Mr Flibble <flibble@reddwarf.jmc> writes:

> On Thu, 07 Jul 2022 21:50:21 +0100
> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>
>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>
>> > On Thu, 07 Jul 2022 20:37:53 +0100
>> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>> >
>> >> Mr Flibble <flibble@reddwarf.jmc> writes:
>> >>
>> >> > On Thu, 07 Jul 2022 01:21:36 +0100
>> >> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>> >> >
>> >> >> Mr Flibble <flibble@reddwarf.jmc> writes:
>> >> >>
>> >> >> > On Wed, 06 Jul 2022 19:15:06 +0100
>> >> >> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>> >>
>> >> >> >> That's not even a useful three-way decider since no one
>> >> >> >> really cares about that one case in practical situations.
>> >> >> >>
>> >> >> >
>> >> >> > Practical situations? It is a thought experiment: a potential
>> >> >> > refutation of the HP proofs.
>> >> >>
>> >> >> No it isn't. The proofs are about halt deciders, and you are
>> >> >> not proposing or describing a halt decider. Programs (TMs,
>> >> >> whatever) that do not get every instance of the halting problem
>> >> >> right are ten-a-penny and say nothing about the proofs.
>> >> >>
>> >> >> Their only value is in practical situations, but you seem to
>> >> >> agree with me that your suggestion was never intended to, and
>> >> >> does not have, that kind of utility.
>> >> >
>> >> > I believe my signaling halt decider should always get the answer
>> >> > right ergo is a potential refutation of the proofs.
>> >>
>> >> I can't see why you believe that since you explicitly state
>> >> otherwise. Your original post a vague about a lot of things, but
>> >> it seemed pretty clear about this.
>> >
>> > Getting the answer right means one of three things for my signaling
>> > halting decider:
>> >
>> > 1) Decision halting
>> > 2) Decision non-halting
>> > 3) Exception (pathological input)
>>
>> Yes, as I said, that much was clear. Such "deciders" and not very
>> interesting unless 3 is a semantic property of the computation being
>> decided, in which case I refer you to Rice's theorem.
>>
>> > If you want to assert that having a third outcome of a exception
>> > signal means this has nothing to do with the HP then you are free
>> > to assert that but I disagree.
>>
>> The fact that such TMs (or C programs, or algorithms, or whatever)
>> exist is a trivial fact not in dispute.
>>
>> Of course, there are /some/ meanings for 3 (and the consequent 1 and
>> 2) for which you would /not/ be able to write the code, (since it
>> would, in fact, imply a real halt decider) but you don't say enough
>> about these conditions to be able to say more.
>
> I am aware of the problems with a simulation-based halting decider: for
> returning a decision of non-halting the SHD would rely on detecting
> repeated machine state given a machine of finite size has a finite
> number of configurations; for returning any decision I also appreciate
> that the SHD might not answer within the lifetime of the observable
> universe but that would still, I suggest, be a finite not infinite
> time.

What has this got to do with explicitly giving an answer that is neither
1 nor 2? All computations halt or they do not halt, so the answer is
always 1 or 2.

Some versions of 1, 2 and 3 are also impossible, but most are simply not
interesting.

--
Ben.

On Thu, 07 Jul 2022 22:41:43 +0100
Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:

> Mr Flibble <flibble@reddwarf.jmc> writes:
>
> > On Thu, 07 Jul 2022 21:50:21 +0100
> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >
> >> Mr Flibble <flibble@reddwarf.jmc> writes:
> >>
> >> > On Thu, 07 Jul 2022 20:37:53 +0100
> >> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >> >
> >> >> Mr Flibble <flibble@reddwarf.jmc> writes:
> >> >>
> >> >> > On Thu, 07 Jul 2022 01:21:36 +0100
> >> >> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >> >> >
> >> >> >> Mr Flibble <flibble@reddwarf.jmc> writes:
> >> >> >>
> >> >> >> > On Wed, 06 Jul 2022 19:15:06 +0100
> >> >> >> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >> >>
> >> >> >> >> That's not even a useful three-way decider since no one
> >> >> >> >> really cares about that one case in practical situations.
> >> >> >> >>
> >> >> >> >
> >> >> >> > Practical situations? It is a thought experiment: a
> >> >> >> > potential refutation of the HP proofs.
> >> >> >>
> >> >> >> No it isn't. The proofs are about halt deciders, and you are
> >> >> >> not proposing or describing a halt decider. Programs (TMs,
> >> >> >> whatever) that do not get every instance of the halting
> >> >> >> problem right are ten-a-penny and say nothing about the
> >> >> >> proofs.
> >> >> >>
> >> >> >> Their only value is in practical situations, but you seem to
> >> >> >> agree with me that your suggestion was never intended to, and
> >> >> >> does not have, that kind of utility.
> >> >> >
> >> >> > I believe my signaling halt decider should always get the
> >> >> > answer right ergo is a potential refutation of the proofs.
> >> >> >
> >> >>
> >> >> I can't see why you believe that since you explicitly state
> >> >> otherwise. Your original post a vague about a lot of things, but
> >> >> it seemed pretty clear about this.
> >> >
> >> > Getting the answer right means one of three things for my
> >> > signaling halting decider:
> >> >
> >> > 1) Decision halting
> >> > 2) Decision non-halting
> >> > 3) Exception (pathological input)
> >>
> >> Yes, as I said, that much was clear. Such "deciders" and not very
> >> interesting unless 3 is a semantic property of the computation
> >> being decided, in which case I refer you to Rice's theorem.
> >>
> >> > If you want to assert that having a third outcome of a exception
> >> > signal means this has nothing to do with the HP then you are free
> >> > to assert that but I disagree.
> >>
> >> The fact that such TMs (or C programs, or algorithms, or whatever)
> >> exist is a trivial fact not in dispute.
> >>
> >> Of course, there are /some/ meanings for 3 (and the consequent 1
> >> and 2) for which you would /not/ be able to write the code, (since
> >> it would, in fact, imply a real halt decider) but you don't say
> >> enough about these conditions to be able to say more.
> >
> > I am aware of the problems with a simulation-based halting decider:
> > for returning a decision of non-halting the SHD would rely on
> > detecting repeated machine state given a machine of finite size has
> > a finite number of configurations; for returning any decision I
> > also appreciate that the SHD might not answer within the lifetime
> > of the observable universe but that would still, I suggest, be a
> > finite not infinite time.
>
> What has this got to do with explicitly giving an answer that is
> neither 1 nor 2? All computations halt or they do not halt, so the
> answer is always 1 or 2.

This is why I class the pathological input contradiction as an error, as
an exception to be raised/signaled, rather than a decision of halting or
non-halting. This is only interesting as a possible refutation of the
HP proofs based on [Strachey 1965]; it doesn't have any practical
utility.

>
> Some versions of 1, 2 and 3 are also impossible, but most are simply
> not interesting.
>

/Flibble

Mr Flibble <flibble@reddwarf.jmc> writes:

> On Thu, 07 Jul 2022 22:41:43 +0100
> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>
>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>
>> > On Thu, 07 Jul 2022 21:50:21 +0100
>> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>> >
>> >> Mr Flibble <flibble@reddwarf.jmc> writes:
>> >>
>> >> > On Thu, 07 Jul 2022 20:37:53 +0100
>> >> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>> >> >
>> >> >> Mr Flibble <flibble@reddwarf.jmc> writes:
>> >> >>
>> >> >> > On Thu, 07 Jul 2022 01:21:36 +0100
>> >> >> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>> >> >> >
>> >> >> >> Mr Flibble <flibble@reddwarf.jmc> writes:
>> >> >> >>
>> >> >> >> > On Wed, 06 Jul 2022 19:15:06 +0100
>> >> >> >> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>> >> >>
>> >> >> >> >> That's not even a useful three-way decider since no one
>> >> >> >> >> really cares about that one case in practical situations.
>> >> >> >> >>
>> >> >> >> >
>> >> >> >> > Practical situations? It is a thought experiment: a
>> >> >> >> > potential refutation of the HP proofs.
>> >> >> >>
>> >> >> >> No it isn't. The proofs are about halt deciders, and you are
>> >> >> >> not proposing or describing a halt decider. Programs (TMs,
>> >> >> >> whatever) that do not get every instance of the halting
>> >> >> >> problem right are ten-a-penny and say nothing about the
>> >> >> >> proofs.
>> >> >> >>
>> >> >> >> Their only value is in practical situations, but you seem to
>> >> >> >> agree with me that your suggestion was never intended to, and
>> >> >> >> does not have, that kind of utility.
>> >> >> >
>> >> >> > I believe my signaling halt decider should always get the
>> >> >> > answer right ergo is a potential refutation of the proofs.
>> >> >> >
>> >> >>
>> >> >> I can't see why you believe that since you explicitly state
>> >> >> otherwise. Your original post a vague about a lot of things, but
>> >> >> it seemed pretty clear about this.
>> >> >
>> >> > Getting the answer right means one of three things for my
>> >> > signaling halting decider:
>> >> >
>> >> > 1) Decision halting
>> >> > 2) Decision non-halting
>> >> > 3) Exception (pathological input)
>> >>
>> >> Yes, as I said, that much was clear. Such "deciders" and not very
>> >> interesting unless 3 is a semantic property of the computation
>> >> being decided, in which case I refer you to Rice's theorem.
>> >>
>> >> > If you want to assert that having a third outcome of a exception
>> >> > signal means this has nothing to do with the HP then you are free
>> >> > to assert that but I disagree.
>> >>
>> >> The fact that such TMs (or C programs, or algorithms, or whatever)
>> >> exist is a trivial fact not in dispute.
>> >>
>> >> Of course, there are /some/ meanings for 3 (and the consequent 1
>> >> and 2) for which you would /not/ be able to write the code, (since
>> >> it would, in fact, imply a real halt decider) but you don't say
>> >> enough about these conditions to be able to say more.
>> >
>> > I am aware of the problems with a simulation-based halting decider:
>> > for returning a decision of non-halting the SHD would rely on
>> > detecting repeated machine state given a machine of finite size has
>> > a finite number of configurations; for returning any decision I
>> > also appreciate that the SHD might not answer within the lifetime
>> > of the observable universe but that would still, I suggest, be a
>> > finite not infinite time.
>>
>> What has this got to do with explicitly giving an answer that is
>> neither 1 nor 2? All computations halt or they do not halt, so the
>> answer is always 1 or 2.
>
> This is why I class the pathological input contradiction as an error, as
> an exception to be raised/signaled, rather than a decision of halting or
> non-halting. This is only interesting as a possible refutation of the
> HP proofs based on [Strachey 1965];

Strachey's 1965 note is about halt deciders. You are not presenting a
halt decider. Yes, the proofs don't apply to you proposed algorithm,
but then proof about primes don't apply to composite numbers.

--
Ben.

On Thu, 07 Jul 2022 23:03:04 +0100
Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:

> Mr Flibble <flibble@reddwarf.jmc> writes:
>
> > On Thu, 07 Jul 2022 22:41:43 +0100
> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >
> >> Mr Flibble <flibble@reddwarf.jmc> writes:
> >>
> >> > On Thu, 07 Jul 2022 21:50:21 +0100
> >> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >> >
> >> >> Mr Flibble <flibble@reddwarf.jmc> writes:
> >> >>
> >> >> > On Thu, 07 Jul 2022 20:37:53 +0100
> >> >> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >> >> >
> >> >> >> Mr Flibble <flibble@reddwarf.jmc> writes:
> >> >> >>
> >> >> >> > On Thu, 07 Jul 2022 01:21:36 +0100
> >> >> >> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >> >> >> >
> >> >> >> >> Mr Flibble <flibble@reddwarf.jmc> writes:
> >> >> >> >>
> >> >> >> >> > On Wed, 06 Jul 2022 19:15:06 +0100
> >> >> >> >> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >> >> >>
> >> >> >> >> >> That's not even a useful three-way decider since no one
> >> >> >> >> >> really cares about that one case in practical
> >> >> >> >> >> situations.
> >> >> >> >> >
> >> >> >> >> > Practical situations? It is a thought experiment: a
> >> >> >> >> > potential refutation of the HP proofs.
> >> >> >> >>
> >> >> >> >> No it isn't. The proofs are about halt deciders, and you
> >> >> >> >> are not proposing or describing a halt decider. Programs
> >> >> >> >> (TMs, whatever) that do not get every instance of the
> >> >> >> >> halting problem right are ten-a-penny and say nothing
> >> >> >> >> about the proofs.
> >> >> >> >>
> >> >> >> >> Their only value is in practical situations, but you seem
> >> >> >> >> to agree with me that your suggestion was never intended
> >> >> >> >> to, and does not have, that kind of utility.
> >> >> >> >
> >> >> >> > I believe my signaling halt decider should always get the
> >> >> >> > answer right ergo is a potential refutation of the proofs.
> >> >> >> >
> >> >> >>
> >> >> >> I can't see why you believe that since you explicitly state
> >> >> >> otherwise. Your original post a vague about a lot of things,
> >> >> >> but it seemed pretty clear about this.
> >> >> >
> >> >> > Getting the answer right means one of three things for my
> >> >> > signaling halting decider:
> >> >> >
> >> >> > 1) Decision halting
> >> >> > 2) Decision non-halting
> >> >> > 3) Exception (pathological input)
> >> >>
> >> >> Yes, as I said, that much was clear. Such "deciders" and not
> >> >> very interesting unless 3 is a semantic property of the
> >> >> computation being decided, in which case I refer you to Rice's
> >> >> theorem.
> >> >> > If you want to assert that having a third outcome of a
> >> >> > exception signal means this has nothing to do with the HP
> >> >> > then you are free to assert that but I disagree.
> >> >>
> >> >> The fact that such TMs (or C programs, or algorithms, or
> >> >> whatever) exist is a trivial fact not in dispute.
> >> >>
> >> >> Of course, there are /some/ meanings for 3 (and the consequent 1
> >> >> and 2) for which you would /not/ be able to write the code,
> >> >> (since it would, in fact, imply a real halt decider) but you
> >> >> don't say enough about these conditions to be able to say more.
> >> >>
> >> >
> >> > I am aware of the problems with a simulation-based halting
> >> > decider: for returning a decision of non-halting the SHD would
> >> > rely on detecting repeated machine state given a machine of
> >> > finite size has a finite number of configurations; for returning
> >> > any decision I also appreciate that the SHD might not answer
> >> > within the lifetime of the observable universe but that would
> >> > still, I suggest, be a finite not infinite time.
> >>
> >> What has this got to do with explicitly giving an answer that is
> >> neither 1 nor 2? All computations halt or they do not halt, so the
> >> answer is always 1 or 2.
> >
> > This is why I class the pathological input contradiction as an
> > error, as an exception to be raised/signaled, rather than a
> > decision of halting or non-halting. This is only interesting as a
> > possible refutation of the HP proofs based on [Strachey 1965];
>
> Strachey's 1965 note is about halt deciders. You are not presenting a
> halt decider. Yes, the proofs don't apply to you proposed algorithm,
> but then proof about primes don't apply to composite numbers.
That is certainly an opinion.

/Flibble

On 7/7/2022 4:04 PM, Mr Flibble wrote:
> On Thu, 07 Jul 2022 23:03:04 +0100
> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>
>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>
>>> On Thu, 07 Jul 2022 22:41:43 +0100
>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>
>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>>>
>>>>> On Thu, 07 Jul 2022 21:50:21 +0100
>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>>>
>>>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>>>>>
>>>>>>> On Thu, 07 Jul 2022 20:37:53 +0100
>>>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>>>>>
>>>>>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>>>>>>>
>>>>>>>>> On Thu, 07 Jul 2022 01:21:36 +0100
>>>>>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>>>>>>>
>>>>>>>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>>>>>>>>>
>>>>>>>>>>> On Wed, 06 Jul 2022 19:15:06 +0100
>>>>>>>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>>>>>>
>>>>>>>>>>>> That's not even a useful three-way decider since no one
>>>>>>>>>>>> really cares about that one case in practical
>>>>>>>>>>>> situations.
>>>>>>>>>>>
>>>>>>>>>>> Practical situations? It is a thought experiment: a
>>>>>>>>>>> potential refutation of the HP proofs.
>>>>>>>>>>
>>>>>>>>>> No it isn't. The proofs are about halt deciders, and you
>>>>>>>>>> are not proposing or describing a halt decider. Programs
>>>>>>>>>> (TMs, whatever) that do not get every instance of the
>>>>>>>>>> halting problem right are ten-a-penny and say nothing
>>>>>>>>>> about the proofs.
>>>>>>>>>>
>>>>>>>>>> Their only value is in practical situations, but you seem
>>>>>>>>>> to agree with me that your suggestion was never intended
>>>>>>>>>> to, and does not have, that kind of utility.
>>>>>>>>>
>>>>>>>>> I believe my signaling halt decider should always get the
>>>>>>>>> answer right ergo is a potential refutation of the proofs.
>>>>>>>>>
>>>>>>>>
>>>>>>>> I can't see why you believe that since you explicitly state
>>>>>>>> otherwise. Your original post a vague about a lot of things,
>>>>>>>> but it seemed pretty clear about this.
>>>>>>>
>>>>>>> Getting the answer right means one of three things for my
>>>>>>> signaling halting decider:
>>>>>>>
>>>>>>> 1) Decision halting
>>>>>>> 2) Decision non-halting
>>>>>>> 3) Exception (pathological input)
>>>>>>
>>>>>> Yes, as I said, that much was clear. Such "deciders" and not
>>>>>> very interesting unless 3 is a semantic property of the
>>>>>> computation being decided, in which case I refer you to Rice's
>>>>>> theorem.
>>>>>>> If you want to assert that having a third outcome of a
>>>>>>> exception signal means this has nothing to do with the HP
>>>>>>> then you are free to assert that but I disagree.
>>>>>>
>>>>>> The fact that such TMs (or C programs, or algorithms, or
>>>>>> whatever) exist is a trivial fact not in dispute.
>>>>>>
>>>>>> Of course, there are /some/ meanings for 3 (and the consequent 1
>>>>>> and 2) for which you would /not/ be able to write the code,
>>>>>> (since it would, in fact, imply a real halt decider) but you
>>>>>> don't say enough about these conditions to be able to say more.
>>>>>>
>>>>>
>>>>> I am aware of the problems with a simulation-based halting
>>>>> decider: for returning a decision of non-halting the SHD would
>>>>> rely on detecting repeated machine state given a machine of
>>>>> finite size has a finite number of configurations; for returning
>>>>> any decision I also appreciate that the SHD might not answer
>>>>> within the lifetime of the observable universe but that would
>>>>> still, I suggest, be a finite not infinite time.
>>>>
>>>> What has this got to do with explicitly giving an answer that is
>>>> neither 1 nor 2? All computations halt or they do not halt, so the
>>>> answer is always 1 or 2.
>>>
>>> This is why I class the pathological input contradiction as an
>>> error, as an exception to be raised/signaled, rather than a
>>> decision of halting or non-halting. This is only interesting as a
>>> possible refutation of the HP proofs based on [Strachey 1965];
>>
>> Strachey's 1965 note is about halt deciders. You are not presenting a
>> halt decider. Yes, the proofs don't apply to you proposed algorithm,
>> but then proof about primes don't apply to composite numbers.
>
> That is certainly an opinion.

An opinion?!?!??!! Is your opinion different? Do you know of any sane
person, i.e., a working mathematician or computer scientist (who isn't
active in these forums as a troll) who shares that opinion? I think you
are just being obstinate and that's not the same as shrewd or smart.
It's just a stall for time while you try to think of something clever to
say. Why not just grant the point and move on?
--
Jeff Barnett

On Thu, 7 Jul 2022 16:18:40 -0600
Jeff Barnett <jbb@notatt.com> wrote:

> On 7/7/2022 4:04 PM, Mr Flibble wrote:
> > On Thu, 07 Jul 2022 23:03:04 +0100
> > Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >
> >> Mr Flibble <flibble@reddwarf.jmc> writes:
> >>
> >>> On Thu, 07 Jul 2022 22:41:43 +0100
> >>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >>>
> >>>> Mr Flibble <flibble@reddwarf.jmc> writes:
> >>>>
> >>>>> On Thu, 07 Jul 2022 21:50:21 +0100
> >>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >>>>>
> >>>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
> >>>>>>
> >>>>>>> On Thu, 07 Jul 2022 20:37:53 +0100
> >>>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >>>>>>>
> >>>>>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
> >>>>>>>>
> >>>>>>>>> On Thu, 07 Jul 2022 01:21:36 +0100
> >>>>>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >>>>>>>>>
> >>>>>>>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
> >>>>>>>>>>
> >>>>>>>>>>> On Wed, 06 Jul 2022 19:15:06 +0100
> >>>>>>>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
> >>>>>>>>
> >>>>>>>>>>>> That's not even a useful three-way decider since no one
> >>>>>>>>>>>> really cares about that one case in practical
> >>>>>>>>>>>> situations.
> >>>>>>>>>>>
> >>>>>>>>>>> Practical situations? It is a thought experiment: a
> >>>>>>>>>>> potential refutation of the HP proofs.
> >>>>>>>>>>
> >>>>>>>>>> No it isn't. The proofs are about halt deciders, and you
> >>>>>>>>>> are not proposing or describing a halt decider. Programs
> >>>>>>>>>> (TMs, whatever) that do not get every instance of the
> >>>>>>>>>> halting problem right are ten-a-penny and say nothing
> >>>>>>>>>> about the proofs.
> >>>>>>>>>>
> >>>>>>>>>> Their only value is in practical situations, but you seem
> >>>>>>>>>> to agree with me that your suggestion was never intended
> >>>>>>>>>> to, and does not have, that kind of utility.
> >>>>>>>>>
> >>>>>>>>> I believe my signaling halt decider should always get the
> >>>>>>>>> answer right ergo is a potential refutation of the proofs.
> >>>>>>>>>
> >>>>>>>>
> >>>>>>>> I can't see why you believe that since you explicitly state
> >>>>>>>> otherwise. Your original post a vague about a lot of things,
> >>>>>>>> but it seemed pretty clear about this.
> >>>>>>>
> >>>>>>> Getting the answer right means one of three things for my
> >>>>>>> signaling halting decider:
> >>>>>>>
> >>>>>>> 1) Decision halting
> >>>>>>> 2) Decision non-halting
> >>>>>>> 3) Exception (pathological input)
> >>>>>>
> >>>>>> Yes, as I said, that much was clear. Such "deciders" and not
> >>>>>> very interesting unless 3 is a semantic property of the
> >>>>>> computation being decided, in which case I refer you to Rice's
> >>>>>> theorem.
> >>>>>>> If you want to assert that having a third outcome of a
> >>>>>>> exception signal means this has nothing to do with the HP
> >>>>>>> then you are free to assert that but I disagree.
> >>>>>>
> >>>>>> The fact that such TMs (or C programs, or algorithms, or
> >>>>>> whatever) exist is a trivial fact not in dispute.
> >>>>>>
> >>>>>> Of course, there are /some/ meanings for 3 (and the consequent
> >>>>>> 1 and 2) for which you would /not/ be able to write the code,
> >>>>>> (since it would, in fact, imply a real halt decider) but you
> >>>>>> don't say enough about these conditions to be able to say more.
> >>>>>>
> >>>>>
> >>>>> I am aware of the problems with a simulation-based halting
> >>>>> decider: for returning a decision of non-halting the SHD would
> >>>>> rely on detecting repeated machine state given a machine of
> >>>>> finite size has a finite number of configurations; for returning
> >>>>> any decision I also appreciate that the SHD might not answer
> >>>>> within the lifetime of the observable universe but that would
> >>>>> still, I suggest, be a finite not infinite time.
> >>>>
> >>>> What has this got to do with explicitly giving an answer that is
> >>>> neither 1 nor 2? All computations halt or they do not halt, so
> >>>> the answer is always 1 or 2.
> >>>
> >>> This is why I class the pathological input contradiction as an
> >>> error, as an exception to be raised/signaled, rather than a
> >>> decision of halting or non-halting. This is only interesting as a
> >>> possible refutation of the HP proofs based on [Strachey 1965];
> >>
> >> Strachey's 1965 note is about halt deciders. You are not
> >> presenting a halt decider. Yes, the proofs don't apply to you
> >> proposed algorithm, but then proof about primes don't apply to
> >> composite numbers.
> >
> > That is certainly an opinion.
>
> An opinion?!?!??!! Is your opinion different? Do you know of any sane
> person, i.e., a working mathematician or computer scientist (who
> isn't active in these forums as a troll) who shares that opinion? I
> think you are just being obstinate and that's not the same as shrewd
> or smart. It's just a stall for time while you try to think of
> something clever to say. Why not just grant the point and move on?

I am moving on; I am done here. I am not going to invest any more time
in the "solved" problem of the Halting Problem. :D

/Flibble

On 7/7/2022 5:22 PM, Mr Flibble wrote:
> On Thu, 7 Jul 2022 16:18:40 -0600
> Jeff Barnett <jbb@notatt.com> wrote:
>
>> On 7/7/2022 4:04 PM, Mr Flibble wrote:
>>> On Thu, 07 Jul 2022 23:03:04 +0100
>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>
>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>>>
>>>>> On Thu, 07 Jul 2022 22:41:43 +0100
>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>>>
>>>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>>>>>
>>>>>>> On Thu, 07 Jul 2022 21:50:21 +0100
>>>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>>>>>
>>>>>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>>>>>>>
>>>>>>>>> On Thu, 07 Jul 2022 20:37:53 +0100
>>>>>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>>>>>>>
>>>>>>>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>>>>>>>>>
>>>>>>>>>>> On Thu, 07 Jul 2022 01:21:36 +0100
>>>>>>>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>>>>>>>>>
>>>>>>>>>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>>>>>>>>>>>
>>>>>>>>>>>>> On Wed, 06 Jul 2022 19:15:06 +0100
>>>>>>>>>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>>>>>>>>
>>>>>>>>>>>>>> That's not even a useful three-way decider since no one
>>>>>>>>>>>>>> really cares about that one case in practical
>>>>>>>>>>>>>> situations.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Practical situations? It is a thought experiment: a
>>>>>>>>>>>>> potential refutation of the HP proofs.
>>>>>>>>>>>>
>>>>>>>>>>>> No it isn't. The proofs are about halt deciders, and you
>>>>>>>>>>>> are not proposing or describing a halt decider. Programs
>>>>>>>>>>>> (TMs, whatever) that do not get every instance of the
>>>>>>>>>>>> halting problem right are ten-a-penny and say nothing
>>>>>>>>>>>> about the proofs.
>>>>>>>>>>>>
>>>>>>>>>>>> Their only value is in practical situations, but you seem
>>>>>>>>>>>> to agree with me that your suggestion was never intended
>>>>>>>>>>>> to, and does not have, that kind of utility.
>>>>>>>>>>>
>>>>>>>>>>> I believe my signaling halt decider should always get the
>>>>>>>>>>> answer right ergo is a potential refutation of the proofs.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I can't see why you believe that since you explicitly state
>>>>>>>>>> otherwise. Your original post a vague about a lot of things,
>>>>>>>>>> but it seemed pretty clear about this.
>>>>>>>>>
>>>>>>>>> Getting the answer right means one of three things for my
>>>>>>>>> signaling halting decider:
>>>>>>>>>
>>>>>>>>> 1) Decision halting
>>>>>>>>> 2) Decision non-halting
>>>>>>>>> 3) Exception (pathological input)
>>>>>>>>
>>>>>>>> Yes, as I said, that much was clear. Such "deciders" and not
>>>>>>>> very interesting unless 3 is a semantic property of the
>>>>>>>> computation being decided, in which case I refer you to Rice's
>>>>>>>> theorem.
>>>>>>>>> If you want to assert that having a third outcome of a
>>>>>>>>> exception signal means this has nothing to do with the HP
>>>>>>>>> then you are free to assert that but I disagree.
>>>>>>>>
>>>>>>>> The fact that such TMs (or C programs, or algorithms, or
>>>>>>>> whatever) exist is a trivial fact not in dispute.
>>>>>>>>
>>>>>>>> Of course, there are /some/ meanings for 3 (and the consequent
>>>>>>>> 1 and 2) for which you would /not/ be able to write the code,
>>>>>>>> (since it would, in fact, imply a real halt decider) but you
>>>>>>>> don't say enough about these conditions to be able to say more.
>>>>>>>>
>>>>>>>
>>>>>>> I am aware of the problems with a simulation-based halting
>>>>>>> decider: for returning a decision of non-halting the SHD would
>>>>>>> rely on detecting repeated machine state given a machine of
>>>>>>> finite size has a finite number of configurations; for returning
>>>>>>> any decision I also appreciate that the SHD might not answer
>>>>>>> within the lifetime of the observable universe but that would
>>>>>>> still, I suggest, be a finite not infinite time.
>>>>>>
>>>>>> What has this got to do with explicitly giving an answer that is
>>>>>> neither 1 nor 2? All computations halt or they do not halt, so
>>>>>> the answer is always 1 or 2.
>>>>>
>>>>> This is why I class the pathological input contradiction as an
>>>>> error, as an exception to be raised/signaled, rather than a
>>>>> decision of halting or non-halting. This is only interesting as a
>>>>> possible refutation of the HP proofs based on [Strachey 1965];
>>>>
>>>> Strachey's 1965 note is about halt deciders. You are not
>>>> presenting a halt decider. Yes, the proofs don't apply to you
>>>> proposed algorithm, but then proof about primes don't apply to
>>>> composite numbers.
>>>
>>> That is certainly an opinion.
>>
>> An opinion?!?!??!! Is your opinion different? Do you know of any sane
>> person, i.e., a working mathematician or computer scientist (who
>> isn't active in these forums as a troll) who shares that opinion? I
>> think you are just being obstinate and that's not the same as shrewd
>> or smart. It's just a stall for time while you try to think of
>> something clever to say. Why not just grant the point and move on?
>
> I am moving on; I am done here. I am not going to invest any more time
> in the "solved" problem of the Halting Problem. :D
>
> /Flibble
>

(1) Input program source code to halt decider
(2) Some magic happens
(3) Report Halting / Not Halting / Pathological self reference using a
signal.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

On 7/7/22 5:53 PM, Mr Flibble wrote:
> On Thu, 07 Jul 2022 22:41:43 +0100
> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>
>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>
>>> On Thu, 07 Jul 2022 21:50:21 +0100
>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>
>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>>>
>>>>> On Thu, 07 Jul 2022 20:37:53 +0100
>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>>>
>>>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>>>>>
>>>>>>> On Thu, 07 Jul 2022 01:21:36 +0100
>>>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>>>>>
>>>>>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>>>>>>>
>>>>>>>>> On Wed, 06 Jul 2022 19:15:06 +0100
>>>>>>>>> Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>>>>>>
>>>>>>>>>> That's not even a useful three-way decider since no one
>>>>>>>>>> really cares about that one case in practical situations.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Practical situations? It is a thought experiment: a
>>>>>>>>> potential refutation of the HP proofs.
>>>>>>>>
>>>>>>>> No it isn't. The proofs are about halt deciders, and you are
>>>>>>>> not proposing or describing a halt decider. Programs (TMs,
>>>>>>>> whatever) that do not get every instance of the halting
>>>>>>>> problem right are ten-a-penny and say nothing about the
>>>>>>>> proofs.
>>>>>>>>
>>>>>>>> Their only value is in practical situations, but you seem to
>>>>>>>> agree with me that your suggestion was never intended to, and
>>>>>>>> does not have, that kind of utility.
>>>>>>>
>>>>>>> I believe my signaling halt decider should always get the
>>>>>>> answer right ergo is a potential refutation of the proofs.
>>>>>>>
>>>>>>
>>>>>> I can't see why you believe that since you explicitly state
>>>>>> otherwise. Your original post a vague about a lot of things, but
>>>>>> it seemed pretty clear about this.
>>>>>
>>>>> Getting the answer right means one of three things for my
>>>>> signaling halting decider:
>>>>>
>>>>> 1) Decision halting
>>>>> 2) Decision non-halting
>>>>> 3) Exception (pathological input)
>>>>
>>>> Yes, as I said, that much was clear. Such "deciders" and not very
>>>> interesting unless 3 is a semantic property of the computation
>>>> being decided, in which case I refer you to Rice's theorem.
>>>>
>>>>> If you want to assert that having a third outcome of a exception
>>>>> signal means this has nothing to do with the HP then you are free
>>>>> to assert that but I disagree.
>>>>
>>>> The fact that such TMs (or C programs, or algorithms, or whatever)
>>>> exist is a trivial fact not in dispute.
>>>>
>>>> Of course, there are /some/ meanings for 3 (and the consequent 1
>>>> and 2) for which you would /not/ be able to write the code, (since
>>>> it would, in fact, imply a real halt decider) but you don't say
>>>> enough about these conditions to be able to say more.
>>>
>>> I am aware of the problems with a simulation-based halting decider:
>>> for returning a decision of non-halting the SHD would rely on
>>> detecting repeated machine state given a machine of finite size has
>>> a finite number of configurations; for returning any decision I
>>> also appreciate that the SHD might not answer within the lifetime
>>> of the observable universe but that would still, I suggest, be a
>>> finite not infinite time.
>>
>> What has this got to do with explicitly giving an answer that is
>> neither 1 nor 2? All computations halt or they do not halt, so the
>> answer is always 1 or 2.
>
> This is why I class the pathological input contradiction as an error, as
> an exception to be raised/signaled, rather than a decision of halting or
> non-halting. This is only interesting as a possible refutation of the
> HP proofs based on [Strachey 1965]; it doesn't have any practical
> utility.

The first problem comes in trying to actually define exactly what the
"exception" should de defined to be.

One big issue is that Peter's H and P aren't really independent
computations. You DON'T have a program H that you provide a description
of an INDEPENDENT program P to, as H and P are intertwined in the same
process space.

This means that there are many possible P's that just can't be given to
H, because they want to put code in their address space that overlaps
with the code for the decider H.

Once you fix that issue, suddenly trying to implement is concept just
becomes impossible, because H can't count on a copy of H in P being at
the same address, because that could easily be some other code at that
address, and if P has a copy of H, that could be at some other address.

Then you have that for computations, "copies" like P is defined to be
using are defined as "functional" equivalents, one that gives the same
answer for every input, not that they need to be coded exactly the same
way (for example, with a Turing Machine, the "names" or "encoding" of
the states just don't matter, but can be permutated, and adding or
removing "null" code is valid. This makes identifying that a piece of
the code in P as being an equivalent of H a tough (i.e. impossible) task.

The second problem is that this "pathological" case isn't the only
"undecidable" one. There also exist programs that represent the
unprovable but true statements, where halting represents disproving the
statement, and proving not halting would be proving that statement. Note
that for some of these, it is also true that you can't even prove that
they are unprovable, because by there nature, a proof that they are
unprovable actually proves that they are true, as if they are false,
this would always be provable (being based on that implies the existance
of a counter example, and testing that counter example is always a
finite operation).

Goldbach's conjecture is a possible example of this (that all even
natural numbers are the sum of two primes). If there IS a counter
example, then there will be a finite number, and given any finite
number, you can cycle through all possible pairss of numbers that could
sum to it, (and there will be a finite number of these) and each of
these can be tested for being a prime in a finite number of steps, so if
it IS false, there WILL exist a number that can be proved to not be able
to be expressible as a pair of prime numbers using only a finite number
of steps.

THus, if we could prove that it IS unprovable, means there can't be a
counter example, which, by definition means it is proven to be true,
which means that the proof it was unprovable must be wrong.

This is part of the logic of Godel's incompleteness proof.

>
>>
>> Some versions of 1, 2 and 3 are also impossible, but most are simply
>> not interesting.
>>
>
> /Flibble
>

On Friday, 8 July 2022 at 03:56:20 UTC+1, richar...@gmail.com wrote:
> On 7/7/22 5:53 PM, Mr Flibble wrote:
> > On Thu, 07 Jul 2022 22:41:43 +0100
> > Ben Bacarisse <ben.u...@bsb.me.uk> wrote:
> >
> >> Mr Flibble <fli...@reddwarf.jmc> writes:
> >>
> >>> On Thu, 07 Jul 2022 21:50:21 +0100
> >>> Ben Bacarisse <ben.u...@bsb.me.uk> wrote:
> >>>
> >>>> Mr Flibble <fli...@reddwarf.jmc> writes:
> >>>>
> >>>>> On Thu, 07 Jul 2022 20:37:53 +0100
> >>>>> Ben Bacarisse <ben.u...@bsb.me.uk> wrote:
> >>>>>
> >>>>>> Mr Flibble <fli...@reddwarf.jmc> writes:
> >>>>>>
> >>>>>>> On Thu, 07 Jul 2022 01:21:36 +0100
> >>>>>>> Ben Bacarisse <ben.u...@bsb.me.uk> wrote:
> >>>>>>>
> >>>>>>>> Mr Flibble <fli...@reddwarf.jmc> writes:
> >>>>>>>>
> >>>>>>>>> On Wed, 06 Jul 2022 19:15:06 +0100
> >>>>>>>>> Ben Bacarisse <ben.u...@bsb.me.uk> wrote:
> >>>>>>
> >>>>>>>>>> That's not even a useful three-way decider since no one
> >>>>>>>>>> really cares about that one case in practical situations.
> >>>>>>>>>>
> >>>>>>>>>
> >>>>>>>>> Practical situations? It is a thought experiment: a
> >>>>>>>>> potential refutation of the HP proofs.
> >>>>>>>>
> >>>>>>>> No it isn't. The proofs are about halt deciders, and you are
> >>>>>>>> not proposing or describing a halt decider. Programs (TMs,
> >>>>>>>> whatever) that do not get every instance of the halting
> >>>>>>>> problem right are ten-a-penny and say nothing about the
> >>>>>>>> proofs.
> >>>>>>>>
> >>>>>>>> Their only value is in practical situations, but you seem to
> >>>>>>>> agree with me that your suggestion was never intended to, and
> >>>>>>>> does not have, that kind of utility.
> >>>>>>>
> >>>>>>> I believe my signaling halt decider should always get the
> >>>>>>> answer right ergo is a potential refutation of the proofs.
> >>>>>>>
> >>>>>>
> >>>>>> I can't see why you believe that since you explicitly state
> >>>>>> otherwise. Your original post a vague about a lot of things, but
> >>>>>> it seemed pretty clear about this.
> >>>>>
> >>>>> Getting the answer right means one of three things for my
> >>>>> signaling halting decider:
> >>>>>
> >>>>> 1) Decision halting
> >>>>> 2) Decision non-halting
> >>>>> 3) Exception (pathological input)
> >>>>
> >>>> Yes, as I said, that much was clear. Such "deciders" and not very
> >>>> interesting unless 3 is a semantic property of the computation
> >>>> being decided, in which case I refer you to Rice's theorem.
> >>>>
> >>>>> If you want to assert that having a third outcome of a exception
> >>>>> signal means this has nothing to do with the HP then you are free
> >>>>> to assert that but I disagree.
> >>>>
> >>>> The fact that such TMs (or C programs, or algorithms, or whatever)
> >>>> exist is a trivial fact not in dispute.
> >>>>
> >>>> Of course, there are /some/ meanings for 3 (and the consequent 1
> >>>> and 2) for which you would /not/ be able to write the code, (since
> >>>> it would, in fact, imply a real halt decider) but you don't say
> >>>> enough about these conditions to be able to say more.
> >>>
> >>> I am aware of the problems with a simulation-based halting decider:
> >>> for returning a decision of non-halting the SHD would rely on
> >>> detecting repeated machine state given a machine of finite size has
> >>> a finite number of configurations; for returning any decision I
> >>> also appreciate that the SHD might not answer within the lifetime
> >>> of the observable universe but that would still, I suggest, be a
> >>> finite not infinite time.
> >>
> >> What has this got to do with explicitly giving an answer that is
> >> neither 1 nor 2? All computations halt or they do not halt, so the
> >> answer is always 1 or 2.
> >
> > This is why I class the pathological input contradiction as an error, as
> > an exception to be raised/signaled, rather than a decision of halting or
> > non-halting. This is only interesting as a possible refutation of the
> > HP proofs based on [Strachey 1965]; it doesn't have any practical
> > utility.
> The first problem comes in trying to actually define exactly what the
> "exception" should de defined to be.
>
> One big issue is that Peter's H and P aren't really independent
> computations. You DON'T have a program H that you provide a description
> of an INDEPENDENT program P to, as H and P are intertwined in the same
> process space.
>
> This means that there are many possible P's that just can't be given to
> H, because they want to put code in their address space that overlaps
> with the code for the decider H.
>
> Once you fix that issue, suddenly trying to implement is concept just
> becomes impossible, because H can't count on a copy of H in P being at
> the same address, because that could easily be some other code at that
> address, and if P has a copy of H, that could be at some other address.
>
> Then you have that for computations, "copies" like P is defined to be
> using are defined as "functional" equivalents, one that gives the same
> answer for every input, not that they need to be coded exactly the same
> way (for example, with a Turing Machine, the "names" or "encoding" of
> the states just don't matter, but can be permutated, and adding or
> removing "null" code is valid. This makes identifying that a piece of
> the code in P as being an equivalent of H a tough (i.e. impossible) task.
>
> The second problem is that this "pathological" case isn't the only
> "undecidable" one. There also exist programs that represent the
> unprovable but true statements, where halting represents disproving the
> statement, and proving not halting would be proving that statement. Note
> that for some of these, it is also true that you can't even prove that
> they are unprovable, because by there nature, a proof that they are
> unprovable actually proves that they are true, as if they are false,
> this would always be provable (being based on that implies the existance
> of a counter example, and testing that counter example is always a
> finite operation).
>
> Goldbach's conjecture is a possible example of this (that all even
> natural numbers are the sum of two primes). If there IS a counter
> example, then there will be a finite number, and given any finite
> number, you can cycle through all possible pairss of numbers that could
> sum to it, (and there will be a finite number of these) and each of
> these can be tested for being a prime in a finite number of steps, so if
> it IS false, there WILL exist a number that can be proved to not be able
> to be expressible as a pair of prime numbers using only a finite number
> of steps.
>
> THus, if we could prove that it IS unprovable, means there can't be a
> counter example, which, by definition means it is proven to be true,
> which means that the proof it was unprovable must be wrong.
>
> This is part of the logic of Godel's incompleteness proof.
>
That's a very nice summary.
There are reasons you can't built halt deciders, other than the "paradox"
proof.

On Thursday, 7 July 2022 at 22:05:29 UTC+1, Mr Flibble wrote:
>
> I am aware of the problems with a simulation-based halting decider: for
> returning a decision of non-halting the SHD would rely on detecting
> repeated machine state given a machine of finite size has a finite
> number of configurations; for returning any decision I also appreciate
> that the SHD might not answer within the lifetime of the observable
> universe but that would still, I suggest, be a finite not infinite time.
>
If the machine halts in finite time, then a simulating halt decider will detect
halting in finite time. Whilst that's important from a logical perspective,
it's of no engineering value, because that finite time might be too long,
and you can't bound it without knowing the busy beaver champion.

A finite machine must always repeat states eventually if it doesn't halt.
Again, that's important logically, but not of any engineering value, because
the cycle time even of a quite small machine is too long.

Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:

> On Friday, 8 July 2022 at 03:56:20 UTC+1, richar...@gmail.com wrote:

>> The first problem comes in trying to actually define exactly what the
>> "exception" should de defined to be.
>>
>> One big issue is that Peter's H and P aren't really independent
>> computations. You DON'T have a program H that you provide a description
>> of an INDEPENDENT program P to, as H and P are intertwined in the same
>> process space.
>>
>> This means that there are many possible P's that just can't be given to
>> H, because they want to put code in their address space that overlaps
>> with the code for the decider H.
>>
>> Once you fix that issue, suddenly trying to implement is concept just
>> becomes impossible, because H can't count on a copy of H in P being at
>> the same address, because that could easily be some other code at that
>> address, and if P has a copy of H, that could be at some other address.
>>
>> Then you have that for computations, "copies" like P is defined to be
>> using are defined as "functional" equivalents, one that gives the same
>> answer for every input, not that they need to be coded exactly the same
>> way (for example, with a Turing Machine, the "names" or "encoding" of
>> the states just don't matter, but can be permutated, and adding or
>> removing "null" code is valid. This makes identifying that a piece of
>> the code in P as being an equivalent of H a tough (i.e. impossible) task.
>>
>> The second problem is that this "pathological" case isn't the only
>> "undecidable" one. There also exist programs that represent the
>> unprovable but true statements, where halting represents disproving the
>> statement, and proving not halting would be proving that statement. Note
>> that for some of these, it is also true that you can't even prove that
>> they are unprovable, because by there nature, a proof that they are
>> unprovable actually proves that they are true, as if they are false,
>> this would always be provable (being based on that implies the existance
>> of a counter example, and testing that counter example is always a
>> finite operation).
>>
>> Goldbach's conjecture is a possible example of this (that all even
>> natural numbers are the sum of two primes). If there IS a counter
>> example, then there will be a finite number, and given any finite
>> number, you can cycle through all possible pairss of numbers that could
>> sum to it, (and there will be a finite number of these) and each of
>> these can be tested for being a prime in a finite number of steps, so if
>> it IS false, there WILL exist a number that can be proved to not be able
>> to be expressible as a pair of prime numbers using only a finite number
>> of steps.
>>
>> THus, if we could prove that it IS unprovable, means there can't be a
>> counter example, which, by definition means it is proven to be true,
>> which means that the proof it was unprovable must be wrong.
>>
>> This is part of the logic of Godel's incompleteness proof.
>>
> That's a very nice summary.
> There are reasons you can't built halt deciders, other than the
> "paradox" proof.

Yes. It's really extraordinary how much time can be wasted on this
utterly trivial theorem. It's obvious that the must be undecidable sets
because there are only countably many TMs with any particular alphabet
but uncountably many sets of possible inputs. The only issue is how
plausible these undecidable sets can be.

Using undecidable arithmetic propositions is not, in my opinion, all
that persuasive since we can't, by definition, know any of these. But
specific undeciable problems (that are not in any way paradoxical) are
known. My favourite is Post's correspondence problem. It's simple to
state, easy to understand, and there is no algorithm to solve it. On
the more practical side there is the question of whether a context free
grammar is ambiguous or not.

--
Ben.

On 7/8/22 2:34 PM, Ben Bacarisse wrote:
> Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:
>
>> On Friday, 8 July 2022 at 03:56:20 UTC+1, richar...@gmail.com wrote:
>
>>> The first problem comes in trying to actually define exactly what the
>>> "exception" should de defined to be.
>>>
>>> One big issue is that Peter's H and P aren't really independent
>>> computations. You DON'T have a program H that you provide a description
>>> of an INDEPENDENT program P to, as H and P are intertwined in the same
>>> process space.
>>>
>>> This means that there are many possible P's that just can't be given to
>>> H, because they want to put code in their address space that overlaps
>>> with the code for the decider H.
>>>
>>> Once you fix that issue, suddenly trying to implement is concept just
>>> becomes impossible, because H can't count on a copy of H in P being at
>>> the same address, because that could easily be some other code at that
>>> address, and if P has a copy of H, that could be at some other address.
>>>
>>> Then you have that for computations, "copies" like P is defined to be
>>> using are defined as "functional" equivalents, one that gives the same
>>> answer for every input, not that they need to be coded exactly the same
>>> way (for example, with a Turing Machine, the "names" or "encoding" of
>>> the states just don't matter, but can be permutated, and adding or
>>> removing "null" code is valid. This makes identifying that a piece of
>>> the code in P as being an equivalent of H a tough (i.e. impossible) task.
>>>
>>> The second problem is that this "pathological" case isn't the only
>>> "undecidable" one. There also exist programs that represent the
>>> unprovable but true statements, where halting represents disproving the
>>> statement, and proving not halting would be proving that statement. Note
>>> that for some of these, it is also true that you can't even prove that
>>> they are unprovable, because by there nature, a proof that they are
>>> unprovable actually proves that they are true, as if they are false,
>>> this would always be provable (being based on that implies the existance
>>> of a counter example, and testing that counter example is always a
>>> finite operation).
>>>
>>> Goldbach's conjecture is a possible example of this (that all even
>>> natural numbers are the sum of two primes). If there IS a counter
>>> example, then there will be a finite number, and given any finite
>>> number, you can cycle through all possible pairss of numbers that could
>>> sum to it, (and there will be a finite number of these) and each of
>>> these can be tested for being a prime in a finite number of steps, so if
>>> it IS false, there WILL exist a number that can be proved to not be able
>>> to be expressible as a pair of prime numbers using only a finite number
>>> of steps.
>>>
>>> THus, if we could prove that it IS unprovable, means there can't be a
>>> counter example, which, by definition means it is proven to be true,
>>> which means that the proof it was unprovable must be wrong.
>>>
>>> This is part of the logic of Godel's incompleteness proof.
>>>
>> That's a very nice summary.
>> There are reasons you can't built halt deciders, other than the
>> "paradox" proof.
>
> Yes. It's really extraordinary how much time can be wasted on this
> utterly trivial theorem. It's obvious that the must be undecidable sets
> because there are only countably many TMs with any particular alphabet
> but uncountably many sets of possible inputs. The only issue is how
> plausible these undecidable sets can be.
>
> Using undecidable arithmetic propositions is not, in my opinion, all
> that persuasive since we can't, by definition, know any of these. But
> specific undeciable problems (that are not in any way paradoxical) are
> known. My favourite is Post's correspondence problem. It's simple to
> state, easy to understand, and there is no algorithm to solve it. On
> the more practical side there is the question of whether a context free
> grammar is ambiguous or not.
>

Part of the reason for that is that Peter isn't actually interested in
the Halting Problem or it proof, but only that the proof of the Halting
Theorem fuels a lot of proofs that not all Truths can actually be
proven, and He firmly is convinced that if you can't prove it, then it
can't be true.

He is so stuck on this idea that he at times tries to make that an axiom
that he then uses to prove a flaw in the proof of the Halting Theorem.

Since the Halting Problem isn't the core thing to him, he just isn't
spending time to understand it, which shows in the fundamental errors he
makes when trying to talk about it.