvoyant is an unreasonable requirement.

The purpose of a halting decider is to be clairvoyant. A halting
decider must decide that a program will never halt even if we run it
forever, without actually running it forever.

Not at all. Something like mathematical induction accurately
extrapolates what the future behavior would be:

In other words: mathematical induction is clairvoyant.

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XPost: sci.logic

On 16/03/24 20:58, olcott wrote:

On 3/16/2024 2:56 PM, immibis wrote:

On 16/03/24 19:19, olcott wrote:

On 3/16/2024 12:30 PM, immibis wrote:

On 16/03/24 16:28, olcott wrote:

The original halt status criteria has the impossible requirement
that H(D,D) must report on behavior that it does not actually see.
Requiring H to be clairvoyant is an unreasonable requirement.

The purpose of a halting decider is to be clairvoyant. A halting
decider must decide that a program will never halt even if we run it
forever, without actually running it forever.

Not at all. Something like mathematical induction accurately
extrapolates what the future behavior would be:

In other words: mathematical induction is clairvoyant.

Not at all. Mathematical induction extrapolates on the basis of
what it sees. Requiring H(D,D) to report on behavior that it cannot
even see is incorrect.

In other words: Mathematical induction reports on behaviour that it
cannot even see.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: sci.logic

On 17/03/24 00:02, olcott wrote:

On 3/16/2024 4:09 PM, immibis wrote:

On 16/03/24 20:58, olcott wrote:

On 3/16/2024 2:56 PM, immibis wrote:

On 16/03/24 19:19, olcott wrote:

On 3/16/2024 12:30 PM, immibis wrote:

On 16/03/24 16:28, olcott wrote:

The original halt status criteria has the impossible requirement >>>>>>> that H(D,D) must report on behavior that it does not actually see. >>>>>>> Requiring H to be clairvoyant is an unreasonable requirement.

The purpose of a halting decider is to be clairvoyant. A halting
decider must decide that a program will never halt even if we run
it forever, without actually running it forever.

Not at all. Something like mathematical induction accurately
extrapolates what the future behavior would be:

In other words: mathematical induction is clairvoyant.

Not at all. Mathematical induction extrapolates on the basis of
what it sees. Requiring H(D,D) to report on behavior that it cannot
even see is incorrect.

In other words: Mathematical induction reports on behaviour that it
cannot even see.

Extrapolating with no basis is not the same as extrapolating from
a basis. H(D,D) has no basis to report on directly executed D(D).

Does mathematical induction have a basis to report on directly executed
D(D)?

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XPost: sci.logic

On 3/16/24 11:19 AM, olcott wrote:

On 3/16/2024 12:30 PM, immibis wrote:

On 16/03/24 16:28, olcott wrote:

The original halt status criteria has the impossible requirement
that H(D,D) must report on behavior that it does not actually see.
Requiring H to be clairvoyant is an unreasonable requirement.

The purpose of a halting decider is to be clairvoyant. A halting
decider must decide that a program will never halt even if we run it
forever, without actually running it forever.

Not at all. Something like mathematical induction accurately
extrapolates what the future behavior would be:

*Proof that H(D,D) must abort the simulation of its input*
(a) main() invokes H(D,D)
(b) H(D,D) simulates D(D)
(c) Simulated D(D) calls simulated H(D,D)
*Simulation invariant*
The cycle between (b) and (c) cannot stop unless H aborts its simulation

But your rule doesn't actually prove non-halting, as it ignores the
action of all the H's

Halting requires proving that if the OUTER H didn't abort, but ohter
instance still will if they woud have, the simulation would not stop.

Yes, there ARE correct induction arguments that handle SOME cases (but
not this one), that can show halting without needing to actually
simulate forever (because the DO prove that the full simulation would
not halt).

You just don't seem to understand how to actual do this form of
induction argument, just like you show you don't know how to prove
something or what truth actually means.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: sci.logic

On 3/16/24 12:58 PM, olcott wrote:

On 3/16/2024 2:56 PM, immibis wrote:

On 16/03/24 19:19, olcott wrote:

On 3/16/2024 12:30 PM, immibis wrote:

On 16/03/24 16:28, olcott wrote:

The original halt status criteria has the impossible requirement
that H(D,D) must report on behavior that it does not actually see.
Requiring H to be clairvoyant is an unreasonable requirement.

The purpose of a halting decider is to be clairvoyant. A halting
decider must decide that a program will never halt even if we run it
forever, without actually running it forever.

Not at all. Something like mathematical induction accurately
extrapolates what the future behavior would be:

In other words: mathematical induction is clairvoyant.

Not at all. Mathematical induction extrapolates on the basis of
what it sees. Requiring H(D,D) to report on behavior that it cannot
even see is incorrect.

Nope.

I guess you don't understand how induction works.

Mathematical induction uses the rules that evolve the series, to be able
to show something follows for all.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: sci.logic

On 3/16/24 4:02 PM, olcott wrote:

On 3/16/2024 4:09 PM, immibis wrote:

On 16/03/24 20:58, olcott wrote:

On 3/16/2024 2:56 PM, immibis wrote:

On 16/03/24 19:19, olcott wrote:

On 3/16/2024 12:30 PM, immibis wrote:

On 16/03/24 16:28, olcott wrote:

The original halt status criteria has the impossible requirement >>>>>>> that H(D,D) must report on behavior that it does not actually see. >>>>>>> Requiring H to be clairvoyant is an unreasonable requirement.

The purpose of a halting decider is to be clairvoyant. A halting
decider must decide that a program will never halt even if we run
it forever, without actually running it forever.

Not at all. Something like mathematical induction accurately
extrapolates what the future behavior would be:

In other words: mathematical induction is clairvoyant.

Not at all. Mathematical induction extrapolates on the basis of
what it sees. Requiring H(D,D) to report on behavior that it cannot
even see is incorrect.

In other words: Mathematical induction reports on behaviour that it
cannot even see.

Extrapolating with no basis is not the same as extrapolating from
a basis. H(D,D) has no basis to report on directly executed D(D).

Which is why it can't use induction.

It has sufficient basis (N steps of D(D) correctly simulated by H)
to report on ∞ steps of D(D) correctly simulated by H.

Nope, since H doesn't correctly simulate D(D) (since aborting isn't
correct simulation)

You logic is that H*(D*,D*) can predict what D(D) does (Where H* is H
modified to not have the abort, and D* is the template built on H*)

But that isn't a sound arguement.

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