On 11/05/2025 14:21, Mr Flibble wrote:
This reframing dissolves the paradox by making the Halting Problem
itself an ill-posed question.
"P is a syntactically correct program in some well-defined
Turing-complete language. Does P stop when it is applied to this data
X?" is a meaningful and well-formed question. It's not a Carrollian
question like Olcott's "what time is it, yes or no?" It has a sensible answer. Either P stops for X, or it doesn't.
It's a question that can in many (but not all) cases be answered quickly
and easily enough (and correctly) by humans, often requiring no more
than a brief glimpse. (I say 'not all' only because it is not beyond the
wit of mankind to trump up extraordinarily complicated and deliberately obfuscated code that might easily defeat a programmer's casual glance.)
Some simple examples in K&R C:
main(){}
main(){for(;;);}
main(){puts("Hello");}
#include <stdio.h>
main(){long c=0;int ch; while((ch = getchar()) !=
EOF)++c;printf("%ld\n", c);} /* input: the complete works of Shakespeare
*/
Any competent C programmer can solve these at a glance - Halts, Loops,
Halts, Halts, in that order - so why shouldn't a programmer be able to?
The Halting Problem asks a more complicated question. ``Is it possible
to write a program that answers the above question for arbitrary P and arbitrary X?"
Again, the question is meaningful and well-formed. It's syntactically
and grammatically adequate, and anyone claiming not to know what it
means is laying themselves open to a charge of disingenuousness. The
only difficult part is the answer, but there's nothing
self-contradictory or self-referential or paradoxical about the
question.
but there's nothing self-contradictory or self-referential orparadoxical about the question.
On 11/05/2025 16:34, Mr Flibble wrote:
On Sun, 11 May 2025 16:25:14 +0100, Richard Heathfield wrote:
For a question to be semantically incorrect, it takes more than just
you and your allies to be unhappy with it.
For a question to be semantically correct, it takes more than just you
and your allies to be happy with it.
Indeed. It has to have meaning. It does. That meaning has to be
understood by sufficiently intelligent people. It is.
You don't like the question. I get that. I don't know /why/ you don't
like it, because all your explanations to date have been complete
expletive deleted. For a Usenet article to be semantically correct, it
helps if your readers can understand what the <exp. del.> you're talking about.
What I get from your stand is that you agree with olcott that a 'pathological' input halts... no, never halts... well, you can't decide between you, but you're agreed that it's definitely decidable, right?
On 5/11/2025 10:49 AM, Mr Flibble wrote:
On Sun, 11 May 2025 16:47:09 +0100, Richard Heathfield wrote:
On 11/05/2025 16:34, Mr Flibble wrote:
On Sun, 11 May 2025 16:25:14 +0100, Richard Heathfield wrote:
For a question to be semantically incorrect, it takes more than just >>>>> you and your allies to be unhappy with it.
For a question to be semantically correct, it takes more than just
you and your allies to be happy with it.
Indeed. It has to have meaning. It does. That meaning has to be
understood by sufficiently intelligent people. It is.
You don't like the question. I get that. I don't know /why/ you don't
like it, because all your explanations to date have been complete
expletive deleted. For a Usenet article to be semantically correct, it
helps if your readers can understand what the <exp. del.> you're
talking about.
What I get from your stand is that you agree with olcott that a
'pathological' input halts... no, never halts... well, you can't
decide between you, but you're agreed that it's definitely decidable,
right?
Re-read the OP for my answer:
Flibble’s Leap: Why Behavioral Divergence Implies a Type Distinction in
the Halting Problem
===========================================================================================
Summary -------
Flibble argues that the Halting Problem's undecidability proof is built
on a category (type) error: it assumes a program and its own
representation (as a finite string) are interchangeable. This
assumption fails under simulating deciders, revealing a type
distinction through behavioral divergence. As such, all deciders must
respect this boundary, and diagonalization becomes ill-formed. This
reframing dissolves the paradox by making the Halting Problem itself an
ill-posed question.
1. Operational Evidence of Type Distinction
-------------------------------------------
- When a program (e.g., `DD()`) is passed to a simulating halt decider
(`HHH`), it leads to infinite recursion.
- This behavior differs from direct execution (e.g., a crash due to a
stack overflow).
The directly executed DD() simply halts because HHH has stopped the
infinite recursion that it specifies on its second recursive call.
DD emulated by HHH according to the rules of the x86 language cannot
possibly halt. Because all deciders are required to report on what their finite string input specifies HHH must reject DD as non-halting.
For a question to be semantically incorrect, it takes more than just you
and your allies to be unhappy with it.
On 5/11/2025 11:05 AM, Mr Flibble wrote:
On Sun, 11 May 2025 10:56:02 -0500, olcott wrote:That fails to meet the spec of a termination analyzer.
On 5/11/2025 10:49 AM, Mr Flibble wrote:===========================================================================================
On Sun, 11 May 2025 16:47:09 +0100, Richard Heathfield wrote:
On 11/05/2025 16:34, Mr Flibble wrote:
On Sun, 11 May 2025 16:25:14 +0100, Richard Heathfield wrote:
For a question to be semantically incorrect, it takes more than
just you and your allies to be unhappy with it.
For a question to be semantically correct, it takes more than just >>>>>> you and your allies to be happy with it.
Indeed. It has to have meaning. It does. That meaning has to be
understood by sufficiently intelligent people. It is.
You don't like the question. I get that. I don't know /why/ you
don't like it, because all your explanations to date have been
complete expletive deleted. For a Usenet article to be semantically
correct, it helps if your readers can understand what the <exp.
del.> you're talking about.
What I get from your stand is that you agree with olcott that a
'pathological' input halts... no, never halts... well, you can't
decide between you, but you're agreed that it's definitely
decidable, right?
Re-read the OP for my answer:
Flibble’s Leap: Why Behavioral Divergence Implies a Type Distinction >>>> in the Halting Problem
Summary -------
Flibble argues that the Halting Problem's undecidability proof is
built on a category (type) error: it assumes a program and its own
representation (as a finite string) are interchangeable. This
assumption fails under simulating deciders, revealing a type
distinction through behavioral divergence. As such, all deciders must
respect this boundary, and diagonalization becomes ill-formed. This
reframing dissolves the paradox by making the Halting Problem itself
an ill-posed question.
1. Operational Evidence of Type Distinction
-------------------------------------------
- When a program (e.g., `DD()`) is passed to a simulating halt
decider (`HHH`), it leads to infinite recursion.
- This behavior differs from direct execution (e.g., a crash due to a
stack overflow).
The directly executed DD() simply halts because HHH has stopped the
infinite recursion that it specifies on its second recursive call.
That behaviour is due to a decision you have made, that I disagree
with,
the correct thing to do is to allow infinite recursion to manifest as
stack overflow rather than return an artificial halting result.
On 5/11/2025 11:59 AM, Mr Flibble wrote:
On Sun, 11 May 2025 11:49:51 -0500, olcott wrote:
On 5/11/2025 11:05 AM, Mr Flibble wrote:===========================================================================================
On Sun, 11 May 2025 10:56:02 -0500, olcott wrote:
On 5/11/2025 10:49 AM, Mr Flibble wrote:
On Sun, 11 May 2025 16:47:09 +0100, Richard Heathfield wrote:
On 11/05/2025 16:34, Mr Flibble wrote:
On Sun, 11 May 2025 16:25:14 +0100, Richard Heathfield wrote:
For a question to be semantically incorrect, it takes more than >>>>>>>>> just you and your allies to be unhappy with it.
For a question to be semantically correct, it takes more than
just you and your allies to be happy with it.
Indeed. It has to have meaning. It does. That meaning has to be
understood by sufficiently intelligent people. It is.
You don't like the question. I get that. I don't know /why/ you
don't like it, because all your explanations to date have been
complete expletive deleted. For a Usenet article to be
semantically correct, it helps if your readers can understand what >>>>>>> the <exp. del.> you're talking about.
What I get from your stand is that you agree with olcott that a
'pathological' input halts... no, never halts... well, you can't >>>>>>> decide between you, but you're agreed that it's definitely
decidable, right?
Re-read the OP for my answer:
Flibble’s Leap: Why Behavioral Divergence Implies a Type
Distinction in the Halting Problem
That fails to meet the spec of a termination analyzer.
Summary -------
Flibble argues that the Halting Problem's undecidability proof is
built on a category (type) error: it assumes a program and its own >>>>>> representation (as a finite string) are interchangeable. This
assumption fails under simulating deciders, revealing a type
distinction through behavioral divergence. As such, all deciders
must respect this boundary, and diagonalization becomes ill-formed. >>>>>> This reframing dissolves the paradox by making the Halting Problem >>>>>> itself an ill-posed question.
1. Operational Evidence of Type Distinction
-------------------------------------------
- When a program (e.g., `DD()`) is passed to a simulating halt
decider (`HHH`), it leads to infinite recursion.
- This behavior differs from direct execution (e.g., a crash due to >>>>>> a stack overflow).
The directly executed DD() simply halts because HHH has stopped the
infinite recursion that it specifies on its second recursive call.
That behaviour is due to a decision you have made, that I disagree
with,
the correct thing to do is to allow infinite recursion to manifest as
stack overflow rather than return an artificial halting result.
Nevertheless it is impossible to obtain a halting result as the problem
is ill-formed: mapping a halting result of non-halting to the infinite
recursion manifesting due to type mismatch is entirely artificial.
/Flibble
When a simulating termination analyzer examines the behavior that its
input actually specifies and reports on this, then in the case of every conventional Halting Problem proof it is correct to reject this input as non-halting.
On 11/05/2025 18:15, Mr Flibble wrote:
The truth is it neither halts nor doesn't halt as the question being
asked is ill-formed.
So it's stopped running, but it's started hopping?
Your answer is bizarre, but it makes a lot more sense when we realise
that you are desperately trying to avoid saying that it's undecidable.
On 11/05/2025 17:59, Mr Flibble wrote:
it is impossible to obtain a halting result
That sure looks like a concession that it's impossible to devise an
algorithm that will produce a halting result.
Well done. We got you there in the end.
On 5/11/25 11:49 AM, Mr Flibble wrote:
On Sun, 11 May 2025 16:47:09 +0100, Richard Heathfield wrote:
On 11/05/2025 16:34, Mr Flibble wrote:
On Sun, 11 May 2025 16:25:14 +0100, Richard Heathfield wrote:
For a question to be semantically incorrect, it takes more than just >>>>> you and your allies to be unhappy with it.
For a question to be semantically correct, it takes more than just
you and your allies to be happy with it.
Indeed. It has to have meaning. It does. That meaning has to be
understood by sufficiently intelligent people. It is.
You don't like the question. I get that. I don't know /why/ you don't
like it, because all your explanations to date have been complete
expletive deleted. For a Usenet article to be semantically correct, it
helps if your readers can understand what the <exp. del.> you're
talking about.
What I get from your stand is that you agree with olcott that a
'pathological' input halts... no, never halts... well, you can't
decide between you, but you're agreed that it's definitely decidable,
right?
Re-read the OP for my answer:
Which is full of errors as I have pointed out.
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