On Mon, 2024-01-22 at 20:40 -0600, olcott wrote:
> On 1/22/2024 8:27 PM, wij wrote:
> > On Mon, 2024-01-22 at 20:20 -0600, olcott wrote:
> > > On 1/22/2024 8:13 PM, wij wrote:
> > > > On Mon, 2024-01-22 at 20:05 -0600, olcott wrote:
> > > > > On 1/22/2024 7:44 PM, wij wrote:
> > > > > > On Mon, 2024-01-22 at 19:19 -0600, olcott wrote:
> > > > > > > On 1/22/2024 6:57 PM, wij wrote:
> > > > > > > > On Mon, 2024-01-22 at 18:39 -0600, olcott wrote:
> > > > > > > > > On 1/22/2024 6:09 PM, wij wrote:
> > > > > > > > > > On Mon, 2024-01-22 at 10:28 +0200, Mikko wrote:
> > > > > > > > > > > On 2024-01-21 19:22:22 +0000, wij said:
> > > > > > > > > > >
> > > > > > > > > > > > I just found an article about the Halting
> > > > > > > > > > > > Problem.
> > > > > > > > > > > > https://arxiv.org/pdf/1906.05340.pdf
> > > > > > > > > > > >
> > > > > > > > > > > > In the conclusion section:
> > > > > > > > > > > > The idea of a universal halting test seems
> > > > > > > > > > > > reasonable,
> > > > > > > > > > > > but
> > > > > > > > > > > > cannot
> > > > > > > > > > > > be
> > > > > > > > > > > > for-
> > > > > > > > > > > > malised as a consistent specification. It has
> > > > > > > > > > > > no
> > > > > > > > > > > > model
> > > > > > > > > > > > and
> > > > > > > > > > > > does
> > > > > > > > > > > > not
> > > > > > > > > > > > exist as
> > > > > > > > > > > > a conceptual object. Assuming its conceptual
> > > > > > > > > > > > existence
> > > > > > > > > > > > leads to
> > > > > > > > > > > > a
> > > > > > > > > > > > paradox.
> > > > > > > > > > > > The halting problem is universally used in
> > > > > > > > > > > > university
> > > > > > > > > > > > courses
> > > > > > > > > > > > on
> > > > > > > > > > > > Computer
> > > > > > > > > > > > Science to illustrate the limits of
> > > > > > > > > > > > computation.
> > > > > > > > > > > > Hehner
> > > > > > > > > > > > claims
> > > > > > > > > > > > the
> > > > > > > > > > > > halting
> > > > > > > > > > > > problem is misconceived......
> > > > > > > > > > > >
> > > > > > > > > > > > It looks like what olcott now is claiming. Am I
> > > > > > > > > > > > missing
> > > > > > > > > > > > something?
> > > > > > > > > > >
> > > > > > > > > > > The error in the article is the claim that an
> > > > > > > > > > > "inconsistent"
> > > > > > > > > > > specification
> > > > > > > > > > > is somehow invalid. But it is not.
> > > > > > > > > > >
> > > > > > > > > > > A problem is a request to find at least one thing
> > > > > > > > > > > that
> > > > > > > > > > > satisfies
> > > > > > > > > > > the
> > > > > > > > > > > requirements of the problem or to prove that no
> > > > > > > > > > > such
> > > > > > > > > > > thing
> > > > > > > > > > > can be
> > > > > > > > > > > found.
> > > > > > > > > > > The problem is well posed if for every thing it
> > > > > > > > > > > is
> > > > > > > > > > > possible
> > > > > > > > > > > to
> > > > > > > > > > > check
> > > > > > > > > > > whether it satisfies all requirements.
> > > > > > > > > > >
> > > > > > > > > > > The halting problem is solved: a proof that no
> > > > > > > > > > > Turing
> > > > > > > > > > > machine
> > > > > > > > > > > satisfies
> > > > > > > > > > > the requirements is known (and nothing else
> > > > > > > > > > > satisfies
> > > > > > > > > > > the
> > > > > > > > > > > requirement
> > > > > > > > > > > that it must be a Turing machine).
> > > > > > > > > > >
> > > > > > > > > > > It is a matter of opinion whether the usual
> > > > > > > > > > > presentation
> > > > > > > > > > > of
> > > > > > > > > > > the
> > > > > > > > > > > halting theorem is the best one. If one does not
> > > > > > > > > > > like
> > > > > > > > > > > the
> > > > > > > > > > > usual
> > > > > > > > > > > statement one may instead use:
> > > > > > > > > > >        For every universal Turing machine U and
> > > > > > > > > > > every
> > > > > > > > > > > Turing
> > > > > > > > > > > machine
> > > > > > > > > > > H
> > > > > > > > > > >        there is an input string S so that
> > > > > > > > > > >        either T(S) halts but H(S) does not accept
> > > > > > > > > > >        or T(S) does not halt but H(S) accepts.
> > > > > > > > > > >
> > > > > > > > > > > This formulation has the disadvantage that it
> > > > > > > > > > > uses
> > > > > > > > > > > the
> > > > > > > > > > > concept of
> > > > > > > > > > > "univesal Turing machine", and therefore depends
> > > > > > > > > > > on
> > > > > > > > > > > the
> > > > > > > > > > > existence
> > > > > > > > > > > of one.
> > > > > > > > > > >
> > > > > > > > > > > Mikko
> > > > > > > > > > >
> > > > > > > > > >
> > > > > > > > > > Thanks for the explanation.
> > > > > > > > > > It looked to me it is the statement of Halting
> > > > > > > > > > Problem
> > > > > > > > > > proved
> > > > > > > > > > neither
> > > > > > > > > > T nor F bugged these people (including olcott).
> > > > > > > > > > There is also a status of proposition called
> > > > > > > > > > contingency,
> > > > > > > > > > https://en.wikipedia.org/wiki/Contingency_(philosophy)
> > > > > > > > >
> > > > > > > > > Ultimately all these things boil down to the fact
> > > > > > > > > that
> > > > > > > > > self-contradictory questions must be rejected as
> > > > > > > > > incorrect
> > > > > > > > > questions. Hehner's paper explains this the best:
> > > > > > > > > https://www.cs.toronto.edu/~hehner/OSS.pdf
> > > > > > > > >
> > > > > > > > > The key part that non-technical people can understand
> > > > > > > > > is
> > > > > > > > > Carol's question:
> > > > > > > > > Can Carol correctly answer “no” to this [yes/no]
> > > > > > > > > question?
> > > > > > > > >
> > > > > > > > > That question is self-contradictory when posed to
> > > > > > > > > Carol
> > > > > > > > > and has the correct answer of "no" when posed to
> > > > > > > > > anyone
> > > > > > > > > else.
> > > > > > > > >
> > > > > > > > > Carol's question actually originates from my own
> > > > > > > > > conversation:
> > > > > > > > >
> > > > > > > > > On 6/25/2004 6:30 PM, Daryl McCullough wrote: 
> > > > > > > > > (USENET
> > > > > > > > > sci.logic)
> > > > > > > > >      > You ask someone (we'll call him "Jack") to
> > > > > > > > > give a
> > > > > > > > > truthful
> > > > > > > > >      > yes/no answer to the following question:
> > > > > > > > >      >
> > > > > > > > >      >  Will Jack's answer to this question be no?
> > > > > > > > >
> > > > > > > > > was addressed to me in 2004.
> > > > > > > > > Hehner had no way of knowing this I repeated this
> > > > > > > > > same question as Bill's question hundreds of times
> > > > > > > > > until I tracked down the original author.
> > > > > > > > >
> > > > > > > >
> > > > > > > > The HP is asking (equivalent) for A PROGRAM that takes
> > > > > > > > another
> > > > > > > > program
> > > > > > > > as its argument and decides whether or not that given
> > > > > > > > program
> > > > > > > > will terminate.
> > > > > > > >
> > > > > > > > The HP is not asking the evaluation of "HP Theorem"
> > > > > > > > (the
> > > > > > > > conclusion)
> > > > > > > > to be true or false!!!
> > > > > >
> > > > > > > The HP uses a counter-example D that does the opposite
> > > > > > > of whatever value that H returns, thus making the
> > > > > > > question
> > > > > > > Does D halt? a self-contradictory question for H.
> > > > > >
> > > > > > It seems you took it as:
> > > > > > Proposition P="A program that decides whether another
> > > > > > program
> > > > > > halts
> > > > > > or
> > > > > > not is undecidable".
> > > > > >
> > > > >
> > > > > I have gone over these details many many thousands of times
> > > > > since
> > > > > 2004.
> > > > > That actual question for H is this:
> > > > >
> > > > > "What correct Boolean value does H return when D is defined
> > > > > to do
> > > > > the
> > > > >     opposite of whatever value that H returns?"
> > > >
> > > > As you already have seen: The H would be stock in an infinite
> > > > recursive
> > > > call. I.e. H is not implementable.
> > > >
> > >
> > > You mean "stuck" not "stock".
> > >
> > > https://github.com/plolcott/x86utm
> > > I spent 1.5 years making sure that H does not get stuck it has
> > > been
> > > fully operational code for several years now.
> > >
> > > > The result as know it that you deliberately fabricate D in way
> > > > to
> > > > say
> > > > whatever you want to say, this is invalid.
> > > >
> > >
> > > https://github.com/plolcott/x86utm/blob/master/Halt7.c
> > > int D(int (*x)())
> > > {
> > >     int Halt_Status = H(x, x);
> > >     if (Halt_Status)
> > >       HERE: goto HERE;
> > >     return Halt_Status;
> > > }
> > >
> > > is on lines 935-941 of FULLY OPERATIONAL CODE
> > >
> >
> > You have been through this for a long time. I would suggest
> > reading something about quantum computing, then, you will
> > become expert soon (because you are a genius), not many people
> > reading by rote can disagree with you with those age old
> > theories.
>
> Thanks for the great compliment.
> My very limited understanding of quantum computing would seem to
> indicate that it still performs computations that are isomorphic
> to Turing machines yet performs these computations at theoretical
> maximum speeds. I am most certain of the TM equivalence part and
> least certain of the theoretical maximum speed part.

On 1/22/2024 8:59 PM, wij wrote:
> On Mon, 2024-01-22 at 20:40 -0600, olcott wrote:
>> On 1/22/2024 8:27 PM, wij wrote:
>>> On Mon, 2024-01-22 at 20:20 -0600, olcott wrote:
>>>> On 1/22/2024 8:13 PM, wij wrote:
>>>>> On Mon, 2024-01-22 at 20:05 -0600, olcott wrote:
>>>>>> On 1/22/2024 7:44 PM, wij wrote:
>>>>>>> On Mon, 2024-01-22 at 19:19 -0600, olcott wrote:
>>>>>>>> On 1/22/2024 6:57 PM, wij wrote:
>>>>>>>>> On Mon, 2024-01-22 at 18:39 -0600, olcott wrote:
>>>>>>>>>> On 1/22/2024 6:09 PM, wij wrote:
>>>>>>>>>>> On Mon, 2024-01-22 at 10:28 +0200, Mikko wrote:
>>>>>>>>>>>> On 2024-01-21 19:22:22 +0000, wij said:
>>>>>>>>>>>>
>>>>>>>>>>>>> I just found an article about the Halting
>>>>>>>>>>>>> Problem.
>>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>>
>>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>>> The idea of a universal halting test seems
>>>>>>>>>>>>> reasonable,
>>>>>>>>>>>>> but
>>>>>>>>>>>>> cannot
>>>>>>>>>>>>> be
>>>>>>>>>>>>> for-
>>>>>>>>>>>>> malised as a consistent specification. It has
>>>>>>>>>>>>> no
>>>>>>>>>>>>> model
>>>>>>>>>>>>> and
>>>>>>>>>>>>> does
>>>>>>>>>>>>> not
>>>>>>>>>>>>> exist as
>>>>>>>>>>>>> a conceptual object. Assuming its conceptual
>>>>>>>>>>>>> existence
>>>>>>>>>>>>> leads to
>>>>>>>>>>>>> a
>>>>>>>>>>>>> paradox.
>>>>>>>>>>>>> The halting problem is universally used in
>>>>>>>>>>>>> university
>>>>>>>>>>>>> courses
>>>>>>>>>>>>> on
>>>>>>>>>>>>> Computer
>>>>>>>>>>>>> Science to illustrate the limits of
>>>>>>>>>>>>> computation.
>>>>>>>>>>>>> Hehner
>>>>>>>>>>>>> claims
>>>>>>>>>>>>> the
>>>>>>>>>>>>> halting
>>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>>
>>>>>>>>>>>>> It looks like what olcott now is claiming. Am I
>>>>>>>>>>>>> missing
>>>>>>>>>>>>> something?
>>>>>>>>>>>>
>>>>>>>>>>>> The error in the article is the claim that an
>>>>>>>>>>>> "inconsistent"
>>>>>>>>>>>> specification
>>>>>>>>>>>> is somehow invalid. But it is not.
>>>>>>>>>>>>
>>>>>>>>>>>> A problem is a request to find at least one thing
>>>>>>>>>>>> that
>>>>>>>>>>>> satisfies
>>>>>>>>>>>> the
>>>>>>>>>>>> requirements of the problem or to prove that no
>>>>>>>>>>>> such
>>>>>>>>>>>> thing
>>>>>>>>>>>> can be
>>>>>>>>>>>> found.
>>>>>>>>>>>> The problem is well posed if for every thing it
>>>>>>>>>>>> is
>>>>>>>>>>>> possible
>>>>>>>>>>>> to
>>>>>>>>>>>> check
>>>>>>>>>>>> whether it satisfies all requirements.
>>>>>>>>>>>>
>>>>>>>>>>>> The halting problem is solved: a proof that no
>>>>>>>>>>>> Turing
>>>>>>>>>>>> machine
>>>>>>>>>>>> satisfies
>>>>>>>>>>>> the requirements is known (and nothing else
>>>>>>>>>>>> satisfies
>>>>>>>>>>>> the
>>>>>>>>>>>> requirement
>>>>>>>>>>>> that it must be a Turing machine).
>>>>>>>>>>>>
>>>>>>>>>>>> It is a matter of opinion whether the usual
>>>>>>>>>>>> presentation
>>>>>>>>>>>> of
>>>>>>>>>>>> the
>>>>>>>>>>>> halting theorem is the best one. If one does not
>>>>>>>>>>>> like
>>>>>>>>>>>> the
>>>>>>>>>>>> usual
>>>>>>>>>>>> statement one may instead use:
>>>>>>>>>>>>        For every universal Turing machine U and
>>>>>>>>>>>> every
>>>>>>>>>>>> Turing
>>>>>>>>>>>> machine
>>>>>>>>>>>> H
>>>>>>>>>>>>        there is an input string S so that
>>>>>>>>>>>>        either T(S) halts but H(S) does not accept
>>>>>>>>>>>>        or T(S) does not halt but H(S) accepts.
>>>>>>>>>>>>
>>>>>>>>>>>> This formulation has the disadvantage that it
>>>>>>>>>>>> uses
>>>>>>>>>>>> the
>>>>>>>>>>>> concept of
>>>>>>>>>>>> "univesal Turing machine", and therefore depends
>>>>>>>>>>>> on
>>>>>>>>>>>> the
>>>>>>>>>>>> existence
>>>>>>>>>>>> of one.
>>>>>>>>>>>>
>>>>>>>>>>>> Mikko
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Thanks for the explanation.
>>>>>>>>>>> It looked to me it is the statement of Halting
>>>>>>>>>>> Problem
>>>>>>>>>>> proved
>>>>>>>>>>> neither
>>>>>>>>>>> T nor F bugged these people (including olcott).
>>>>>>>>>>> There is also a status of proposition called
>>>>>>>>>>> contingency,
>>>>>>>>>>> https://en.wikipedia.org/wiki/Contingency_(philosophy)
>>>>>>>>>>
>>>>>>>>>> Ultimately all these things boil down to the fact
>>>>>>>>>> that
>>>>>>>>>> self-contradictory questions must be rejected as
>>>>>>>>>> incorrect
>>>>>>>>>> questions. Hehner's paper explains this the best:
>>>>>>>>>> https://www.cs.toronto.edu/~hehner/OSS.pdf
>>>>>>>>>>
>>>>>>>>>> The key part that non-technical people can understand
>>>>>>>>>> is
>>>>>>>>>> Carol's question:
>>>>>>>>>> Can Carol correctly answer “no” to this [yes/no]
>>>>>>>>>> question?
>>>>>>>>>>
>>>>>>>>>> That question is self-contradictory when posed to
>>>>>>>>>> Carol
>>>>>>>>>> and has the correct answer of "no" when posed to
>>>>>>>>>> anyone
>>>>>>>>>> else.
>>>>>>>>>>
>>>>>>>>>> Carol's question actually originates from my own
>>>>>>>>>> conversation:
>>>>>>>>>>
>>>>>>>>>> On 6/25/2004 6:30 PM, Daryl McCullough wrote:
>>>>>>>>>> (USENET
>>>>>>>>>> sci.logic)
>>>>>>>>>>      > You ask someone (we'll call him "Jack") to
>>>>>>>>>> give a
>>>>>>>>>> truthful
>>>>>>>>>>      > yes/no answer to the following question:
>>>>>>>>>>      >
>>>>>>>>>>      >  Will Jack's answer to this question be no?
>>>>>>>>>>
>>>>>>>>>> was addressed to me in 2004.
>>>>>>>>>> Hehner had no way of knowing this I repeated this
>>>>>>>>>> same question as Bill's question hundreds of times
>>>>>>>>>> until I tracked down the original author.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> The HP is asking (equivalent) for A PROGRAM that takes
>>>>>>>>> another
>>>>>>>>> program
>>>>>>>>> as its argument and decides whether or not that given
>>>>>>>>> program
>>>>>>>>> will terminate.
>>>>>>>>>
>>>>>>>>> The HP is not asking the evaluation of "HP Theorem"
>>>>>>>>> (the
>>>>>>>>> conclusion)
>>>>>>>>> to be true or false!!!
>>>>>>>
>>>>>>>> The HP uses a counter-example D that does the opposite
>>>>>>>> of whatever value that H returns, thus making the
>>>>>>>> question
>>>>>>>> Does D halt? a self-contradictory question for H.
>>>>>>>
>>>>>>> It seems you took it as:
>>>>>>> Proposition P="A program that decides whether another
>>>>>>> program
>>>>>>> halts
>>>>>>> or
>>>>>>> not is undecidable".
>>>>>>>
>>>>>>
>>>>>> I have gone over these details many many thousands of times
>>>>>> since
>>>>>> 2004.
>>>>>> That actual question for H is this:
>>>>>>
>>>>>> "What correct Boolean value does H return when D is defined
>>>>>> to do
>>>>>> the
>>>>>>     opposite of whatever value that H returns?"
>>>>>
>>>>> As you already have seen: The H would be stock in an infinite
>>>>> recursive
>>>>> call. I.e. H is not implementable.
>>>>>
>>>>
>>>> You mean "stuck" not "stock".
>>>>
>>>> https://github.com/plolcott/x86utm
>>>> I spent 1.5 years making sure that H does not get stuck it has
>>>> been
>>>> fully operational code for several years now.
>>>>
>>>>> The result as know it that you deliberately fabricate D in way
>>>>> to
>>>>> say
>>>>> whatever you want to say, this is invalid.
>>>>>
>>>>
>>>> https://github.com/plolcott/x86utm/blob/master/Halt7.c
>>>> int D(int (*x)())
>>>> {
>>>>     int Halt_Status = H(x, x);
>>>>     if (Halt_Status)
>>>>       HERE: goto HERE;
>>>>     return Halt_Status;
>>>> }
>>>>
>>>> is on lines 935-941 of FULLY OPERATIONAL CODE
>>>>
>>>
>>> You have been through this for a long time. I would suggest
>>> reading something about quantum computing, then, you will
>>> become expert soon (because you are a genius), not many people
>>> reading by rote can disagree with you with those age old
>>> theories.
>>
>> Thanks for the great compliment.
>> My very limited understanding of quantum computing would seem to
>> indicate that it still performs computations that are isomorphic
>> to Turing machines yet performs these computations at theoretical
>> maximum speeds. I am most certain of the TM equivalence part and
>> least certain of the theoretical maximum speed part.
>
> There are already books teaching quantum programming (an several books
> I saw are cheap), it would not be difficult for you because you
> had been good in dealing with symbols. You don't have to be
> certain about the real quantum things, no one is certain about
> quantum stuff.
> Anyway, at least, you will have additional arsenal to support what
> you claimed.
>
>

On 1/22/24 1:59 PM, olcott wrote:
> On 1/22/2024 6:23 AM, Richard Damon wrote:
>> On 1/21/24 11:37 PM, olcott wrote:
>>> On 1/21/2024 10:06 PM, Richard Damon wrote:
>>>> On 1/21/24 11:01 PM, olcott wrote:
>>>>> On 1/21/2024 9:39 PM, Richard Damon wrote:
>>>>>> On 1/21/24 10:30 PM, olcott wrote:
>>>>>>> On 1/21/2024 9:28 PM, Richard Damon wrote:
>>>>>>>> On 1/21/24 10:22 PM, olcott wrote:
>>>>>>>>> On 1/21/2024 9:19 PM, Richard Damon wrote:
>>>>>>>>>> On 1/21/24 9:55 PM, olcott wrote:
>>>>>>>>>>> On 1/21/2024 8:28 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/21/24 9:18 PM, olcott wrote:
>>>>>>>>>>>>> On 1/21/2024 8:07 PM, immibis wrote:
>>>>>>>>>>>>>> On 1/22/24 02:43, olcott wrote:
>>>>>>>>>>>>>>> On 1/21/2024 7:38 PM, immibis wrote:
>>>>>>>>>>>>>>>> On 1/22/24 02:04, olcott wrote:
>>>>>>>>>>>>>>>>> On 1/21/2024 6:58 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 1/21/24 7:54 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 1/21/2024 6:50 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>> On 1/22/24 01:37, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 1/21/2024 6:27 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>> On 1/22/24 01:13, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 1/21/2024 6:04 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 1/21/24 23:56, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> Tarski didn't understand that the correct
>>>>>>>>>>>>>>>>>>>>>>>>> evaluation of the Liar Paradox requires
>>>>>>>>>>>>>>>>>>>>>>>>> an infinite cycle in the directed graph
>>>>>>>>>>>>>>>>>>>>>>>>> of its evaluation sequence.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> You don't understand the difference between
>>>>>>>>>>>>>>>>>>>>>>>> diagonalization and infinite recursion.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Do you think the real numbers are countable?
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Diagonalization is a process by which we know that
>>>>>>>>>>>>>>>>>>>>>>> x is unprovable in L that makes sure to ignore the
>>>>>>>>>>>>>>>>>>>>>>> reason why x is unprovable in L.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> So are the real numbers countable? Isn't Cantor's
>>>>>>>>>>>>>>>>>>>>>> number pathologically self-referential, making his
>>>>>>>>>>>>>>>>>>>>>> argument invalid?
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> unify_with_occurs_check(LP, not(true(LP))).
>>>>>>>>>>>>>>>>>>>>>>> correctly determines that LP is unprovable
>>>>>>>>>>>>>>>>>>>>>>> BECAUSE the directed graph of its evaluation
>>>>>>>>>>>>>>>>>>>>>>> sequence contains an infinite cycle.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Provability doesn't give a flying fuck about
>>>>>>>>>>>>>>>>>>>>>> evaluation cycles, whatever those are.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> It sure does in Prolog.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Then Prolog is wrong.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> That Prolog pays attention to details that other systems
>>>>>>>>>>>>>>>>>>> ignore make it wrong is like saying that ignorance is
>>>>>>>>>>>>>>>>>>> knowledge and knowledge is incorrect.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Prolog handles SIMPLE logic system and problems. It
>>>>>>>>>>>>>>>>>> rejects ALL cycles, even if they don't cause logical
>>>>>>>>>>>>>>>>>> issues (as I understand it)
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> As you fail to understand it.
>>>>>>>>>>>>>>>>> I took 18 months creating Minimal Type Theory that
>>>>>>>>>>>>>>>>> automatically generated the directed graph of the
>>>>>>>>>>>>>>>>> evaluation sequence of any of its expressions.
>>>>>>>>>>>>>>>>> It sued syntax similar to FOL yet is as expressive
>>>>>>>>>>>>>>>>> as HOL. I encode a SOL expression in MTT.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> You are rebutting the infinite formulas such as
>>>>>>>>>>>>>>>> ¬True(¬True(¬True(...)))
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> But this is already in the standard theory. Infinite
>>>>>>>>>>>>>>>> formulas such as ¬True(¬True(¬True(...))) are already
>>>>>>>>>>>>>>>> not valid.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Olcott doesn't understand that diagonalization is not
>>>>>>>>>>>>>>>> the same as infinite recursion.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Finally a reply that is not nonsense.
>>>>>>>>>>>>>>> Diagonalization only knows that for some reason or another
>>>>>>>>>>>>>>> x is unprovable in L.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I dispute the notion of "reasons". It's just a fact that
>>>>>>>>>>>>>> it's unprovable. There are different ways to find out that
>>>>>>>>>>>>>> it's unprovable, or different ways to understand that it's
>>>>>>>>>>>>>> unprovable, but not reasons why it's unprovable.
>>>>>>>>>>>>>
>>>>>>>>>>>>> If the reason that x is unprovable in L is that x
>>>>>>>>>>>>> is semantically incorrect in L then instead of saying
>>>>>>>>>>>>> that x is undecidable in L the decider rejects x
>>>>>>>>>>>>> as invalid input.
>>>>>>>>>>>>>
>>>>>>>>>>>>> This what Tarski should have done.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> But there are x that are unprovable in L because the chain
>>>>>>>>>>>> to them is infinitely long, which makes them true but
>>>>>>>>>>>> unprovale.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> (1) x ∉ Provable if and only if p
>>>>>>>>>>> (2) x ∈ True if and only if p
>>>>>>>>>>> (3) x ∉ Provable if and only if x ∈ True.
>>>>>>>>>>>
>>>>>>>>>>> When we correct the erroneous line (1) then line (3) becomes
>>>>>>>>>>> (3) x ∈ Provable if and only if x ∈ True.
>>>>>>>>>>> Thus making your (infinite chain) x simply untrue.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> WHy is it "erroneous", it is a simple statement previously
>>>>>>>>>> proven.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> He proved that there are some things that we know
>>>>>>>>> are true yet have no way what-so-ever to know that
>>>>>>>>> they are true?
>>>>>>>>>
>>>>>>>>
>>>>>>>> No, he proved that there are some things that ARE true that we
>>>>>>>> can not prove to be true.
>>>>>>>>
>>>>>>>
>>>>>>> How the Hell is he going to do that on his basis
>>>>>>> of the Liar Paradox?
>>>>>>>
>>>>>>
>>>>>> Read his proof. And it isn't "based' on the Liar's paradox,
>>>>>
>>>>> *It sure as Hell is anchored in the Liar Paradox*
>>>>> He get his line (1) directly from the Liar Paradox
>>>>>
>>>>> Below he shows how he transforms the Liar Paradox
>>>>> x ∉ True if and only if p
>>>>>
>>>>> into his line (1) by replacing "Tr" (for True)
>>>>> with 'Pr" (for provable) Here is his line
>>>>> (1) x ∉ Provable if and only if p
>>>>>
>>>>> <page 275>
>>>>>     In accordance with the first
>>>>>     part of Th. I we can obtain the negation of one of the sentences
>>>>>     in condition (α) of convention T of § 3 as a consequence of the
>>>>>     definition of the symbol 'Pr' (provided we replace 'Tr' in this
>>>>>     convention by 'Pr'). https://liarparadox.org/Tarski_275_276.pdf
>>>>> </page 275>
>>>>>
>>>>> <page 248> Liar Paradox
>>>>>     Should we succeed in constructing in the metalanguage
>>>>>     a correct definition of truth, then
>>>>>
>>>>>     It would
>>>>>     then be possible to reconstruct the antinomy of the liar in the
>>>>>     metalanguage, by forming in the language itself a sentence x
>>>>>     such that the sentence of the metalanguage which is correlated
>>>>>     with x asserts that x is not a true sentence.
>>>>>     https://liarparadox.org/Tarski_247_248.pdf
>>>>> </page 248>
>>>>>
>>>>> Many people today are simply too stupid to understand
>>>>> that the Liar Paradox is simply not a truth bearer
>>>>> thus must be rejected by any correct True(L, x) predicate.
>>>>>
>>>>> When Tarski assumes the Liar Paradox as a premise
>>>>> this must be rejected and over-ruled.
>>>>
>>>> Where does he assume it as a premise?
>>>>
>>>
>>> His line (1) is a premise.
>>
>> Then why does he say, "In other words, we can construct ... " just
>> above it.
>>
>> (1) is a CONCLUSION from the previous paragraph.
>>
>> you clearly don't know much about logic.
>>
>>>
>>>>>
>>>>> (1) x ∉ Provable if and only if p
>>>>> must be corrected to say
>>>>> (1) x ∈ Provable if and only if p
>>>>>
>>>>
>>>> What was actually wrong with (1). You haven't shown the error in logic.
>>>
>>> His line (1) <is> an adapted form of the actual Liar
>>> Paradox as I have shown by the quotes above.
>>
>> NO, the liar paradox says NOTHING about "Provable".
>
> Tarski says that he takes the Liar Paradox:
> x ∉ True if and only if p
> and changes it to this
> (1) x ∉ Provable if and only if p
> on page <275> quoted above.
>
> It is <page 248> quoted above where he says
> that he is using the actual Liar Paradox.
>
> You have to carefully study what I say before
> providing a rebuttal. It took me a half hour
> to compose the Tarski quotes.
>
>

On 1/22/24 1:39 PM, olcott wrote:
> On 1/22/2024 4:17 AM, Mikko wrote:
>> On 2024-01-22 02:18:35 +0000, olcott said:
>>
>>> On 1/21/2024 8:07 PM, immibis wrote:
>>>> On 1/22/24 02:43, olcott wrote:
>>>>> On 1/21/2024 7:38 PM, immibis wrote:
>>>>>> On 1/22/24 02:04, olcott wrote:
>>>>>>> On 1/21/2024 6:58 PM, Richard Damon wrote:
>>>>>>>> On 1/21/24 7:54 PM, olcott wrote:
>>>>>>>>> On 1/21/2024 6:50 PM, immibis wrote:
>>>>>>>>>> On 1/22/24 01:37, olcott wrote:
>>>>>>>>>>> On 1/21/2024 6:27 PM, immibis wrote:
>>>>>>>>>>>> On 1/22/24 01:13, olcott wrote:
>>>>>>>>>>>>> On 1/21/2024 6:04 PM, immibis wrote:
>>>>>>>>>>>>>> On 1/21/24 23:56, olcott wrote:
>>>>>>>>>>>>>>> Tarski didn't understand that the correct
>>>>>>>>>>>>>>> evaluation of the Liar Paradox requires
>>>>>>>>>>>>>>> an infinite cycle in the directed graph
>>>>>>>>>>>>>>> of its evaluation sequence.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You don't understand the difference between
>>>>>>>>>>>>>> diagonalization and infinite recursion.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Do you think the real numbers are countable?
>>>>>>>>>>>>>
>>>>>>>>>>>>> Diagonalization is a process by which we know that
>>>>>>>>>>>>> x is unprovable in L that makes sure to ignore the
>>>>>>>>>>>>> reason why x is unprovable in L.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> So are the real numbers countable? Isn't Cantor's number
>>>>>>>>>>>> pathologically self-referential, making his argument invalid?
>>>>>>>>>>>>
>>>>>>>>>>>>> unify_with_occurs_check(LP, not(true(LP))).
>>>>>>>>>>>>> correctly determines that LP is unprovable
>>>>>>>>>>>>> BECAUSE the directed graph of its evaluation
>>>>>>>>>>>>> sequence contains an infinite cycle.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Provability doesn't give a flying fuck about evaluation
>>>>>>>>>>>> cycles, whatever those are.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> It sure does in Prolog.
>>>>>>>>>>
>>>>>>>>>> Then Prolog is wrong.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> That Prolog pays attention to details that other systems
>>>>>>>>> ignore make it wrong is like saying that ignorance is
>>>>>>>>> knowledge and knowledge is incorrect.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Prolog handles SIMPLE logic system and problems. It rejects ALL
>>>>>>>> cycles, even if they don't cause logical issues (as I understand
>>>>>>>> it)
>>>>>>>
>>>>>>> As you fail to understand it.
>>>>>>> I took 18 months creating Minimal Type Theory that
>>>>>>> automatically generated the directed graph of the
>>>>>>> evaluation sequence of any of its expressions.
>>>>>>> It sued syntax similar to FOL yet is as expressive
>>>>>>> as HOL. I encode a SOL expression in MTT.
>>>>>>>
>>>>>>> https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
>>>>>>>
>>>>>>
>>>>>> You are rebutting the infinite formulas such as
>>>>>> ¬True(¬True(¬True(...)))
>>>>>>
>>>>>> But this is already in the standard theory. Infinite formulas such
>>>>>> as ¬True(¬True(¬True(...))) are already not valid.
>>>>>>
>>>>>> Olcott doesn't understand that diagonalization is not the same as
>>>>>> infinite recursion.
>>>>>
>>>>> Finally a reply that is not nonsense.
>>>>> Diagonalization only knows that for some reason or another
>>>>> x is unprovable in L.
>>>>
>>>> I dispute the notion of "reasons". It's just a fact that it's
>>>> unprovable. There are different ways to find out that it's
>>>> unprovable, or different ways to understand that it's unprovable,
>>>> but not reasons why it's unprovable.
>>>
>>> If the reason that x is unprovable in L is that x
>>> is semantically incorrect in L then instead of saying
>>> that x is undecidable in L the decider rejects x
>>> as invalid input.
>>>
>>> This what Tarski should have done.
>>
>> In a formal theory nothing is semantically anything.
>
> That it the reason why formal theories get confused
> and make semantic errors that are invisible to them.

While you try to use natural language and claim things that are
impossible must be, becuase you don't understand logic.

>
>> The semantics only
>> enter when the theory is interpreted. In a first order theory if x is
>> undecidable then it is true in some models and false in all others.
>> If neither x nor ¬x is provable you can add either one (but not both)
>> to the axioms of the theory and get another theory where x is decidable.
>>
>> Mikko
>>
>

On 1/22/24 2:04 PM, olcott wrote:
> On 1/22/2024 9:36 AM, immibis wrote:
>> On 1/22/24 16:29, olcott wrote:
>>> On 1/22/2024 2:28 AM, Mikko wrote:
>>>> On 2024-01-21 19:22:22 +0000, wij said:
>>>>
>>>>> I just found an article about the Halting Problem.
>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>
>>>>> In the conclusion section:
>>>>> The idea of a universal halting test seems reasonable, but cannot be
>>>>> for-
>>>>> malised as a consistent specification. It has no model and does not
>>>>> exist as
>>>>> a conceptual object. Assuming its conceptual existence leads to a
>>>>> paradox.
>>>>> The halting problem is universally used in university courses on
>>>>> Computer
>>>>> Science to illustrate the limits of computation. Hehner claims the
>>>>> halting
>>>>> problem is misconceived......
>>>>>
>>>>> It looks like what olcott now is claiming. Am I missing something?
>>>>
>>>> The error in the article is the claim that an "inconsistent"
>>>> specification is somehow invalid. But it is not.
>>>
>>> So if I asked you: What time is it (yes or no)?
>>
>> Why can't you understand the difference between "is this sequence
>> infinite?" and "is the time yes or no?"
>>
>> Every sequence is finite or infinite. The time is not yes or no.
>> That's the difference.
>>
>> There is no type mismatch when you ask if a sequence of execution
>> points (see my post which you ignored, but I know you read it because
>> you read all posts) is infinite.
>>
>>> Professor Hehner wrote many papers on the Halting problem:
>>> https://www.cs.toronto.edu/~hehner/halting.html
>>>
>>> This is one where he and I perfectly agree:
>>> https://www.cs.toronto.edu/~hehner/OSS.pdf
>>>
>>> Here is professor Hehner's update with my loophole correction.
>>> Can Carol correctly answer “no” to this [yes/no] question?
>>
>> Can you express this question mathematically?
>>
>>
>
> It is exactly isomorphic to the HP decider/input pair,
> that <is> its mathematical formalization.
>
> The context of who is asked Carol's question changes
> the meaning of the question in the same way that the
> context of who is asked this question:
> Are you a little girl?
> has different answers depending on who is asked.
>

Only because the actual question references the person being questioned.

The behavior of the input doesn't ask about the Decider, but about
something that just happens to be a copy of the decider.

That means that when you do the arguement about changing H, the input
doesn't actually change, so the correct simulation of that input by the
alternate H' does see the input call the original decider, then
eventually that decider returning 0 to it and it halting.

YOU made the (incorrect) "self-reference" by trying to define D to call
what ever machine was deciding it, as opposed to the specific machine
that is claimed to get the right answer.

In fact, as you have admitted, your "D" isn't actually a program( aka
for Computation), becausse it CAN'T be as it doesn't have defined
behavior on its own.

Thus, all the problems are of your own making because you don't
understand what you are talking about.

On 1/22/24 8:47 AM, immibis wrote:
> On 1/22/24 13:43, Richard Damon wrote:
>> On 1/22/24 4:01 AM, Mikko wrote:
>>> On 2024-01-22 00:12:12 +0000, Richard Damon said:
>>>> Was this even peer reviewed, or is this site just like your pre-pub
>>>> site?
>>>
>>> It is arxiv.org, a pre-publication site. The site requires endorsement,
>>> see https://info.arxiv.org/help/endorsement.html .
>>>
>>> Mikko
>>>
>>
>> Which means he knows someone how think he knows something about a
>> somewhat related field.
>>
>> It doesn't provide qualification for this particular paper.
>
> Please note that papers don't need to be peer-reviewed to be correct.
> Truth is a property of the world, not a property of scientists.
>
> Nonetheless, having other scientists review a paper is very useful to
> avoid errors. I think Bill Stoddart's paper is not formalized well
> enough to allow us to make inferences. I can't see what, EXTREMELY
> PRECISELY, is the meaning of:
> S1̂ = if H1(S1) then Loop end
>
> The Turing machine model has extremely precise, indisputably semantics
> where every detail is specified so that we can always calculate exactly
> what a Turing machine will do in the next 100 steps. Likewise for the
> x86 model. Stoddart's model is just the seed of an idea, and he needs to
> give more detail if he wants to make it an alternative to Turing
> machines. Then we can find the self-contradictory program that proves
> halting is still impossible in his model, OR we can find
> non-self-contradictory things that Stoddart's model can't compute.
>

No, it doesn't need to be reviewed to be correct, but to say that some
"random" person agrees with you, doesn't add much support for your
statement, especially when the argument you are tring to use has been
shot down.

IF you want to try to "Appeal to an authority" to add credance to your
side (knowing it isn't proof) you want to try to choose someone who is
recognised as an authority.

The Halting Theorem isn't right just because Turing wrote it, we know it
is right because he showed a correct proof of it.

From what I read of the two papers mentioned, neither person really
understand the nature of computation Theory.

For example, Stoddart says:

There is no reason, however, why the halt test cannot terminate in other
situations, or why failure to halt cannot be reported via an error
message when the halt test itself cannot halt.

But, yes, there IS a reason the halt test cannot act that way, as it is
contrary to the defintion that a decider produces its answer to its
caller. Not understanding that just breaks the foundations of
Computation theory.

Similarly Hehner makes the error of saying:

In Turing's time, programs were commands to a computer. Today, they are
also mathematical expressions in their own right

But mathematical expression aren't programs. Yes, sometimes we express
the results of a program with a mathematical expression, and use that
for correctness proofs, but when we need to look at finiteness of
compuation, they need a closer look. Yes, many equations can be directly
converted to "code" by simple "compiling" operation, but something like
find x such that x*x + 1 == 0 doesn't directly convert to code.

As I have mentioned, "Find the right answer" is NOT an algorithm.

This shows a basic misunderstanding of the actual nature of the Theory
and confusing it with similar fields within computer science.

On 1/22/24 2:06 PM, olcott wrote:
> On 1/22/2024 8:15 AM, immibis wrote:
>> On 1/22/24 09:48, Mikko wrote:
>>>
>>> That is false. For every program H there is a way to construct
>>> a program Ĥ so that either Ĥ halts and H does not say it halts
>>> or Ĥ does not halt and H does not say it halts. Perhaps Stoddart's
>>> S is not Ĥ but that does not prevent the construction of Ĥ.
>>>
>>
>> Stoddart speaks of a system of computation with only three possible
>> programs: Halt, Loop, and S. Nothing else can be constructed. Of
>> course, you also can't compute anything.
>
> Stoddart agrees with Hehner and Hehner agrees with me.
>

Which apparently puts you in "great" company.

If you are saying they are smart, then you are just showing how dumb you
are.

If you are agreeing the the program description S can't be converted
into a real program, you are just showing your utter stupidity.

On 1/22/24 11:07 AM, olcott wrote:
> On 1/22/2024 2:48 AM, Mikko wrote:
>> On 2024-01-21 23:05:50 +0000, olcott said:
>>
>>> On 1/21/2024 4:53 PM, immibis wrote:
>>>> On 1/21/24 23:36, olcott wrote:
>>>>> On 1/21/2024 4:18 PM, immibis wrote:
>>>>>> On 1/21/24 22:52, olcott wrote:
>>>>>>> On 1/21/2024 3:48 PM, immibis wrote:
>>>>>>>> On 1/21/24 22:20, olcott wrote:
>>>>>>>>> On 1/21/2024 3:13 PM, immibis wrote:
>>>>>>>>>> On 1/21/24 22:04, olcott wrote:
>>>>>>>>>>> On 1/21/2024 2:48 PM, immibis wrote:
>>>>>>>>>>>> On 1/21/24 20:54, olcott wrote:
>>>>>>>>>>>>> *Professor Stoddart doesn't say anything like this*
>>>>>>>>>>>>> You didn't read what he said you only guessed what he said.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Professor Stoddart quite literally says it. His hidden
>>>>>>>>>>>> variable is called InS1. Did you read what he wrote? I think
>>>>>>>>>>>> you are lying.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Good catch. That was part of his intermediate analysis
>>>>>>>>>>> and his conclusion does not reference anything like that.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> If you are talking about section 5, he says that S (which is
>>>>>>>>>> what he calls D) does not exist.
>>>>>>>>>
>>>>>>>>> *Read Stoddart's conclusion*
>>>>>>>>> *Read Stoddart's conclusion*
>>>>>>>>> *Read Stoddart's conclusion*
>>>>>>>>> *Read Stoddart's conclusion*
>>>>>>>>>
>>>>>>>>> I and wij are talking about the fact that three computer science
>>>>>>>>> professors agree that the halting problem itself is wrong.
>>>>>>>>>
>>>>>>>>> wij only referred to Stoddart's view, yet also quoted Professor
>>>>>>>>> Hehner's agreement. This is two of the three.
>>>>>>>>>
>>>>>>>>
>>>>>>>> You dishonestly ignored the question part of the post you
>>>>>>>> replied to.
>>>>>>>
>>>>>>> I soon as I hit the first fatal flaw quit reading.
>>>>>>> *Read Stoddart's conclusion*
>>>>>>> *Read Stoddart's conclusion*
>>>>>>> *Read Stoddart's conclusion*
>>>>>>>
>>>>>>> Don't freaking attempt to change the subject away from this.
>>>>>>>
>>>>>>
>>>>>> So you admit to dishonesty. Nice. I don't think you've read any
>>>>>> part of Stoddart's writing except for the conclusion.
>>>>>>
>>>>>> I think you'll also find that Stoddart failed to formalize anything.
>>>>>
>>>>> It is Stoddart's conclusion thus agreeing with Hehner's
>>>>> conclusion that the halting problem itself is incorrect.
>>>>>
>>>>>
>>>> Thanks for admitting you understand neither.
>>>
>>> *I simplified the language here are his exact words*
>>>
>>>     The proof of the halting problem assumes a universal halt
>>>     test exists and then provides S as an example of a program
>>>     that the test cannot handle. But S is not a program at all.
>>>     It is not even a conceptual object, and this is due to
>>>     inconsistencies in the specification of the halting function.
>>>     (Stoddart: 2017)
>>
>> That is false. For every program H there is a way to construct
>> a program Ĥ so that either Ĥ halts and H does not say it halts
>> or Ĥ does not halt and H does not say it halts. Perhaps Stoddart's
>> S is not Ĥ but that does not prevent the construction of Ĥ.
>>
>> Mikko
>>
>
> As I have already proved countless times when D has been
> intentionally defined to do the opposite of whatever
> Boolean value that H returns the question:
>
> D does halt on its input?
> Is an incorrect question when posed to H because both true
> and false are the wrong answer when this question is posed to H.

Why is it Incorrect?

And both answers are NOT wrong, as a given H can only give one of the
answere, and the other one is right.

You are just showing your as stupid (or more so) than your buddies.

>
> The above only applied when H is required to report on the
> directly executed D(D). This is an incorrect requirement
> because it contradiction the correct definition of a decider.

What contradiction to the correct definition of a decider?

A Decider is required to accept or reject its input based on it having
or not having the required property. For a "Halt Decider" that is the
computation described halting in a finte number of step.

Nothing wrong with that property, so a valuid question.

>
> Deciders always must compute the mapping from an input finite string to
> their own accept or reject state on the basis of a syntactic or semantic
> property of this finite string. Semantic properties and syntactic
> properties are the meanings of these terms referenced by Rice's Theorem.

And Halting of the Computation described by the input is a valid
semantic property of the finite string.

>
> *D correctly simulated by H specifies recursive simulation to H*
> Every idiot here believes that when the simulated D calls H that
> a correct simulation is to ignore this call.

But D simulated is NOT the property in question, so a Strawman.

If H doesn't actually do a correct simulation, your property is just
meaningless.

You CAN say (by the property of ACTUAL UTMS) if the Correct Simulation
of the input by an actual UTM never halts. But since H doesn't do such a
simulation, it isn't a UTM, so you can't look at the (incorrect)
simulation by H as your guide.

You COULD try to define H to actually do a correct simulation, but such
an H then needs to be *THE* H to count, and it has been shown that this
H never answers, so fails too.

>
> Richard finally admitted that a correct simulation of D by H
> never reaches its simulated final state.
>

OUT OF CONTEXT LIE.

That only applies to an H that actually DOES a correct simulation, and
such an H never answers so wasn't correct.

On 1/22/24 11:22 AM, Fred. Zwarts wrote:
> Op 22.jan.2024 om 17:07 schreef olcott:
>
>>>
>>
>> As I have already proved countless times when D has been
>> intentionally defined to do the opposite of whatever
>> Boolean value that H returns the question:
>>
>> D does halt on its input?
>> Is an incorrect question when posed to H because both true
>> and false are the wrong answer when this question is posed to H.
>>
>
> Why is it so difficult for olcott to see that not both answers are wrong?
> Olcott's H answers that D does not halt, so D halts. Therefore, only the
> answer that D does not halt is wrong. The answer that D does halt is
> correct. So there is a correct answer, but H returned the wrong answer.
>

Because Olcott doesn't understand the difference between a Program and a
set of program / input pairs, and just because one of the programs he
calls "H" which does a correct simulation of the input and gets stuck in
the resulting infinite recursion shows the the D built on it is
non-halting, that he can let every other program called H just assume
the the D built on them calls the H that other H instead.

Part of the problem is he doesn't consider H to be part of the "program"
D, because he doesn't really understand what a program actually is.

Sometimes he admits that his D isn't actually a program and then dodges
when it is pointed out that if his D isn't a program, it isn't a valid
input for a Halt Decider, and then he just shifts the topic and ignores
it, proving that he knows his argument is just a big lie.

On 1/22/24 2:48 PM, olcott wrote:
> On 1/22/2024 1:17 PM, immibis wrote:
>> On 1/22/24 20:01, olcott wrote:
>>> On 1/22/2024 10:19 AM, immibis wrote:
>>>> On 1/22/24 16:51, olcott wrote:
>>>>> On 1/22/2024 2:39 AM, Mikko wrote:
>>>>>> On 2024-01-21 19:54:47 +0000, olcott said:
>>>>>>
>>>>>>> On 1/21/2024 1:49 PM, immibis wrote:
>>>>>>>> On 1/21/24 20:24, olcott wrote:
>>>>>>>>> On 1/21/2024 1:22 PM, wij wrote:
>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>
>>>>>>>>>> In the conclusion section:
>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>> cannot be
>>>>>>>>>> for-
>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>> does not
>>>>>>>>>> exist as
>>>>>>>>>> a conceptual object. Assuming its conceptual existence leads to a
>>>>>>>>>> paradox.
>>>>>>>>>> The halting problem is universally used in university courses on
>>>>>>>>>> Computer
>>>>>>>>>> Science to illustrate the limits of computation. Hehner claims
>>>>>>>>>> the
>>>>>>>>>> halting
>>>>>>>>>> problem is misconceived......
>>>>>>>>>>
>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>> something?
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> He is one of three authors that agree on this.
>>>>>>>>>
>>>>>>>>
>>>>>>>> It is known that if you restrict the halting problem to programs
>>>>>>>> with a certain memory limit, it can be solved by a halting
>>>>>>>> decider which uses more memory than the limit. When a program
>>>>>>>> has limited memory, it has to  halt or loop within a certain
>>>>>>>> number of steps (2 to the power of the number of bits of memory
>>>>>>>> available, including the program counter/state number). The Linz
>>>>>>>> counterexample program doesn't lead to a contradiction, because
>>>>>>>> it uses more memory than the limit, so the halting decider is
>>>>>>>> unable to analyze it.
>>>>>>>>
>>>>>>>> Stoddart has the same idea as Olcott: there's a hidden variable
>>>>>>>> which tells the program whether it's already in a simulation,
>>>>>>>> and the program does something different if it's in a simulation
>>>>>>>> than if it isn't.
>>>>>>>
>>>>>>> *Professor Stoddart doesn't say anything like this*
>>>>>>> You didn't read what he said you only guessed what he said.
>>>>>>
>>>>>> In the section 4.1 of the article:
>>>>>> "Implementation of H₁ requires it to determine whether it is being
>>>>>> invoked
>>>>>> from within S₁."
>>>>>>
>>>>>> Mikko
>>>>>>
>>>>>
>>>>> S ≙ if H(S) then Loop end.
>>>>>
>>>>> He did not use that for a solution.
>>>>> He did use it to reject pathological inputs:
>>>>
>>>> A halting decider works for ABSOLUTELY ALL PROGRAMS WITH ABSOLUTELY
>>>> ZERO EXCEPTIONS, so he hasn't disproved the halting problem.
>>>
>>> You can't even understand that the Liar Paradox is neither true nor
>>> false.
>>>
>> You can't even understand that a halting decoder works for ABSOLUTELY
>> ALL PROGRAMS WITH ABSOLUTELY NO EXCEPTIONS.
>
> It has been proven otherwise and the proof is simply over your head.
>

No, it hasn't.
PERIOD.

You are just to dumb to understand the problems.

This is proven by your refusal to reply to any of the problems found,
which is an admission that you know your argument is fallacious (or you
have just copied it from somewhere and don't understand anything about it).

At least these other people can clearly state their problem with the
existing system, even if those problems seem to be based on
misunderstanding.

I suspect they would attempt to discuss the basis for their belief, and
not just repeat rote dogma as a retort, like you do.

On 1/22/24 4:40 PM, olcott wrote:
> On 1/22/2024 1:55 PM, immibis wrote:
>> On 1/22/24 20:48, olcott wrote:
>>> On 1/22/2024 1:17 PM, immibis wrote:
>>>> On 1/22/24 20:01, olcott wrote:
>>>>> On 1/22/2024 10:19 AM, immibis wrote:
>>>>>> On 1/22/24 16:51, olcott wrote:
>>>>>>> On 1/22/2024 2:39 AM, Mikko wrote:
>>>>>>>> On 2024-01-21 19:54:47 +0000, olcott said:
>>>>>>>>
>>>>>>>>> On 1/21/2024 1:49 PM, immibis wrote:
>>>>>>>>>> On 1/21/24 20:24, olcott wrote:
>>>>>>>>>>> On 1/21/2024 1:22 PM, wij wrote:
>>>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>
>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>>>> cannot be
>>>>>>>>>>>> for-
>>>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>>>> does not
>>>>>>>>>>>> exist as
>>>>>>>>>>>> a conceptual object. Assuming its conceptual existence leads
>>>>>>>>>>>> to a
>>>>>>>>>>>> paradox.
>>>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>>>> courses on
>>>>>>>>>>>> Computer
>>>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>>>> claims the
>>>>>>>>>>>> halting
>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>
>>>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>>>> something?
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> He is one of three authors that agree on this.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It is known that if you restrict the halting problem to
>>>>>>>>>> programs with a certain memory limit, it can be solved by a
>>>>>>>>>> halting decider which uses more memory than the limit. When a
>>>>>>>>>> program has limited memory, it has to  halt or loop within a
>>>>>>>>>> certain number of steps (2 to the power of the number of bits
>>>>>>>>>> of memory available, including the program counter/state
>>>>>>>>>> number). The Linz counterexample program doesn't lead to a
>>>>>>>>>> contradiction, because it uses more memory than the limit, so
>>>>>>>>>> the halting decider is unable to analyze it.
>>>>>>>>>>
>>>>>>>>>> Stoddart has the same idea as Olcott: there's a hidden
>>>>>>>>>> variable which tells the program whether it's already in a
>>>>>>>>>> simulation, and the program does something different if it's
>>>>>>>>>> in a simulation than if it isn't.
>>>>>>>>>
>>>>>>>>> *Professor Stoddart doesn't say anything like this*
>>>>>>>>> You didn't read what he said you only guessed what he said.
>>>>>>>>
>>>>>>>> In the section 4.1 of the article:
>>>>>>>> "Implementation of H₁ requires it to determine whether it is
>>>>>>>> being invoked
>>>>>>>> from within S₁."
>>>>>>>>
>>>>>>>> Mikko
>>>>>>>>
>>>>>>>
>>>>>>> S ≙ if H(S) then Loop end.
>>>>>>>
>>>>>>> He did not use that for a solution.
>>>>>>> He did use it to reject pathological inputs:
>>>>>>
>>>>>> A halting decider works for ABSOLUTELY ALL PROGRAMS WITH
>>>>>> ABSOLUTELY ZERO EXCEPTIONS, so he hasn't disproved the halting
>>>>>> problem.
>>>>>
>>>>> You can't even understand that the Liar Paradox is neither true nor
>>>>> false.
>>>>>
>>>> You can't even understand that a halting decoder works for
>>>> ABSOLUTELY ALL PROGRAMS WITH ABSOLUTELY NO EXCEPTIONS.
>>>
>>> It has been proven otherwise and the proof is simply over your head.
>>>
>>
>> You cannot refute a stipulative definition.
>
> ZFC did show that the definition stipulated by naive set theory of the
> term {set} was incoherent.
>

NOPE.

Russel did that.

ZFC just founded a new set theory.

If you think Computation Theory is that broken, develop your
PO-Computation theory (and to the same detail as ZFC has done for set
theoyr) and show how much better it works that the currect one.

Might help to find something actually wrong with the current one that
breaks a lot of the problems that people are using it for, that yours fixes.

On 1/22/24 8:56 AM, immibis wrote:
> On 1/22/24 13:41, Richard Damon wrote:
>> On 1/22/24 4:15 AM, Mikko wrote:
>>>
>>> The article is essentially a comment on
>>> https://www.cs.utoronto.ca/~hehner/PHP.pdf .
>>>
>>
>> Which questions the ability to make a program from another program,
>> showing a fundamental misunderstanding of what a program is.
>>
>
> People are free to come up with alternative definitions of what a
> program is.

Yes, but not the try to put it into a system that defines it.

>
> All of them will either not solve the halting problem, or they'll be too
> limited to do certain computations that have nothing to do with halting.

If "program" isn't close enough to "computation" then the theory doesn't
hold. In fact, Halting might not even be a defined property if the
"program" doesn't have consistant behavior in all cases.

>
> Stoddart's paper is imprecise enough that we don't really know which one
> it is. Maybe Olcott can formalize Stoddart's idea of what he thinks a
> program is, and how to execute one. I guarantee there will still be a
> problem.
>

On 1/22/24 7:39 PM, olcott wrote:
> On 1/22/2024 6:09 PM, wij wrote:
>> On Mon, 2024-01-22 at 10:28 +0200, Mikko wrote:
>>> On 2024-01-21 19:22:22 +0000, wij said:
>>>
>>>> I just found an article about the Halting Problem.
>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>
>>>> In the conclusion section:
>>>> The idea of a universal halting test seems reasonable, but cannot
>>>> be
>>>> for-
>>>> malised as a consistent specification. It has no model and does not
>>>> exist as
>>>> a conceptual object. Assuming its conceptual existence leads to a
>>>> paradox.
>>>> The halting problem is universally used in university courses on
>>>> Computer
>>>> Science to illustrate the limits of computation. Hehner claims the
>>>> halting
>>>> problem is misconceived......
>>>>
>>>> It looks like what olcott now is claiming. Am I missing something?
>>>
>>> The error in the article is the claim that an "inconsistent"
>>> specification
>>> is somehow invalid. But it is not.
>>>
>>> A problem is a request to find at least one thing that satisfies the
>>> requirements of the problem or to prove that no such thing can be
>>> found.
>>> The problem is well posed if for every thing it is possible to check
>>> whether it satisfies all requirements.
>>>
>>> The halting problem is solved: a proof that no Turing machine
>>> satisfies
>>> the requirements is known (and nothing else satisfies the requirement
>>> that it must be a Turing machine).
>>>
>>> It is a matter of opinion whether the usual presentation of the
>>> halting theorem is the best one. If one does not like the usual
>>> statement one may instead use:
>>>    For every universal Turing machine U and every Turing machine H
>>>    there is an input string S so that
>>>    either T(S) halts but H(S) does not accept
>>>    or T(S) does not halt but H(S) accepts.
>>>
>>> This formulation has the disadvantage that it uses the concept of
>>> "univesal Turing machine", and therefore depends on the existence
>>> of one.
>>>
>>> Mikko
>>>
>>
>> Thanks for the explanation.
>> It looked to me it is the statement of Halting Problem proved neither
>> T nor F bugged these people (including olcott).
>> There is also a status of proposition called contingency,
>> https://en.wikipedia.org/wiki/Contingency_(philosophy)
>
> Ultimately all these things boil down to the fact that
> self-contradictory questions must be rejected as incorrect
> questions. Hehner's paper explains this the best:
> https://www.cs.toronto.edu/~hehner/OSS.pdf

And there is nothing "Self-Contradictory" to the properly presented
Halting Problem, in part because Turing Machines don't have "references"
to become self-contradictory.

And what is not "Objective" about the qustion: "Does the computation
described by this input Halt when it is run?"

Such a machine, when run will either Halt or not, so has an objective
answer.

The fact that "programs" are consistant in there output when given a
specific input, and the language is sufficiently powerful that we can
build a new program based on any other one, is what gives the system the
power to create inputs, that HAVE correct answers, but that show that no
program can answer all inputs correctly.

This isn't a "Subjective" issue, it is a computational complexity issue,
the system have become powerful enough that it can not "solve" itself.

>
> The key part that non-technical people can understand is
> Carol's question:
> Can Carol correctly answer “no” to this [yes/no] question?

WHich mentions "Carol" in the question, so not equivalent.

>
> That question is self-contradictory when posed to Carol
> and has the correct answer of "no" when posed to anyone else.
>
> Carol's question actually originates from my own conversation:
>
> On 6/25/2004 6:30 PM, Daryl McCullough wrote:  (USENET sci.logic)
> > You ask someone (we'll call him "Jack") to give a truthful
> > yes/no answer to the following question:
> >
> >  Will Jack's answer to this question be no?
>
> was addressed to me in 2004.
> Hehner had no way of knowing this I repeated this
> same question as Bill's question hundreds of times
> until I tracked down the original author.
>

On 1/22/24 8:19 PM, olcott wrote:
> On 1/22/2024 6:57 PM, wij wrote:
>> On Mon, 2024-01-22 at 18:39 -0600, olcott wrote:
>>> On 1/22/2024 6:09 PM, wij wrote:
>>>> On Mon, 2024-01-22 at 10:28 +0200, Mikko wrote:
>>>>> On 2024-01-21 19:22:22 +0000, wij said:
>>>>>
>>>>>> I just found an article about the Halting Problem.
>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>
>>>>>> In the conclusion section:
>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>> cannot
>>>>>> be
>>>>>> for-
>>>>>> malised as a consistent specification. It has no model and does
>>>>>> not
>>>>>> exist as
>>>>>> a conceptual object. Assuming its conceptual existence leads to
>>>>>> a
>>>>>> paradox.
>>>>>> The halting problem is universally used in university courses
>>>>>> on
>>>>>> Computer
>>>>>> Science to illustrate the limits of computation. Hehner claims
>>>>>> the
>>>>>> halting
>>>>>> problem is misconceived......
>>>>>>
>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>> something?
>>>>>
>>>>> The error in the article is the claim that an "inconsistent"
>>>>> specification
>>>>> is somehow invalid. But it is not.
>>>>>
>>>>> A problem is a request to find at least one thing that satisfies
>>>>> the
>>>>> requirements of the problem or to prove that no such thing can be
>>>>> found.
>>>>> The problem is well posed if for every thing it is possible to
>>>>> check
>>>>> whether it satisfies all requirements.
>>>>>
>>>>> The halting problem is solved: a proof that no Turing machine
>>>>> satisfies
>>>>> the requirements is known (and nothing else satisfies the
>>>>> requirement
>>>>> that it must be a Turing machine).
>>>>>
>>>>> It is a matter of opinion whether the usual presentation of the
>>>>> halting theorem is the best one. If one does not like the usual
>>>>> statement one may instead use:
>>>>>     For every universal Turing machine U and every Turing machine
>>>>> H
>>>>>     there is an input string S so that
>>>>>     either T(S) halts but H(S) does not accept
>>>>>     or T(S) does not halt but H(S) accepts.
>>>>>
>>>>> This formulation has the disadvantage that it uses the concept of
>>>>> "univesal Turing machine", and therefore depends on the existence
>>>>> of one.
>>>>>
>>>>> Mikko
>>>>>
>>>>
>>>> Thanks for the explanation.
>>>> It looked to me it is the statement of Halting Problem proved
>>>> neither
>>>> T nor F bugged these people (including olcott).
>>>> There is also a status of proposition called contingency,
>>>> https://en.wikipedia.org/wiki/Contingency_(philosophy)
>>>
>>> Ultimately all these things boil down to the fact that
>>> self-contradictory questions must be rejected as incorrect
>>> questions. Hehner's paper explains this the best:
>>> https://www.cs.toronto.edu/~hehner/OSS.pdf
>>>
>>> The key part that non-technical people can understand is
>>> Carol's question:
>>> Can Carol correctly answer “no” to this [yes/no] question?
>>>
>>> That question is self-contradictory when posed to Carol
>>> and has the correct answer of "no" when posed to anyone else.
>>>
>>> Carol's question actually originates from my own conversation:
>>>
>>> On 6/25/2004 6:30 PM, Daryl McCullough wrote:  (USENET sci.logic)
>>>   > You ask someone (we'll call him "Jack") to give a truthful
>>>   > yes/no answer to the following question:
>>>   >
>>>   >  Will Jack's answer to this question be no?
>>>
>>> was addressed to me in 2004.
>>> Hehner had no way of knowing this I repeated this
>>> same question as Bill's question hundreds of times
>>> until I tracked down the original author.
>>>
>>
>> The HP is asking (equivalent) for A PROGRAM that takes another program
>> as its argument and decides whether or not that given program
>> will terminate.
>>
>> The HP is not asking the evaluation of "HP Theorem" (the conclusion)
>> to be true or false!!!
>
> The HP uses a counter-example D that does the opposite
> of whatever value that H returns, thus making the question
> Does D halt? a self-contradictory question for H.

Nope.

>
> Professor Hehner understood this exactly the same way with his:
> Can Carol correctly answer “no” to this [yes/no] question?

Which is not an equivalent question, It just shows that Turing Machines
have the complexity to be beyond the ability of Turing Machines to fully
analyze.

>
> Richard deserves credit for finding a loophole in the
> version in Hehner's paper.
>

On 1/22/24 9:05 PM, olcott wrote:
> On 1/22/2024 7:44 PM, wij wrote:
>> On Mon, 2024-01-22 at 19:19 -0600, olcott wrote:
>>> On 1/22/2024 6:57 PM, wij wrote:
>>>> On Mon, 2024-01-22 at 18:39 -0600, olcott wrote:
>>>>> On 1/22/2024 6:09 PM, wij wrote:
>>>>>> On Mon, 2024-01-22 at 10:28 +0200, Mikko wrote:
>>>>>>> On 2024-01-21 19:22:22 +0000, wij said:
>>>>>>>
>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>
>>>>>>>> In the conclusion section:
>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>> cannot
>>>>>>>> be
>>>>>>>> for-
>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>> does
>>>>>>>> not
>>>>>>>> exist as
>>>>>>>> a conceptual object. Assuming its conceptual existence
>>>>>>>> leads to
>>>>>>>> a
>>>>>>>> paradox.
>>>>>>>> The halting problem is universally used in university
>>>>>>>> courses
>>>>>>>> on
>>>>>>>> Computer
>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>> claims
>>>>>>>> the
>>>>>>>> halting
>>>>>>>> problem is misconceived......
>>>>>>>>
>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>> something?
>>>>>>>
>>>>>>> The error in the article is the claim that an "inconsistent"
>>>>>>> specification
>>>>>>> is somehow invalid. But it is not.
>>>>>>>
>>>>>>> A problem is a request to find at least one thing that
>>>>>>> satisfies
>>>>>>> the
>>>>>>> requirements of the problem or to prove that no such thing
>>>>>>> can be
>>>>>>> found.
>>>>>>> The problem is well posed if for every thing it is possible
>>>>>>> to
>>>>>>> check
>>>>>>> whether it satisfies all requirements.
>>>>>>>
>>>>>>> The halting problem is solved: a proof that no Turing machine
>>>>>>> satisfies
>>>>>>> the requirements is known (and nothing else satisfies the
>>>>>>> requirement
>>>>>>> that it must be a Turing machine).
>>>>>>>
>>>>>>> It is a matter of opinion whether the usual presentation of
>>>>>>> the
>>>>>>> halting theorem is the best one. If one does not like the
>>>>>>> usual
>>>>>>> statement one may instead use:
>>>>>>>      For every universal Turing machine U and every Turing
>>>>>>> machine
>>>>>>> H
>>>>>>>      there is an input string S so that
>>>>>>>      either T(S) halts but H(S) does not accept
>>>>>>>      or T(S) does not halt but H(S) accepts.
>>>>>>>
>>>>>>> This formulation has the disadvantage that it uses the
>>>>>>> concept of
>>>>>>> "univesal Turing machine", and therefore depends on the
>>>>>>> existence
>>>>>>> of one.
>>>>>>>
>>>>>>> Mikko
>>>>>>>
>>>>>>
>>>>>> Thanks for the explanation.
>>>>>> It looked to me it is the statement of Halting Problem proved
>>>>>> neither
>>>>>> T nor F bugged these people (including olcott).
>>>>>> There is also a status of proposition called contingency,
>>>>>> https://en.wikipedia.org/wiki/Contingency_(philosophy)
>>>>>
>>>>> Ultimately all these things boil down to the fact that
>>>>> self-contradictory questions must be rejected as incorrect
>>>>> questions. Hehner's paper explains this the best:
>>>>> https://www.cs.toronto.edu/~hehner/OSS.pdf
>>>>>
>>>>> The key part that non-technical people can understand is
>>>>> Carol's question:
>>>>> Can Carol correctly answer “no” to this [yes/no] question?
>>>>>
>>>>> That question is self-contradictory when posed to Carol
>>>>> and has the correct answer of "no" when posed to anyone else.
>>>>>
>>>>> Carol's question actually originates from my own conversation:
>>>>>
>>>>> On 6/25/2004 6:30 PM, Daryl McCullough wrote:  (USENET sci.logic)
>>>>>    > You ask someone (we'll call him "Jack") to give a truthful
>>>>>    > yes/no answer to the following question:
>>>>>    >
>>>>>    >  Will Jack's answer to this question be no?
>>>>>
>>>>> was addressed to me in 2004.
>>>>> Hehner had no way of knowing this I repeated this
>>>>> same question as Bill's question hundreds of times
>>>>> until I tracked down the original author.
>>>>>
>>>>
>>>> The HP is asking (equivalent) for A PROGRAM that takes another
>>>> program
>>>> as its argument and decides whether or not that given program
>>>> will terminate.
>>>>
>>>> The HP is not asking the evaluation of "HP Theorem" (the
>>>> conclusion)
>>>> to be true or false!!!
>>
>>> The HP uses a counter-example D that does the opposite
>>> of whatever value that H returns, thus making the question
>>> Does D halt? a self-contradictory question for H.
>>
>> It seems you took it as:
>> Proposition P="A program that decides whether another program halts or
>> not is undecidable".
>>
>
> I have gone over these details many many thousands of times since 2004.
> That actual question for H is this:
>
> "What correct Boolean value does H return when D is defined to do the
>  opposite of whatever value that H returns?"

So, you are just admitting that you have been working on a false premsis
for 20 years,

The actual question is: "Does the Computation described by the input
Halt when run?"

"What correct value can H return?" or similar questions are NOT valid,
as H returns a specific value for every input, and thus either that is
or is not correct. THAT H cannot return any other possible value, so
asking what it could do in this way is just wrong.

What value would have been correct? would be ok, as that accepts that it
might not be what H did.

Your reformulation introduces EXACTLY the form of pathological
self-reference that you claim is invalid, thus, by your own logic, your
change is impropper.

The fact that you think it is ok to do so just shows that you don't
understand what a "Program" is in computation theory.

This is sort of like you friends thought that "mathematical forumlas"
define programs, they don't. PRograms can define Mathematical Formulas
(the formula derived from the behavior of the program) or Mathematical
Formulas can define the GOAL of the program (we want to see if we can
create a program that computes the results of the formula)

Your transformation has converted the definition of the original
problem, into a the problem of trying to make a program that satifies
the original problem. Since part of the original problem was asking if
that operation was possible, the results of it being impossible doesn't
make the question invalid, just proves the function we are trying to
compute is non-computable (but a valid mathematical function).

>
> *immibis came up with the exact isomorphism of the Barber Paradox*
> On 1/6/2024 1:54 PM, immibis wrote:
> > "Does a barber who shaves every man who does not shave himself shave
> > himself?" has no correct answer.
>
> Stoddart proposes the same method that I came up
> with for making a halting decidability decider.
>

On 1/22/24 9:20 PM, olcott wrote:
> On 1/22/2024 8:13 PM, wij wrote:
>> On Mon, 2024-01-22 at 20:05 -0600, olcott wrote:
>>> On 1/22/2024 7:44 PM, wij wrote:
>>>> On Mon, 2024-01-22 at 19:19 -0600, olcott wrote:
>>>>> On 1/22/2024 6:57 PM, wij wrote:
>>>>>> On Mon, 2024-01-22 at 18:39 -0600, olcott wrote:
>>>>>>> On 1/22/2024 6:09 PM, wij wrote:
>>>>>>>> On Mon, 2024-01-22 at 10:28 +0200, Mikko wrote:
>>>>>>>>> On 2024-01-21 19:22:22 +0000, wij said:
>>>>>>>>>
>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>
>>>>>>>>>> In the conclusion section:
>>>>>>>>>> The idea of a universal halting test seems reasonable,
>>>>>>>>>> but
>>>>>>>>>> cannot
>>>>>>>>>> be
>>>>>>>>>> for-
>>>>>>>>>> malised as a consistent specification. It has no model
>>>>>>>>>> and
>>>>>>>>>> does
>>>>>>>>>> not
>>>>>>>>>> exist as
>>>>>>>>>> a conceptual object. Assuming its conceptual existence
>>>>>>>>>> leads to
>>>>>>>>>> a
>>>>>>>>>> paradox.
>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>> courses
>>>>>>>>>> on
>>>>>>>>>> Computer
>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>> claims
>>>>>>>>>> the
>>>>>>>>>> halting
>>>>>>>>>> problem is misconceived......
>>>>>>>>>>
>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>> something?
>>>>>>>>>
>>>>>>>>> The error in the article is the claim that an
>>>>>>>>> "inconsistent"
>>>>>>>>> specification
>>>>>>>>> is somehow invalid. But it is not.
>>>>>>>>>
>>>>>>>>> A problem is a request to find at least one thing that
>>>>>>>>> satisfies
>>>>>>>>> the
>>>>>>>>> requirements of the problem or to prove that no such
>>>>>>>>> thing
>>>>>>>>> can be
>>>>>>>>> found.
>>>>>>>>> The problem is well posed if for every thing it is
>>>>>>>>> possible
>>>>>>>>> to
>>>>>>>>> check
>>>>>>>>> whether it satisfies all requirements.
>>>>>>>>>
>>>>>>>>> The halting problem is solved: a proof that no Turing
>>>>>>>>> machine
>>>>>>>>> satisfies
>>>>>>>>> the requirements is known (and nothing else satisfies the
>>>>>>>>> requirement
>>>>>>>>> that it must be a Turing machine).
>>>>>>>>>
>>>>>>>>> It is a matter of opinion whether the usual presentation
>>>>>>>>> of
>>>>>>>>> the
>>>>>>>>> halting theorem is the best one. If one does not like the
>>>>>>>>> usual
>>>>>>>>> statement one may instead use:
>>>>>>>>>       For every universal Turing machine U and every
>>>>>>>>> Turing
>>>>>>>>> machine
>>>>>>>>> H
>>>>>>>>>       there is an input string S so that
>>>>>>>>>       either T(S) halts but H(S) does not accept
>>>>>>>>>       or T(S) does not halt but H(S) accepts.
>>>>>>>>>
>>>>>>>>> This formulation has the disadvantage that it uses the
>>>>>>>>> concept of
>>>>>>>>> "univesal Turing machine", and therefore depends on the
>>>>>>>>> existence
>>>>>>>>> of one.
>>>>>>>>>
>>>>>>>>> Mikko
>>>>>>>>>
>>>>>>>>
>>>>>>>> Thanks for the explanation.
>>>>>>>> It looked to me it is the statement of Halting Problem
>>>>>>>> proved
>>>>>>>> neither
>>>>>>>> T nor F bugged these people (including olcott).
>>>>>>>> There is also a status of proposition called contingency,
>>>>>>>> https://en.wikipedia.org/wiki/Contingency_(philosophy)
>>>>>>>
>>>>>>> Ultimately all these things boil down to the fact that
>>>>>>> self-contradictory questions must be rejected as incorrect
>>>>>>> questions. Hehner's paper explains this the best:
>>>>>>> https://www.cs.toronto.edu/~hehner/OSS.pdf
>>>>>>>
>>>>>>> The key part that non-technical people can understand is
>>>>>>> Carol's question:
>>>>>>> Can Carol correctly answer “no” to this [yes/no] question?
>>>>>>>
>>>>>>> That question is self-contradictory when posed to Carol
>>>>>>> and has the correct answer of "no" when posed to anyone else.
>>>>>>>
>>>>>>> Carol's question actually originates from my own
>>>>>>> conversation:
>>>>>>>
>>>>>>> On 6/25/2004 6:30 PM, Daryl McCullough wrote:  (USENET
>>>>>>> sci.logic)
>>>>>>>     > You ask someone (we'll call him "Jack") to give a
>>>>>>> truthful
>>>>>>>     > yes/no answer to the following question:
>>>>>>>     >
>>>>>>>     >  Will Jack's answer to this question be no?
>>>>>>>
>>>>>>> was addressed to me in 2004.
>>>>>>> Hehner had no way of knowing this I repeated this
>>>>>>> same question as Bill's question hundreds of times
>>>>>>> until I tracked down the original author.
>>>>>>>
>>>>>>
>>>>>> The HP is asking (equivalent) for A PROGRAM that takes another
>>>>>> program
>>>>>> as its argument and decides whether or not that given program
>>>>>> will terminate.
>>>>>>
>>>>>> The HP is not asking the evaluation of "HP Theorem" (the
>>>>>> conclusion)
>>>>>> to be true or false!!!
>>>>
>>>>> The HP uses a counter-example D that does the opposite
>>>>> of whatever value that H returns, thus making the question
>>>>> Does D halt? a self-contradictory question for H.
>>>>
>>>> It seems you took it as:
>>>> Proposition P="A program that decides whether another program halts
>>>> or
>>>> not is undecidable".
>>>>
>>>
>>> I have gone over these details many many thousands of times since
>>> 2004.
>>> That actual question for H is this:
>>>
>>> "What correct Boolean value does H return when D is defined to do the
>>>    opposite of whatever value that H returns?"
>>
>> As you already have seen: The H would be stock in an infinite recursive
>> call. I.e. H is not implementable.
>>
>
> You mean "stuck" not "stock".
>
> https://github.com/plolcott/x86utm
> I spent 1.5 years making sure that H does not get stuck it has been
> fully operational code for several years now.

On 1/22/2024 9:43 PM, Richard Damon wrote:
> On 1/22/24 1:59 PM, olcott wrote:
>> On 1/22/2024 6:23 AM, Richard Damon wrote:
>>> On 1/21/24 11:37 PM, olcott wrote:
>>>> On 1/21/2024 10:06 PM, Richard Damon wrote:
>>>>> On 1/21/24 11:01 PM, olcott wrote:
>>>>>> On 1/21/2024 9:39 PM, Richard Damon wrote:
>>>>>>> On 1/21/24 10:30 PM, olcott wrote:
>>>>>>>> On 1/21/2024 9:28 PM, Richard Damon wrote:
>>>>>>>>> On 1/21/24 10:22 PM, olcott wrote:
>>>>>>>>>> On 1/21/2024 9:19 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/21/24 9:55 PM, olcott wrote:
>>>>>>>>>>>> On 1/21/2024 8:28 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/21/24 9:18 PM, olcott wrote:
>>>>>>>>>>>>>> On 1/21/2024 8:07 PM, immibis wrote:
>>>>>>>>>>>>>>> On 1/22/24 02:43, olcott wrote:
>>>>>>>>>>>>>>>> On 1/21/2024 7:38 PM, immibis wrote:
>>>>>>>>>>>>>>>>> On 1/22/24 02:04, olcott wrote:
>>>>>>>>>>>>>>>>>> On 1/21/2024 6:58 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 1/21/24 7:54 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 1/21/2024 6:50 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>> On 1/22/24 01:37, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 1/21/2024 6:27 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 1/22/24 01:13, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 1/21/2024 6:04 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 1/21/24 23:56, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> Tarski didn't understand that the correct
>>>>>>>>>>>>>>>>>>>>>>>>>> evaluation of the Liar Paradox requires
>>>>>>>>>>>>>>>>>>>>>>>>>> an infinite cycle in the directed graph
>>>>>>>>>>>>>>>>>>>>>>>>>> of its evaluation sequence.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand the difference between
>>>>>>>>>>>>>>>>>>>>>>>>> diagonalization and infinite recursion.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Do you think the real numbers are countable?
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Diagonalization is a process by which we know that
>>>>>>>>>>>>>>>>>>>>>>>> x is unprovable in L that makes sure to ignore the
>>>>>>>>>>>>>>>>>>>>>>>> reason why x is unprovable in L.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> So are the real numbers countable? Isn't Cantor's
>>>>>>>>>>>>>>>>>>>>>>> number pathologically self-referential, making
>>>>>>>>>>>>>>>>>>>>>>> his argument invalid?
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> unify_with_occurs_check(LP, not(true(LP))).
>>>>>>>>>>>>>>>>>>>>>>>> correctly determines that LP is unprovable
>>>>>>>>>>>>>>>>>>>>>>>> BECAUSE the directed graph of its evaluation
>>>>>>>>>>>>>>>>>>>>>>>> sequence contains an infinite cycle.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Provability doesn't give a flying fuck about
>>>>>>>>>>>>>>>>>>>>>>> evaluation cycles, whatever those are.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> It sure does in Prolog.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Then Prolog is wrong.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> That Prolog pays attention to details that other
>>>>>>>>>>>>>>>>>>>> systems
>>>>>>>>>>>>>>>>>>>> ignore make it wrong is like saying that ignorance is
>>>>>>>>>>>>>>>>>>>> knowledge and knowledge is incorrect.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Prolog handles SIMPLE logic system and problems. It
>>>>>>>>>>>>>>>>>>> rejects ALL cycles, even if they don't cause logical
>>>>>>>>>>>>>>>>>>> issues (as I understand it)
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> As you fail to understand it.
>>>>>>>>>>>>>>>>>> I took 18 months creating Minimal Type Theory that
>>>>>>>>>>>>>>>>>> automatically generated the directed graph of the
>>>>>>>>>>>>>>>>>> evaluation sequence of any of its expressions.
>>>>>>>>>>>>>>>>>> It sued syntax similar to FOL yet is as expressive
>>>>>>>>>>>>>>>>>> as HOL. I encode a SOL expression in MTT.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> You are rebutting the infinite formulas such as
>>>>>>>>>>>>>>>>> ¬True(¬True(¬True(...)))
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> But this is already in the standard theory. Infinite
>>>>>>>>>>>>>>>>> formulas such as ¬True(¬True(¬True(...))) are already
>>>>>>>>>>>>>>>>> not valid.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Olcott doesn't understand that diagonalization is not
>>>>>>>>>>>>>>>>> the same as infinite recursion.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Finally a reply that is not nonsense.
>>>>>>>>>>>>>>>> Diagonalization only knows that for some reason or another
>>>>>>>>>>>>>>>> x is unprovable in L.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I dispute the notion of "reasons". It's just a fact that
>>>>>>>>>>>>>>> it's unprovable. There are different ways to find out
>>>>>>>>>>>>>>> that it's unprovable, or different ways to understand
>>>>>>>>>>>>>>> that it's unprovable, but not reasons why it's unprovable.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> If the reason that x is unprovable in L is that x
>>>>>>>>>>>>>> is semantically incorrect in L then instead of saying
>>>>>>>>>>>>>> that x is undecidable in L the decider rejects x
>>>>>>>>>>>>>> as invalid input.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> This what Tarski should have done.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> But there are x that are unprovable in L because the chain
>>>>>>>>>>>>> to them is infinitely long, which makes them true but
>>>>>>>>>>>>> unprovale.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> (1) x ∉ Provable if and only if p
>>>>>>>>>>>> (2) x ∈ True if and only if p
>>>>>>>>>>>> (3) x ∉ Provable if and only if x ∈ True.
>>>>>>>>>>>>
>>>>>>>>>>>> When we correct the erroneous line (1) then line (3) becomes
>>>>>>>>>>>> (3) x ∈ Provable if and only if x ∈ True.
>>>>>>>>>>>> Thus making your (infinite chain) x simply untrue.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> WHy is it "erroneous", it is a simple statement previously
>>>>>>>>>>> proven.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> He proved that there are some things that we know
>>>>>>>>>> are true yet have no way what-so-ever to know that
>>>>>>>>>> they are true?
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> No, he proved that there are some things that ARE true that we
>>>>>>>>> can not prove to be true.
>>>>>>>>>
>>>>>>>>
>>>>>>>> How the Hell is he going to do that on his basis
>>>>>>>> of the Liar Paradox?
>>>>>>>>
>>>>>>>
>>>>>>> Read his proof. And it isn't "based' on the Liar's paradox,
>>>>>>
>>>>>> *It sure as Hell is anchored in the Liar Paradox*
>>>>>> He get his line (1) directly from the Liar Paradox
>>>>>>
>>>>>> Below he shows how he transforms the Liar Paradox
>>>>>> x ∉ True if and only if p
>>>>>>
>>>>>> into his line (1) by replacing "Tr" (for True)
>>>>>> with 'Pr" (for provable) Here is his line
>>>>>> (1) x ∉ Provable if and only if p
>>>>>>
>>>>>> <page 275>
>>>>>>     In accordance with the first
>>>>>>     part of Th. I we can obtain the negation of one of the sentences
>>>>>>     in condition (α) of convention T of § 3 as a consequence of the
>>>>>>     definition of the symbol 'Pr' (provided we replace 'Tr' in this
>>>>>>     convention by 'Pr'). https://liarparadox.org/Tarski_275_276.pdf
>>>>>> </page 275>
>>>>>>
>>>>>> <page 248> Liar Paradox
>>>>>>     Should we succeed in constructing in the metalanguage
>>>>>>     a correct definition of truth, then
>>>>>>
>>>>>>     It would
>>>>>>     then be possible to reconstruct the antinomy of the liar in the
>>>>>>     metalanguage, by forming in the language itself a sentence x
>>>>>>     such that the sentence of the metalanguage which is correlated
>>>>>>     with x asserts that x is not a true sentence.
>>>>>>     https://liarparadox.org/Tarski_247_248.pdf
>>>>>> </page 248>
>>>>>>
>>>>>> Many people today are simply too stupid to understand
>>>>>> that the Liar Paradox is simply not a truth bearer
>>>>>> thus must be rejected by any correct True(L, x) predicate.
>>>>>>
>>>>>> When Tarski assumes the Liar Paradox as a premise
>>>>>> this must be rejected and over-ruled.
>>>>>
>>>>> Where does he assume it as a premise?
>>>>>
>>>>
>>>> His line (1) is a premise.
>>>
>>> Then why does he say, "In other words, we can construct ... " just
>>> above it.
>>>
>>> (1) is a CONCLUSION from the previous paragraph.
>>>
>>> you clearly don't know much about logic.
>>>
>>>>
>>>>>>
>>>>>> (1) x ∉ Provable if and only if p
>>>>>> must be corrected to say
>>>>>> (1) x ∈ Provable if and only if p
>>>>>>
>>>>>
>>>>> What was actually wrong with (1). You haven't shown the error in
>>>>> logic.
>>>>
>>>> His line (1) <is> an adapted form of the actual Liar
>>>> Paradox as I have shown by the quotes above.
>>>
>>> NO, the liar paradox says NOTHING about "Provable".
>>
>> Tarski says that he takes the Liar Paradox:
>> x ∉ True if and only if p
>> and changes it to this
>> (1) x ∉ Provable if and only if p
>> on page <275> quoted above.
>>
>> It is <page 248> quoted above where he says
>> that he is using the actual Liar Paradox.
>>
>> You have to carefully study what I say before
>> providing a rebuttal. It took me a half hour
>> to compose the Tarski quotes.
>>
>>
>
> Note, page 247 doesn't say "start with the Liar's Paradox" he points out
> that IT WOULD BE POSSIBLE TO RECONSTRUCT THE LIAR, ie, show that the
Carefully study every single word of my quotes from
<page 248> and <page 275> again and again until you
see that what I say is true.

On 1/22/2024 9:45 PM, Richard Damon wrote:
> On 1/22/24 9:05 PM, olcott wrote:
>> On 1/22/2024 7:44 PM, wij wrote:
>>> On Mon, 2024-01-22 at 19:19 -0600, olcott wrote:
>>>> On 1/22/2024 6:57 PM, wij wrote:
>>>>> On Mon, 2024-01-22 at 18:39 -0600, olcott wrote:
>>>>>> On 1/22/2024 6:09 PM, wij wrote:
>>>>>>> On Mon, 2024-01-22 at 10:28 +0200, Mikko wrote:
>>>>>>>> On 2024-01-21 19:22:22 +0000, wij said:
>>>>>>>>
>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>
>>>>>>>>> In the conclusion section:
>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>> cannot
>>>>>>>>> be
>>>>>>>>> for-
>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>> does
>>>>>>>>> not
>>>>>>>>> exist as
>>>>>>>>> a conceptual object. Assuming its conceptual existence
>>>>>>>>> leads to
>>>>>>>>> a
>>>>>>>>> paradox.
>>>>>>>>> The halting problem is universally used in university
>>>>>>>>> courses
>>>>>>>>> on
>>>>>>>>> Computer
>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>> claims
>>>>>>>>> the
>>>>>>>>> halting
>>>>>>>>> problem is misconceived......
>>>>>>>>>
>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>> something?
>>>>>>>>
>>>>>>>> The error in the article is the claim that an "inconsistent"
>>>>>>>> specification
>>>>>>>> is somehow invalid. But it is not.
>>>>>>>>
>>>>>>>> A problem is a request to find at least one thing that
>>>>>>>> satisfies
>>>>>>>> the
>>>>>>>> requirements of the problem or to prove that no such thing
>>>>>>>> can be
>>>>>>>> found.
>>>>>>>> The problem is well posed if for every thing it is possible
>>>>>>>> to
>>>>>>>> check
>>>>>>>> whether it satisfies all requirements.
>>>>>>>>
>>>>>>>> The halting problem is solved: a proof that no Turing machine
>>>>>>>> satisfies
>>>>>>>> the requirements is known (and nothing else satisfies the
>>>>>>>> requirement
>>>>>>>> that it must be a Turing machine).
>>>>>>>>
>>>>>>>> It is a matter of opinion whether the usual presentation of
>>>>>>>> the
>>>>>>>> halting theorem is the best one. If one does not like the
>>>>>>>> usual
>>>>>>>> statement one may instead use:
>>>>>>>>      For every universal Turing machine U and every Turing
>>>>>>>> machine
>>>>>>>> H
>>>>>>>>      there is an input string S so that
>>>>>>>>      either T(S) halts but H(S) does not accept
>>>>>>>>      or T(S) does not halt but H(S) accepts.
>>>>>>>>
>>>>>>>> This formulation has the disadvantage that it uses the
>>>>>>>> concept of
>>>>>>>> "univesal Turing machine", and therefore depends on the
>>>>>>>> existence
>>>>>>>> of one.
>>>>>>>>
>>>>>>>> Mikko
>>>>>>>>
>>>>>>>
>>>>>>> Thanks for the explanation.
>>>>>>> It looked to me it is the statement of Halting Problem proved
>>>>>>> neither
>>>>>>> T nor F bugged these people (including olcott).
>>>>>>> There is also a status of proposition called contingency,
>>>>>>> https://en.wikipedia.org/wiki/Contingency_(philosophy)
>>>>>>
>>>>>> Ultimately all these things boil down to the fact that
>>>>>> self-contradictory questions must be rejected as incorrect
>>>>>> questions. Hehner's paper explains this the best:
>>>>>> https://www.cs.toronto.edu/~hehner/OSS.pdf
>>>>>>
>>>>>> The key part that non-technical people can understand is
>>>>>> Carol's question:
>>>>>> Can Carol correctly answer “no” to this [yes/no] question?
>>>>>>
>>>>>> That question is self-contradictory when posed to Carol
>>>>>> and has the correct answer of "no" when posed to anyone else.
>>>>>>
>>>>>> Carol's question actually originates from my own conversation:
>>>>>>
>>>>>> On 6/25/2004 6:30 PM, Daryl McCullough wrote:  (USENET sci.logic)
>>>>>>    > You ask someone (we'll call him "Jack") to give a truthful
>>>>>>    > yes/no answer to the following question:
>>>>>>    >
>>>>>>    >  Will Jack's answer to this question be no?
>>>>>>
>>>>>> was addressed to me in 2004.
>>>>>> Hehner had no way of knowing this I repeated this
>>>>>> same question as Bill's question hundreds of times
>>>>>> until I tracked down the original author.
>>>>>>
>>>>>
>>>>> The HP is asking (equivalent) for A PROGRAM that takes another
>>>>> program
>>>>> as its argument and decides whether or not that given program
>>>>> will terminate.
>>>>>
>>>>> The HP is not asking the evaluation of "HP Theorem" (the
>>>>> conclusion)
>>>>> to be true or false!!!
>>>
>>>> The HP uses a counter-example D that does the opposite
>>>> of whatever value that H returns, thus making the question
>>>> Does D halt? a self-contradictory question for H.
>>>
>>> It seems you took it as:
>>> Proposition P="A program that decides whether another program halts or
>>> not is undecidable".
>>>
>>
>> I have gone over these details many many thousands of times since 2004.
>> That actual question for H is this:
>>
>> "What correct Boolean value does H return when D is defined to do the
>>   opposite of whatever value that H returns?"
>
> So, you are just admitting that you have been working on a false premsis
> for 20 years

I merely put the full context of the question posed to H directly in the
question the same way that immibis did for the Barber Paradox.

The question superficially seems to be: Does the barber shave himself?
This is NOT the actual question. immibis poses the actual question
with its full context directly in the question.

USENET Message-ID: <uncb5j$npjn$2@dont-email.me>
On 1/6/2024 1:54 PM, immibis wrote:
> "Does a barber who shaves every man who does not shave himself shave
> himself?" has no correct answer.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Mon, 2024-01-22 at 21:29 -0600, olcott wrote:
> On 1/22/2024 8:59 PM, wij wrote:
> > On Mon, 2024-01-22 at 20:40 -0600, olcott wrote:
> > > On 1/22/2024 8:27 PM, wij wrote:
> > > > On Mon, 2024-01-22 at 20:20 -0600, olcott wrote:
> > > > > On 1/22/2024 8:13 PM, wij wrote:
> > > > > > On Mon, 2024-01-22 at 20:05 -0600, olcott wrote:
> > > > > > > On 1/22/2024 7:44 PM, wij wrote:
> > > > > > > > On Mon, 2024-01-22 at 19:19 -0600, olcott wrote:
> > > > > > > > > On 1/22/2024 6:57 PM, wij wrote:
> > > > > > > > > > On Mon, 2024-01-22 at 18:39 -0600, olcott wrote:
> > > > > > > > > > > On 1/22/2024 6:09 PM, wij wrote:
> > > > > > > > > > > > On Mon, 2024-01-22 at 10:28 +0200, Mikko wrote:
> > > > > > > > > > > > > On 2024-01-21 19:22:22 +0000, wij said:
> > > > > > > > > > > > >
> > > > > > > > > > > > > > I just found an article about the Halting
> > > > > > > > > > > > > > Problem.
> > > > > > > > > > > > > > https://arxiv.org/pdf/1906.05340.pdf
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > In the conclusion section:
> > > > > > > > > > > > > > The idea of a universal halting test seems
> > > > > > > > > > > > > > reasonable,
> > > > > > > > > > > > > > but
> > > > > > > > > > > > > > cannot
> > > > > > > > > > > > > > be
> > > > > > > > > > > > > > for-
> > > > > > > > > > > > > > malised as a consistent specification. It
> > > > > > > > > > > > > > has
> > > > > > > > > > > > > > no
> > > > > > > > > > > > > > model
> > > > > > > > > > > > > > and
> > > > > > > > > > > > > > does
> > > > > > > > > > > > > > not
> > > > > > > > > > > > > > exist as
> > > > > > > > > > > > > > a conceptual object. Assuming its
> > > > > > > > > > > > > > conceptual
> > > > > > > > > > > > > > existence
> > > > > > > > > > > > > > leads to
> > > > > > > > > > > > > > a
> > > > > > > > > > > > > > paradox.
> > > > > > > > > > > > > > The halting problem is universally used in
> > > > > > > > > > > > > > university
> > > > > > > > > > > > > > courses
> > > > > > > > > > > > > > on
> > > > > > > > > > > > > > Computer
> > > > > > > > > > > > > > Science to illustrate the limits of
> > > > > > > > > > > > > > computation.
> > > > > > > > > > > > > > Hehner
> > > > > > > > > > > > > > claims
> > > > > > > > > > > > > > the
> > > > > > > > > > > > > > halting
> > > > > > > > > > > > > > problem is misconceived......
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > It looks like what olcott now is claiming.
> > > > > > > > > > > > > > Am I
> > > > > > > > > > > > > > missing
> > > > > > > > > > > > > > something?
> > > > > > > > > > > > >
> > > > > > > > > > > > > The error in the article is the claim that an
> > > > > > > > > > > > > "inconsistent"
> > > > > > > > > > > > > specification
> > > > > > > > > > > > > is somehow invalid. But it is not.
> > > > > > > > > > > > >
> > > > > > > > > > > > > A problem is a request to find at least one
> > > > > > > > > > > > > thing
> > > > > > > > > > > > > that
> > > > > > > > > > > > > satisfies
> > > > > > > > > > > > > the
> > > > > > > > > > > > > requirements of the problem or to prove that
> > > > > > > > > > > > > no
> > > > > > > > > > > > > such
> > > > > > > > > > > > > thing
> > > > > > > > > > > > > can be
> > > > > > > > > > > > > found.
> > > > > > > > > > > > > The problem is well posed if for every thing
> > > > > > > > > > > > > it
> > > > > > > > > > > > > is
> > > > > > > > > > > > > possible
> > > > > > > > > > > > > to
> > > > > > > > > > > > > check
> > > > > > > > > > > > > whether it satisfies all requirements.
> > > > > > > > > > > > >
> > > > > > > > > > > > > The halting problem is solved: a proof that
> > > > > > > > > > > > > no
> > > > > > > > > > > > > Turing
> > > > > > > > > > > > > machine
> > > > > > > > > > > > > satisfies
> > > > > > > > > > > > > the requirements is known (and nothing else
> > > > > > > > > > > > > satisfies
> > > > > > > > > > > > > the
> > > > > > > > > > > > > requirement
> > > > > > > > > > > > > that it must be a Turing machine).
> > > > > > > > > > > > >
> > > > > > > > > > > > > It is a matter of opinion whether the usual
> > > > > > > > > > > > > presentation
> > > > > > > > > > > > > of
> > > > > > > > > > > > > the
> > > > > > > > > > > > > halting theorem is the best one. If one does
> > > > > > > > > > > > > not
> > > > > > > > > > > > > like
> > > > > > > > > > > > > the
> > > > > > > > > > > > > usual
> > > > > > > > > > > > > statement one may instead use:
> > > > > > > > > > > > >         For every universal Turing machine U
> > > > > > > > > > > > > and
> > > > > > > > > > > > > every
> > > > > > > > > > > > > Turing
> > > > > > > > > > > > > machine
> > > > > > > > > > > > > H
> > > > > > > > > > > > >         there is an input string S so that
> > > > > > > > > > > > >         either T(S) halts but H(S) does not
> > > > > > > > > > > > > accept
> > > > > > > > > > > > >         or T(S) does not halt but H(S)
> > > > > > > > > > > > > accepts.
> > > > > > > > > > > > >
> > > > > > > > > > > > > This formulation has the disadvantage that it
> > > > > > > > > > > > > uses
> > > > > > > > > > > > > the
> > > > > > > > > > > > > concept of
> > > > > > > > > > > > > "univesal Turing machine", and therefore
> > > > > > > > > > > > > depends
> > > > > > > > > > > > > on
> > > > > > > > > > > > > the
> > > > > > > > > > > > > existence
> > > > > > > > > > > > > of one.
> > > > > > > > > > > > >
> > > > > > > > > > > > > Mikko
> > > > > > > > > > > > >
> > > > > > > > > > > >
> > > > > > > > > > > > Thanks for the explanation.
> > > > > > > > > > > > It looked to me it is the statement of Halting
> > > > > > > > > > > > Problem
> > > > > > > > > > > > proved
> > > > > > > > > > > > neither
> > > > > > > > > > > > T nor F bugged these people (including olcott)..
> > > > > > > > > > > > There is also a status of proposition called
> > > > > > > > > > > > contingency,
> > > > > > > > > > > > https://en.wikipedia.org/wiki/Contingency_(philosophy)
> > > > > > > > > > >
> > > > > > > > > > > Ultimately all these things boil down to the fact
> > > > > > > > > > > that
> > > > > > > > > > > self-contradictory questions must be rejected as
> > > > > > > > > > > incorrect
> > > > > > > > > > > questions. Hehner's paper explains this the best:
> > > > > > > > > > > https://www.cs.toronto.edu/~hehner/OSS.pdf
> > > > > > > > > > >
> > > > > > > > > > > The key part that non-technical people can
> > > > > > > > > > > understand
> > > > > > > > > > > is
> > > > > > > > > > > Carol's question:
> > > > > > > > > > > Can Carol correctly answer “no” to this [yes/no]
> > > > > > > > > > > question?
> > > > > > > > > > >
> > > > > > > > > > > That question is self-contradictory when posed to
> > > > > > > > > > > Carol
> > > > > > > > > > > and has the correct answer of "no" when posed to
> > > > > > > > > > > anyone
> > > > > > > > > > > else.
> > > > > > > > > > >
> > > > > > > > > > > Carol's question actually originates from my own
> > > > > > > > > > > conversation:
> > > > > > > > > > >
> > > > > > > > > > > On 6/25/2004 6:30 PM, Daryl McCullough wrote:
> > > > > > > > > > > (USENET
> > > > > > > > > > > sci.logic)
> > > > > > > > > > >       > You ask someone (we'll call him "Jack")
> > > > > > > > > > > to
> > > > > > > > > > > give a
> > > > > > > > > > > truthful
> > > > > > > > > > >       > yes/no answer to the following question:
> > > > > > > > > > >       >
> > > > > > > > > > >       >  Will Jack's answer to this question be
> > > > > > > > > > > no?
> > > > > > > > > > >
> > > > > > > > > > > was addressed to me in 2004.
> > > > > > > > > > > Hehner had no way of knowing this I repeated this
> > > > > > > > > > > same question as Bill's question hundreds of
> > > > > > > > > > > times
> > > > > > > > > > > until I tracked down the original author.
> > > > > > > > > > >
> > > > > > > > > >
> > > > > > > > > > The HP is asking (equivalent) for A PROGRAM that
> > > > > > > > > > takes
> > > > > > > > > > another
> > > > > > > > > > program
> > > > > > > > > > as its argument and decides whether or not that
> > > > > > > > > > given
> > > > > > > > > > program
> > > > > > > > > > will terminate.
> > > > > > > > > >
> > > > > > > > > > The HP is not asking the evaluation of "HP Theorem"
> > > > > > > > > > (the
> > > > > > > > > > conclusion)
> > > > > > > > > > to be true or false!!!
> > > > > > > >
> > > > > > > > > The HP uses a counter-example D that does the
> > > > > > > > > opposite
> > > > > > > > > of whatever value that H returns, thus making the
> > > > > > > > > question
> > > > > > > > > Does D halt? a self-contradictory question for H.
> > > > > > > >
> > > > > > > > It seems you took it as:
> > > > > > > > Proposition P="A program that decides whether another
> > > > > > > > program
> > > > > > > > halts
> > > > > > > > or
> > > > > > > > not is undecidable".
> > > > > > > >
> > > > > > >
> > > > > > > I have gone over these details many many thousands of
> > > > > > > times
> > > > > > > since
> > > > > > > 2004.
> > > > > > > That actual question for H is this:
> > > > > > >
> > > > > > > "What correct Boolean value does H return when D is
> > > > > > > defined
> > > > > > > to do
> > > > > > > the
> > > > > > >      opposite of whatever value that H returns?"
> > > > > >
> > > > > > As you already have seen: The H would be stock in an
> > > > > > infinite
> > > > > > recursive
> > > > > > call. I.e. H is not implementable.
> > > > > >
> > > > >
> > > > > You mean "stuck" not "stock".
> > > > >
> > > > > https://github.com/plolcott/x86utm
> > > > > I spent 1.5 years making sure that H does not get stuck it
> > > > > has
> > > > > been
> > > > > fully operational code for several years now.
> > > > >
> > > > > > The result as know it that you deliberately fabricate D in
> > > > > > way
> > > > > > to
> > > > > > say
> > > > > > whatever you want to say, this is invalid.
> > > > > >
> > > > >
> > > > > https://github.com/plolcott/x86utm/blob/master/Halt7.c
> > > > > int D(int (*x)())
> > > > > {
> > > > >      int Halt_Status = H(x, x);
> > > > >      if (Halt_Status)
> > > > >        HERE: goto HERE;
> > > > >      return Halt_Status;
> > > > > }
> > > > >
> > > > > is on lines 935-941 of FULLY OPERATIONAL CODE
> > > > >
> > > >
> > > > You have been through this for a long time. I would suggest
> > > > reading something about quantum computing, then, you will
> > > > become expert soon (because you are a genius), not many people
> > > > reading by rote can disagree with you with those age old
> > > > theories.
> > >
> > > Thanks for the great compliment.
> > > My very limited understanding of quantum computing would seem to
> > > indicate that it still performs computations that are isomorphic
> > > to Turing machines yet performs these computations at theoretical
> > > maximum speeds. I am most certain of the TM equivalence part and
> > > least certain of the theoretical maximum speed part.
> >
> > There are already books teaching quantum programming (an several
> > books
> > I saw are cheap), it would not be difficult for you because you
> > had been good in dealing with symbols. You don't have to be
> > certain about the real quantum things, no one is certain about
> > quantum stuff.
> > Anyway, at least, you will have additional arsenal to support what
> > you claimed.
> >
> >
>
> 01 int D(ptr x)  // ptr is pointer to int function
> 02 {
> 03   int Halt_Status = H(x, x);
> 04   if (Halt_Status)
> 05     HERE: goto HERE;
> 06   return Halt_Status;
> 07 }
> 08
> 09 void main()
> 10 {
> 11   H(D,D);
> 12 }
>
> *Execution Trace*
> Line 11: main() invokes H(D,D);
>
> *keeps repeating* (unless aborted)
> Line 03: simulated D(D) invokes simulated H(D,D) that simulates D(D)
>
> *Simulation invariant*
> D correctly simulated by H cannot possibly reach past its own line
> 03.
>
> D correctly simulated by H cannot possibly reach its simulated final
> state in 1 to ∞ steps of correct simulation.
>
> I translated it into C so that it would be as simple as
> possible to see every single detail of exactly what is
> really going on. *People insist on denying reality anyway*

On 1/22/2024 9:59 PM, wij wrote:
> On Mon, 2024-01-22 at 21:29 -0600, olcott wrote:
>> On 1/22/2024 8:59 PM, wij wrote:
>>> On Mon, 2024-01-22 at 20:40 -0600, olcott wrote:
>>>> On 1/22/2024 8:27 PM, wij wrote:
>>>>> On Mon, 2024-01-22 at 20:20 -0600, olcott wrote:
>>>>>> On 1/22/2024 8:13 PM, wij wrote:
>>>>>>> On Mon, 2024-01-22 at 20:05 -0600, olcott wrote:
>>>>>>>> On 1/22/2024 7:44 PM, wij wrote:
>>>>>>>>> On Mon, 2024-01-22 at 19:19 -0600, olcott wrote:
>>>>>>>>>> On 1/22/2024 6:57 PM, wij wrote:
>>>>>>>>>>> On Mon, 2024-01-22 at 18:39 -0600, olcott wrote:
>>>>>>>>>>>> On 1/22/2024 6:09 PM, wij wrote:
>>>>>>>>>>>>> On Mon, 2024-01-22 at 10:28 +0200, Mikko wrote:
>>>>>>>>>>>>>> On 2024-01-21 19:22:22 +0000, wij said:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I just found an article about the Halting
>>>>>>>>>>>>>>> Problem.
>>>>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>>>>> The idea of a universal halting test seems
>>>>>>>>>>>>>>> reasonable,
>>>>>>>>>>>>>>> but
>>>>>>>>>>>>>>> cannot
>>>>>>>>>>>>>>> be
>>>>>>>>>>>>>>> for-
>>>>>>>>>>>>>>> malised as a consistent specification. It
>>>>>>>>>>>>>>> has
>>>>>>>>>>>>>>> no
>>>>>>>>>>>>>>> model
>>>>>>>>>>>>>>> and
>>>>>>>>>>>>>>> does
>>>>>>>>>>>>>>> not
>>>>>>>>>>>>>>> exist as
>>>>>>>>>>>>>>> a conceptual object. Assuming its
>>>>>>>>>>>>>>> conceptual
>>>>>>>>>>>>>>> existence
>>>>>>>>>>>>>>> leads to
>>>>>>>>>>>>>>> a
>>>>>>>>>>>>>>> paradox.
>>>>>>>>>>>>>>> The halting problem is universally used in
>>>>>>>>>>>>>>> university
>>>>>>>>>>>>>>> courses
>>>>>>>>>>>>>>> on
>>>>>>>>>>>>>>> Computer
>>>>>>>>>>>>>>> Science to illustrate the limits of
>>>>>>>>>>>>>>> computation.
>>>>>>>>>>>>>>> Hehner
>>>>>>>>>>>>>>> claims
>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>> halting
>>>>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It looks like what olcott now is claiming.
>>>>>>>>>>>>>>> Am I
>>>>>>>>>>>>>>> missing
>>>>>>>>>>>>>>> something?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The error in the article is the claim that an
>>>>>>>>>>>>>> "inconsistent"
>>>>>>>>>>>>>> specification
>>>>>>>>>>>>>> is somehow invalid. But it is not.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> A problem is a request to find at least one
>>>>>>>>>>>>>> thing
>>>>>>>>>>>>>> that
>>>>>>>>>>>>>> satisfies
>>>>>>>>>>>>>> the
>>>>>>>>>>>>>> requirements of the problem or to prove that
>>>>>>>>>>>>>> no
>>>>>>>>>>>>>> such
>>>>>>>>>>>>>> thing
>>>>>>>>>>>>>> can be
>>>>>>>>>>>>>> found.
>>>>>>>>>>>>>> The problem is well posed if for every thing
>>>>>>>>>>>>>> it
>>>>>>>>>>>>>> is
>>>>>>>>>>>>>> possible
>>>>>>>>>>>>>> to
>>>>>>>>>>>>>> check
>>>>>>>>>>>>>> whether it satisfies all requirements.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The halting problem is solved: a proof that
>>>>>>>>>>>>>> no
>>>>>>>>>>>>>> Turing
>>>>>>>>>>>>>> machine
>>>>>>>>>>>>>> satisfies
>>>>>>>>>>>>>> the requirements is known (and nothing else
>>>>>>>>>>>>>> satisfies
>>>>>>>>>>>>>> the
>>>>>>>>>>>>>> requirement
>>>>>>>>>>>>>> that it must be a Turing machine).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> It is a matter of opinion whether the usual
>>>>>>>>>>>>>> presentation
>>>>>>>>>>>>>> of
>>>>>>>>>>>>>> the
>>>>>>>>>>>>>> halting theorem is the best one. If one does
>>>>>>>>>>>>>> not
>>>>>>>>>>>>>> like
>>>>>>>>>>>>>> the
>>>>>>>>>>>>>> usual
>>>>>>>>>>>>>> statement one may instead use:
>>>>>>>>>>>>>>         For every universal Turing machine U
>>>>>>>>>>>>>> and
>>>>>>>>>>>>>> every
>>>>>>>>>>>>>> Turing
>>>>>>>>>>>>>> machine
>>>>>>>>>>>>>> H
>>>>>>>>>>>>>>         there is an input string S so that
>>>>>>>>>>>>>>         either T(S) halts but H(S) does not
>>>>>>>>>>>>>> accept
>>>>>>>>>>>>>>         or T(S) does not halt but H(S)
>>>>>>>>>>>>>> accepts.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> This formulation has the disadvantage that it
>>>>>>>>>>>>>> uses
>>>>>>>>>>>>>> the
>>>>>>>>>>>>>> concept of
>>>>>>>>>>>>>> "univesal Turing machine", and therefore
>>>>>>>>>>>>>> depends
>>>>>>>>>>>>>> on
>>>>>>>>>>>>>> the
>>>>>>>>>>>>>> existence
>>>>>>>>>>>>>> of one.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Mikko
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Thanks for the explanation.
>>>>>>>>>>>>> It looked to me it is the statement of Halting
>>>>>>>>>>>>> Problem
>>>>>>>>>>>>> proved
>>>>>>>>>>>>> neither
>>>>>>>>>>>>> T nor F bugged these people (including olcott).
>>>>>>>>>>>>> There is also a status of proposition called
>>>>>>>>>>>>> contingency,
>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Contingency_(philosophy)
>>>>>>>>>>>>
>>>>>>>>>>>> Ultimately all these things boil down to the fact
>>>>>>>>>>>> that
>>>>>>>>>>>> self-contradictory questions must be rejected as
>>>>>>>>>>>> incorrect
>>>>>>>>>>>> questions. Hehner's paper explains this the best:
>>>>>>>>>>>> https://www.cs.toronto.edu/~hehner/OSS.pdf
>>>>>>>>>>>>
>>>>>>>>>>>> The key part that non-technical people can
>>>>>>>>>>>> understand
>>>>>>>>>>>> is
>>>>>>>>>>>> Carol's question:
>>>>>>>>>>>> Can Carol correctly answer “no” to this [yes/no]
>>>>>>>>>>>> question?
>>>>>>>>>>>>
>>>>>>>>>>>> That question is self-contradictory when posed to
>>>>>>>>>>>> Carol
>>>>>>>>>>>> and has the correct answer of "no" when posed to
>>>>>>>>>>>> anyone
>>>>>>>>>>>> else.
>>>>>>>>>>>>
>>>>>>>>>>>> Carol's question actually originates from my own
>>>>>>>>>>>> conversation:
>>>>>>>>>>>>
>>>>>>>>>>>> On 6/25/2004 6:30 PM, Daryl McCullough wrote:
>>>>>>>>>>>> (USENET
>>>>>>>>>>>> sci.logic)
>>>>>>>>>>>>       > You ask someone (we'll call him "Jack")
>>>>>>>>>>>> to
>>>>>>>>>>>> give a
>>>>>>>>>>>> truthful
>>>>>>>>>>>>       > yes/no answer to the following question:
>>>>>>>>>>>>       >
>>>>>>>>>>>>       >  Will Jack's answer to this question be
>>>>>>>>>>>> no?
>>>>>>>>>>>>
>>>>>>>>>>>> was addressed to me in 2004.
>>>>>>>>>>>> Hehner had no way of knowing this I repeated this
>>>>>>>>>>>> same question as Bill's question hundreds of
>>>>>>>>>>>> times
>>>>>>>>>>>> until I tracked down the original author.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> The HP is asking (equivalent) for A PROGRAM that
>>>>>>>>>>> takes
>>>>>>>>>>> another
>>>>>>>>>>> program
>>>>>>>>>>> as its argument and decides whether or not that
>>>>>>>>>>> given
>>>>>>>>>>> program
>>>>>>>>>>> will terminate.
>>>>>>>>>>>
>>>>>>>>>>> The HP is not asking the evaluation of "HP Theorem"
>>>>>>>>>>> (the
>>>>>>>>>>> conclusion)
>>>>>>>>>>> to be true or false!!!
>>>>>>>>>
>>>>>>>>>> The HP uses a counter-example D that does the
>>>>>>>>>> opposite
>>>>>>>>>> of whatever value that H returns, thus making the
>>>>>>>>>> question
>>>>>>>>>> Does D halt? a self-contradictory question for H.
>>>>>>>>>
>>>>>>>>> It seems you took it as:
>>>>>>>>> Proposition P="A program that decides whether another
>>>>>>>>> program
>>>>>>>>> halts
>>>>>>>>> or
>>>>>>>>> not is undecidable".
>>>>>>>>>
>>>>>>>>
>>>>>>>> I have gone over these details many many thousands of
>>>>>>>> times
>>>>>>>> since
>>>>>>>> 2004.
>>>>>>>> That actual question for H is this:
>>>>>>>>
>>>>>>>> "What correct Boolean value does H return when D is
>>>>>>>> defined
>>>>>>>> to do
>>>>>>>> the
>>>>>>>>      opposite of whatever value that H returns?"
>>>>>>>
>>>>>>> As you already have seen: The H would be stock in an
>>>>>>> infinite
>>>>>>> recursive
>>>>>>> call. I.e. H is not implementable.
>>>>>>>
>>>>>>
>>>>>> You mean "stuck" not "stock".
>>>>>>
>>>>>> https://github.com/plolcott/x86utm
>>>>>> I spent 1.5 years making sure that H does not get stuck it
>>>>>> has
>>>>>> been
>>>>>> fully operational code for several years now.
>>>>>>
>>>>>>> The result as know it that you deliberately fabricate D in
>>>>>>> way
>>>>>>> to
>>>>>>> say
>>>>>>> whatever you want to say, this is invalid.
>>>>>>>
>>>>>>
>>>>>> https://github.com/plolcott/x86utm/blob/master/Halt7.c
>>>>>> int D(int (*x)())
>>>>>> {
>>>>>>      int Halt_Status = H(x, x);
>>>>>>      if (Halt_Status)
>>>>>>        HERE: goto HERE;
>>>>>>      return Halt_Status;
>>>>>> }
>>>>>>
>>>>>> is on lines 935-941 of FULLY OPERATIONAL CODE
>>>>>>
>>>>>
>>>>> You have been through this for a long time. I would suggest
>>>>> reading something about quantum computing, then, you will
>>>>> become expert soon (because you are a genius), not many people
>>>>> reading by rote can disagree with you with those age old
>>>>> theories.
>>>>
>>>> Thanks for the great compliment.
>>>> My very limited understanding of quantum computing would seem to
>>>> indicate that it still performs computations that are isomorphic
>>>> to Turing machines yet performs these computations at theoretical
>>>> maximum speeds. I am most certain of the TM equivalence part and
>>>> least certain of the theoretical maximum speed part.
>>>
>>> There are already books teaching quantum programming (an several
>>> books
>>> I saw are cheap), it would not be difficult for you because you
>>> had been good in dealing with symbols. You don't have to be
>>> certain about the real quantum things, no one is certain about
>>> quantum stuff.
>>> Anyway, at least, you will have additional arsenal to support what
>>> you claimed.
>>>
>>>
>>
>> 01 int D(ptr x)  // ptr is pointer to int function
>> 02 {
>> 03   int Halt_Status = H(x, x);
>> 04   if (Halt_Status)
>> 05     HERE: goto HERE;
>> 06   return Halt_Status;
>> 07 }
>> 08
>> 09 void main()
>> 10 {
>> 11   H(D,D);
>> 12 }
>>
>> *Execution Trace*
>> Line 11: main() invokes H(D,D);
>>
>> *keeps repeating* (unless aborted)
>> Line 03: simulated D(D) invokes simulated H(D,D) that simulates D(D)
>>
>> *Simulation invariant*
>> D correctly simulated by H cannot possibly reach past its own line
>> 03.
>>
>> D correctly simulated by H cannot possibly reach its simulated final
>> state in 1 to ∞ steps of correct simulation.
>>
>> I translated it into C so that it would be as simple as
>> possible to see every single detail of exactly what is
>> really going on. *People insist on denying reality anyway*
>
> This is right. But why you insist on something people can't see it?

On Mon, 2024-01-22 at 22:01 -0600, olcott wrote:
> On 1/22/2024 9:59 PM, wij wrote:
> > On Mon, 2024-01-22 at 21:29 -0600, olcott wrote:
> > > On 1/22/2024 8:59 PM, wij wrote:
> > > > On Mon, 2024-01-22 at 20:40 -0600, olcott wrote:
> > > > > On 1/22/2024 8:27 PM, wij wrote:
> > > > > > On Mon, 2024-01-22 at 20:20 -0600, olcott wrote:
> > > > > > > On 1/22/2024 8:13 PM, wij wrote:
> > > > > > > > On Mon, 2024-01-22 at 20:05 -0600, olcott wrote:
> > > > > > > > > On 1/22/2024 7:44 PM, wij wrote:
> > > > > > > > > > On Mon, 2024-01-22 at 19:19 -0600, olcott wrote:
> > > > > > > > > > > On 1/22/2024 6:57 PM, wij wrote:
> > > > > > > > > > > > On Mon, 2024-01-22 at 18:39 -0600, olcott
> > > > > > > > > > > > wrote:
> > > > > > > > > > > > > On 1/22/2024 6:09 PM, wij wrote:
> > > > > > > > > > > > > > On Mon, 2024-01-22 at 10:28 +0200, Mikko
> > > > > > > > > > > > > > wrote:
> > > > > > > > > > > > > > > On 2024-01-21 19:22:22 +0000, wij said:
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > I just found an article about the
> > > > > > > > > > > > > > > > Halting
> > > > > > > > > > > > > > > > Problem.
> > > > > > > > > > > > > > > > https://arxiv.org/pdf/1906.05340.pdf
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > In the conclusion section:
> > > > > > > > > > > > > > > > The idea of a universal halting test
> > > > > > > > > > > > > > > > seems
> > > > > > > > > > > > > > > > reasonable,
> > > > > > > > > > > > > > > > but
> > > > > > > > > > > > > > > > cannot
> > > > > > > > > > > > > > > > be
> > > > > > > > > > > > > > > > for-
> > > > > > > > > > > > > > > > malised as a consistent specification.
> > > > > > > > > > > > > > > > It
> > > > > > > > > > > > > > > > has
> > > > > > > > > > > > > > > > no
> > > > > > > > > > > > > > > > model
> > > > > > > > > > > > > > > > and
> > > > > > > > > > > > > > > > does
> > > > > > > > > > > > > > > > not
> > > > > > > > > > > > > > > > exist as
> > > > > > > > > > > > > > > > a conceptual object. Assuming its
> > > > > > > > > > > > > > > > conceptual
> > > > > > > > > > > > > > > > existence
> > > > > > > > > > > > > > > > leads to
> > > > > > > > > > > > > > > > a
> > > > > > > > > > > > > > > > paradox.
> > > > > > > > > > > > > > > > The halting problem is universally used
> > > > > > > > > > > > > > > > in
> > > > > > > > > > > > > > > > university
> > > > > > > > > > > > > > > > courses
> > > > > > > > > > > > > > > > on
> > > > > > > > > > > > > > > > Computer
> > > > > > > > > > > > > > > > Science to illustrate the limits of
> > > > > > > > > > > > > > > > computation.
> > > > > > > > > > > > > > > > Hehner
> > > > > > > > > > > > > > > > claims
> > > > > > > > > > > > > > > > the
> > > > > > > > > > > > > > > > halting
> > > > > > > > > > > > > > > > problem is misconceived......
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > It looks like what olcott now is
> > > > > > > > > > > > > > > > claiming.
> > > > > > > > > > > > > > > > Am I
> > > > > > > > > > > > > > > > missing
> > > > > > > > > > > > > > > > something?
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > The error in the article is the claim
> > > > > > > > > > > > > > > that an
> > > > > > > > > > > > > > > "inconsistent"
> > > > > > > > > > > > > > > specification
> > > > > > > > > > > > > > > is somehow invalid. But it is not.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > A problem is a request to find at least
> > > > > > > > > > > > > > > one
> > > > > > > > > > > > > > > thing
> > > > > > > > > > > > > > > that
> > > > > > > > > > > > > > > satisfies
> > > > > > > > > > > > > > > the
> > > > > > > > > > > > > > > requirements of the problem or to prove
> > > > > > > > > > > > > > > that
> > > > > > > > > > > > > > > no
> > > > > > > > > > > > > > > such
> > > > > > > > > > > > > > > thing
> > > > > > > > > > > > > > > can be
> > > > > > > > > > > > > > > found.
> > > > > > > > > > > > > > > The problem is well posed if for every
> > > > > > > > > > > > > > > thing
> > > > > > > > > > > > > > > it
> > > > > > > > > > > > > > > is
> > > > > > > > > > > > > > > possible
> > > > > > > > > > > > > > > to
> > > > > > > > > > > > > > > check
> > > > > > > > > > > > > > > whether it satisfies all requirements.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > The halting problem is solved: a proof
> > > > > > > > > > > > > > > that
> > > > > > > > > > > > > > > no
> > > > > > > > > > > > > > > Turing
> > > > > > > > > > > > > > > machine
> > > > > > > > > > > > > > > satisfies
> > > > > > > > > > > > > > > the requirements is known (and nothing
> > > > > > > > > > > > > > > else
> > > > > > > > > > > > > > > satisfies
> > > > > > > > > > > > > > > the
> > > > > > > > > > > > > > > requirement
> > > > > > > > > > > > > > > that it must be a Turing machine).
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > It is a matter of opinion whether the
> > > > > > > > > > > > > > > usual
> > > > > > > > > > > > > > > presentation
> > > > > > > > > > > > > > > of
> > > > > > > > > > > > > > > the
> > > > > > > > > > > > > > > halting theorem is the best one. If one
> > > > > > > > > > > > > > > does
> > > > > > > > > > > > > > > not
> > > > > > > > > > > > > > > like
> > > > > > > > > > > > > > > the
> > > > > > > > > > > > > > > usual
> > > > > > > > > > > > > > > statement one may instead use:
> > > > > > > > > > > > > > >          For every universal Turing
> > > > > > > > > > > > > > > machine U
> > > > > > > > > > > > > > > and
> > > > > > > > > > > > > > > every
> > > > > > > > > > > > > > > Turing
> > > > > > > > > > > > > > > machine
> > > > > > > > > > > > > > > H
> > > > > > > > > > > > > > >          there is an input string S so
> > > > > > > > > > > > > > > that
> > > > > > > > > > > > > > >          either T(S) halts but H(S) does
> > > > > > > > > > > > > > > not
> > > > > > > > > > > > > > > accept
> > > > > > > > > > > > > > >          or T(S) does not halt but H(S)
> > > > > > > > > > > > > > > accepts.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > This formulation has the disadvantage
> > > > > > > > > > > > > > > that it
> > > > > > > > > > > > > > > uses
> > > > > > > > > > > > > > > the
> > > > > > > > > > > > > > > concept of
> > > > > > > > > > > > > > > "univesal Turing machine", and therefore
> > > > > > > > > > > > > > > depends
> > > > > > > > > > > > > > > on
> > > > > > > > > > > > > > > the
> > > > > > > > > > > > > > > existence
> > > > > > > > > > > > > > > of one.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > Mikko
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Thanks for the explanation.
> > > > > > > > > > > > > > It looked to me it is the statement of
> > > > > > > > > > > > > > Halting
> > > > > > > > > > > > > > Problem
> > > > > > > > > > > > > > proved
> > > > > > > > > > > > > > neither
> > > > > > > > > > > > > > T nor F bugged these people (including
> > > > > > > > > > > > > > olcott).
> > > > > > > > > > > > > > There is also a status of proposition
> > > > > > > > > > > > > > called
> > > > > > > > > > > > > > contingency,
> > > > > > > > > > > > > > https://en.wikipedia.org/wiki/Contingency_(philosophy)
> > > > > > > > > > > > >
> > > > > > > > > > > > > Ultimately all these things boil down to the
> > > > > > > > > > > > > fact
> > > > > > > > > > > > > that
> > > > > > > > > > > > > self-contradictory questions must be rejected
> > > > > > > > > > > > > as
> > > > > > > > > > > > > incorrect
> > > > > > > > > > > > > questions. Hehner's paper explains this the
> > > > > > > > > > > > > best:
> > > > > > > > > > > > > https://www.cs.toronto.edu/~hehner/OSS.pdf
> > > > > > > > > > > > >
> > > > > > > > > > > > > The key part that non-technical people can
> > > > > > > > > > > > > understand
> > > > > > > > > > > > > is
> > > > > > > > > > > > > Carol's question:
> > > > > > > > > > > > > Can Carol correctly answer “no” to this
> > > > > > > > > > > > > [yes/no]
> > > > > > > > > > > > > question?
> > > > > > > > > > > > >
> > > > > > > > > > > > > That question is self-contradictory when
> > > > > > > > > > > > > posed to
> > > > > > > > > > > > > Carol
> > > > > > > > > > > > > and has the correct answer of "no" when posed
> > > > > > > > > > > > > to
> > > > > > > > > > > > > anyone
> > > > > > > > > > > > > else.
> > > > > > > > > > > > >
> > > > > > > > > > > > > Carol's question actually originates from my
> > > > > > > > > > > > > own
> > > > > > > > > > > > > conversation:
> > > > > > > > > > > > >
> > > > > > > > > > > > > On 6/25/2004 6:30 PM, Daryl McCullough wrote:
> > > > > > > > > > > > > (USENET
> > > > > > > > > > > > > sci.logic)
> > > > > > > > > > > > >        > You ask someone (we'll call him
> > > > > > > > > > > > > "Jack")
> > > > > > > > > > > > > to
> > > > > > > > > > > > > give a
> > > > > > > > > > > > > truthful
> > > > > > > > > > > > >        > yes/no answer to the following
> > > > > > > > > > > > > question:
> > > > > > > > > > > > >        >
> > > > > > > > > > > > >        >  Will Jack's answer to this question
> > > > > > > > > > > > > be
> > > > > > > > > > > > > no?
> > > > > > > > > > > > >
> > > > > > > > > > > > > was addressed to me in 2004.
> > > > > > > > > > > > > Hehner had no way of knowing this I repeated
> > > > > > > > > > > > > this
> > > > > > > > > > > > > same question as Bill's question hundreds of
> > > > > > > > > > > > > times
> > > > > > > > > > > > > until I tracked down the original author.
> > > > > > > > > > > > >
> > > > > > > > > > > >
> > > > > > > > > > > > The HP is asking (equivalent) for A PROGRAM
> > > > > > > > > > > > that
> > > > > > > > > > > > takes
> > > > > > > > > > > > another
> > > > > > > > > > > > program
> > > > > > > > > > > > as its argument and decides whether or not that
> > > > > > > > > > > > given
> > > > > > > > > > > > program
> > > > > > > > > > > > will terminate.
> > > > > > > > > > > >
> > > > > > > > > > > > The HP is not asking the evaluation of "HP
> > > > > > > > > > > > Theorem"
> > > > > > > > > > > > (the
> > > > > > > > > > > > conclusion)
> > > > > > > > > > > > to be true or false!!!
> > > > > > > > > >
> > > > > > > > > > > The HP uses a counter-example D that does the
> > > > > > > > > > > opposite
> > > > > > > > > > > of whatever value that H returns, thus making the
> > > > > > > > > > > question
> > > > > > > > > > > Does D halt? a self-contradictory question for H.
> > > > > > > > > >
> > > > > > > > > > It seems you took it as:
> > > > > > > > > > Proposition P="A program that decides whether
> > > > > > > > > > another
> > > > > > > > > > program
> > > > > > > > > > halts
> > > > > > > > > > or
> > > > > > > > > > not is undecidable".
> > > > > > > > > >
> > > > > > > > >
> > > > > > > > > I have gone over these details many many thousands of
> > > > > > > > > times
> > > > > > > > > since
> > > > > > > > > 2004.
> > > > > > > > > That actual question for H is this:
> > > > > > > > >
> > > > > > > > > "What correct Boolean value does H return when D is
> > > > > > > > > defined
> > > > > > > > > to do
> > > > > > > > > the
> > > > > > > > >       opposite of whatever value that H returns?"
> > > > > > > >
> > > > > > > > As you already have seen: The H would be stock in an
> > > > > > > > infinite
> > > > > > > > recursive
> > > > > > > > call. I.e. H is not implementable.
> > > > > > > >
> > > > > > >
> > > > > > > You mean "stuck" not "stock".
> > > > > > >
> > > > > > > https://github.com/plolcott/x86utm
> > > > > > > I spent 1.5 years making sure that H does not get stuck
> > > > > > > it
> > > > > > > has
> > > > > > > been
> > > > > > > fully operational code for several years now.
> > > > > > >
> > > > > > > > The result as know it that you deliberately fabricate D
> > > > > > > > in
> > > > > > > > way
> > > > > > > > to
> > > > > > > > say
> > > > > > > > whatever you want to say, this is invalid.
> > > > > > > >
> > > > > > >
> > > > > > > https://github.com/plolcott/x86utm/blob/master/Halt7.c
> > > > > > > int D(int (*x)())
> > > > > > > {
> > > > > > >       int Halt_Status = H(x, x);
> > > > > > >       if (Halt_Status)
> > > > > > >         HERE: goto HERE;
> > > > > > >       return Halt_Status;
> > > > > > > }
> > > > > > >
> > > > > > > is on lines 935-941 of FULLY OPERATIONAL CODE
> > > > > > >
> > > > > >
> > > > > > You have been through this for a long time. I would suggest
> > > > > > reading something about quantum computing, then, you will
> > > > > > become expert soon (because you are a genius), not many
> > > > > > people
> > > > > > reading by rote can disagree with you with those age old
> > > > > > theories.
> > > > >
> > > > > Thanks for the great compliment.
> > > > > My very limited understanding of quantum computing would seem
> > > > > to
> > > > > indicate that it still performs computations that are
> > > > > isomorphic
> > > > > to Turing machines yet performs these computations at
> > > > > theoretical
> > > > > maximum speeds. I am most certain of the TM equivalence part
> > > > > and
> > > > > least certain of the theoretical maximum speed part.
> > > >
> > > > There are already books teaching quantum programming (an
> > > > several
> > > > books
> > > > I saw are cheap), it would not be difficult for you because you
> > > > had been good in dealing with symbols. You don't have to be
> > > > certain about the real quantum things, no one is certain about
> > > > quantum stuff.
> > > > Anyway, at least, you will have additional arsenal to support
> > > > what
> > > > you claimed.
> > > >
> > > >
> > >
> > > 01 int D(ptr x)  // ptr is pointer to int function
> > > 02 {
> > > 03   int Halt_Status = H(x, x);
> > > 04   if (Halt_Status)
> > > 05     HERE: goto HERE;
> > > 06   return Halt_Status;
> > > 07 }
> > > 08
> > > 09 void main()
> > > 10 {
> > > 11   H(D,D);
> > > 12 }
> > >
> > > *Execution Trace*
> > > Line 11: main() invokes H(D,D);
> > >
> > > *keeps repeating* (unless aborted)
> > > Line 03: simulated D(D) invokes simulated H(D,D) that simulates
> > > D(D)
> > >
> > > *Simulation invariant*
> > > D correctly simulated by H cannot possibly reach past its own
> > > line
> > > 03.
> > >
> > > D correctly simulated by H cannot possibly reach its simulated
> > > final
> > > state in 1 to ∞ steps of correct simulation.
> > >
> > > I translated it into C so that it would be as simple as
> > > possible to see every single detail of exactly what is
> > > really going on. *People insist on denying reality anyway*
> >
> > This is right. But why you insist on something people can't see it?
>
> It does seem to solve the halting problem correctly.
> People don't see it only because they care about disagreement
> much more than they care about truth.

On 1/22/24 11:01 PM, olcott wrote:
> On 1/22/2024 9:59 PM, wij wrote:
>> On Mon, 2024-01-22 at 21:29 -0600, olcott wrote:
>>> On 1/22/2024 8:59 PM, wij wrote:
>>>> On Mon, 2024-01-22 at 20:40 -0600, olcott wrote:
>>>>> On 1/22/2024 8:27 PM, wij wrote:
>>>>>> On Mon, 2024-01-22 at 20:20 -0600, olcott wrote:
>>>>>>> On 1/22/2024 8:13 PM, wij wrote:
>>>>>>>> On Mon, 2024-01-22 at 20:05 -0600, olcott wrote:
>>>>>>>>> On 1/22/2024 7:44 PM, wij wrote:
>>>>>>>>>> On Mon, 2024-01-22 at 19:19 -0600, olcott wrote:
>>>>>>>>>>> On 1/22/2024 6:57 PM, wij wrote:
>>>>>>>>>>>> On Mon, 2024-01-22 at 18:39 -0600, olcott wrote:
>>>>>>>>>>>>> On 1/22/2024 6:09 PM, wij wrote:
>>>>>>>>>>>>>> On Mon, 2024-01-22 at 10:28 +0200, Mikko wrote:
>>>>>>>>>>>>>>> On 2024-01-21 19:22:22 +0000, wij said:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I just found an article about the Halting
>>>>>>>>>>>>>>>> Problem.
>>>>>>>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> In the conclusion section:
>>>>>>>>>>>>>>>> The idea of a universal halting test seems
>>>>>>>>>>>>>>>> reasonable,
>>>>>>>>>>>>>>>> but
>>>>>>>>>>>>>>>> cannot
>>>>>>>>>>>>>>>> be
>>>>>>>>>>>>>>>> for-
>>>>>>>>>>>>>>>> malised as a consistent specification. It
>>>>>>>>>>>>>>>> has
>>>>>>>>>>>>>>>> no
>>>>>>>>>>>>>>>> model
>>>>>>>>>>>>>>>> and
>>>>>>>>>>>>>>>> does
>>>>>>>>>>>>>>>> not
>>>>>>>>>>>>>>>> exist as
>>>>>>>>>>>>>>>> a conceptual object. Assuming its
>>>>>>>>>>>>>>>> conceptual
>>>>>>>>>>>>>>>> existence
>>>>>>>>>>>>>>>> leads to
>>>>>>>>>>>>>>>> a
>>>>>>>>>>>>>>>> paradox.
>>>>>>>>>>>>>>>> The halting problem is universally used in
>>>>>>>>>>>>>>>> university
>>>>>>>>>>>>>>>> courses
>>>>>>>>>>>>>>>> on
>>>>>>>>>>>>>>>> Computer
>>>>>>>>>>>>>>>> Science to illustrate the limits of
>>>>>>>>>>>>>>>> computation.
>>>>>>>>>>>>>>>> Hehner
>>>>>>>>>>>>>>>> claims
>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>> halting
>>>>>>>>>>>>>>>> problem is misconceived......
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> It looks like what olcott now is claiming.
>>>>>>>>>>>>>>>> Am I
>>>>>>>>>>>>>>>> missing
>>>>>>>>>>>>>>>> something?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The error in the article is the claim that an
>>>>>>>>>>>>>>> "inconsistent"
>>>>>>>>>>>>>>> specification
>>>>>>>>>>>>>>> is somehow invalid. But it is not.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> A problem is a request to find at least one
>>>>>>>>>>>>>>> thing
>>>>>>>>>>>>>>> that
>>>>>>>>>>>>>>> satisfies
>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>> requirements of the problem or to prove that
>>>>>>>>>>>>>>> no
>>>>>>>>>>>>>>> such
>>>>>>>>>>>>>>> thing
>>>>>>>>>>>>>>> can be
>>>>>>>>>>>>>>> found.
>>>>>>>>>>>>>>> The problem is well posed if for every thing
>>>>>>>>>>>>>>> it
>>>>>>>>>>>>>>> is
>>>>>>>>>>>>>>> possible
>>>>>>>>>>>>>>> to
>>>>>>>>>>>>>>> check
>>>>>>>>>>>>>>> whether it satisfies all requirements.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The halting problem is solved: a proof that
>>>>>>>>>>>>>>> no
>>>>>>>>>>>>>>> Turing
>>>>>>>>>>>>>>> machine
>>>>>>>>>>>>>>> satisfies
>>>>>>>>>>>>>>> the requirements is known (and nothing else
>>>>>>>>>>>>>>> satisfies
>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>> requirement
>>>>>>>>>>>>>>> that it must be a Turing machine).
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It is a matter of opinion whether the usual
>>>>>>>>>>>>>>> presentation
>>>>>>>>>>>>>>> of
>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>> halting theorem is the best one. If one does
>>>>>>>>>>>>>>> not
>>>>>>>>>>>>>>> like
>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>> usual
>>>>>>>>>>>>>>> statement one may instead use:
>>>>>>>>>>>>>>>          For every universal Turing machine U
>>>>>>>>>>>>>>> and
>>>>>>>>>>>>>>> every
>>>>>>>>>>>>>>> Turing
>>>>>>>>>>>>>>> machine
>>>>>>>>>>>>>>> H
>>>>>>>>>>>>>>>          there is an input string S so that
>>>>>>>>>>>>>>>          either T(S) halts but H(S) does not
>>>>>>>>>>>>>>> accept
>>>>>>>>>>>>>>>          or T(S) does not halt but H(S)
>>>>>>>>>>>>>>> accepts.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> This formulation has the disadvantage that it
>>>>>>>>>>>>>>> uses
>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>> concept of
>>>>>>>>>>>>>>> "univesal Turing machine", and therefore
>>>>>>>>>>>>>>> depends
>>>>>>>>>>>>>>> on
>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>> existence
>>>>>>>>>>>>>>> of one.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Mikko
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Thanks for the explanation.
>>>>>>>>>>>>>> It looked to me it is the statement of Halting
>>>>>>>>>>>>>> Problem
>>>>>>>>>>>>>> proved
>>>>>>>>>>>>>> neither
>>>>>>>>>>>>>> T nor F bugged these people (including olcott).
>>>>>>>>>>>>>> There is also a status of proposition called
>>>>>>>>>>>>>> contingency,
>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Contingency_(philosophy)
>>>>>>>>>>>>>
>>>>>>>>>>>>> Ultimately all these things boil down to the fact
>>>>>>>>>>>>> that
>>>>>>>>>>>>> self-contradictory questions must be rejected as
>>>>>>>>>>>>> incorrect
>>>>>>>>>>>>> questions. Hehner's paper explains this the best:
>>>>>>>>>>>>> https://www.cs.toronto.edu/~hehner/OSS.pdf
>>>>>>>>>>>>>
>>>>>>>>>>>>> The key part that non-technical people can
>>>>>>>>>>>>> understand
>>>>>>>>>>>>> is
>>>>>>>>>>>>> Carol's question:
>>>>>>>>>>>>> Can Carol correctly answer “no” to this [yes/no]
>>>>>>>>>>>>> question?
>>>>>>>>>>>>>
>>>>>>>>>>>>> That question is self-contradictory when posed to
>>>>>>>>>>>>> Carol
>>>>>>>>>>>>> and has the correct answer of "no" when posed to
>>>>>>>>>>>>> anyone
>>>>>>>>>>>>> else.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Carol's question actually originates from my own
>>>>>>>>>>>>> conversation:
>>>>>>>>>>>>>
>>>>>>>>>>>>> On 6/25/2004 6:30 PM, Daryl McCullough wrote:
>>>>>>>>>>>>> (USENET
>>>>>>>>>>>>> sci.logic)
>>>>>>>>>>>>>        > You ask someone (we'll call him "Jack")
>>>>>>>>>>>>> to
>>>>>>>>>>>>> give a
>>>>>>>>>>>>> truthful
>>>>>>>>>>>>>        > yes/no answer to the following question:
>>>>>>>>>>>>>        >
>>>>>>>>>>>>>        >  Will Jack's answer to this question be
>>>>>>>>>>>>> no?
>>>>>>>>>>>>>
>>>>>>>>>>>>> was addressed to me in 2004.
>>>>>>>>>>>>> Hehner had no way of knowing this I repeated this
>>>>>>>>>>>>> same question as Bill's question hundreds of
>>>>>>>>>>>>> times
>>>>>>>>>>>>> until I tracked down the original author.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> The HP is asking (equivalent) for A PROGRAM that
>>>>>>>>>>>> takes
>>>>>>>>>>>> another
>>>>>>>>>>>> program
>>>>>>>>>>>> as its argument and decides whether or not that
>>>>>>>>>>>> given
>>>>>>>>>>>> program
>>>>>>>>>>>> will terminate.
>>>>>>>>>>>>
>>>>>>>>>>>> The HP is not asking the evaluation of "HP Theorem"
>>>>>>>>>>>> (the
>>>>>>>>>>>> conclusion)
>>>>>>>>>>>> to be true or false!!!
>>>>>>>>>>
>>>>>>>>>>> The HP uses a counter-example D that does the
>>>>>>>>>>> opposite
>>>>>>>>>>> of whatever value that H returns, thus making the
>>>>>>>>>>> question
>>>>>>>>>>> Does D halt? a self-contradictory question for H.
>>>>>>>>>>
>>>>>>>>>> It seems you took it as:
>>>>>>>>>> Proposition P="A program that decides whether another
>>>>>>>>>> program
>>>>>>>>>> halts
>>>>>>>>>> or
>>>>>>>>>> not is undecidable".
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> I have gone over these details many many thousands of
>>>>>>>>> times
>>>>>>>>> since
>>>>>>>>> 2004.
>>>>>>>>> That actual question for H is this:
>>>>>>>>>
>>>>>>>>> "What correct Boolean value does H return when D is
>>>>>>>>> defined
>>>>>>>>> to do
>>>>>>>>> the
>>>>>>>>>       opposite of whatever value that H returns?"
>>>>>>>>
>>>>>>>> As you already have seen: The H would be stock in an
>>>>>>>> infinite
>>>>>>>> recursive
>>>>>>>> call. I.e. H is not implementable.
>>>>>>>>
>>>>>>>
>>>>>>> You mean "stuck" not "stock".
>>>>>>>
>>>>>>> https://github.com/plolcott/x86utm
>>>>>>> I spent 1.5 years making sure that H does not get stuck it
>>>>>>> has
>>>>>>> been
>>>>>>> fully operational code for several years now.
>>>>>>>
>>>>>>>> The result as know it that you deliberately fabricate D in
>>>>>>>> way
>>>>>>>> to
>>>>>>>> say
>>>>>>>> whatever you want to say, this is invalid.
>>>>>>>>
>>>>>>>
>>>>>>> https://github.com/plolcott/x86utm/blob/master/Halt7.c
>>>>>>> int D(int (*x)())
>>>>>>> {
>>>>>>>       int Halt_Status = H(x, x);
>>>>>>>       if (Halt_Status)
>>>>>>>         HERE: goto HERE;
>>>>>>>       return Halt_Status;
>>>>>>> }
>>>>>>>
>>>>>>> is on lines 935-941 of FULLY OPERATIONAL CODE
>>>>>>>
>>>>>>
>>>>>> You have been through this for a long time. I would suggest
>>>>>> reading something about quantum computing, then, you will
>>>>>> become expert soon (because you are a genius), not many people
>>>>>> reading by rote can disagree with you with those age old
>>>>>> theories.
>>>>>
>>>>> Thanks for the great compliment.
>>>>> My very limited understanding of quantum computing would seem to
>>>>> indicate that it still performs computations that are isomorphic
>>>>> to Turing machines yet performs these computations at theoretical
>>>>> maximum speeds. I am most certain of the TM equivalence part and
>>>>> least certain of the theoretical maximum speed part.
>>>>
>>>> There are already books teaching quantum programming (an several
>>>> books
>>>> I saw are cheap), it would not be difficult for you because you
>>>> had been good in dealing with symbols. You don't have to be
>>>> certain about the real quantum things, no one is certain about
>>>> quantum stuff.
>>>> Anyway, at least, you will have additional arsenal to support what
>>>> you claimed.
>>>>
>>>>
>>>
>>> 01 int D(ptr x)  // ptr is pointer to int function
>>> 02 {
>>> 03   int Halt_Status = H(x, x);
>>> 04   if (Halt_Status)
>>> 05     HERE: goto HERE;
>>> 06   return Halt_Status;
>>> 07 }
>>> 08
>>> 09 void main()
>>> 10 {
>>> 11   H(D,D);
>>> 12 }
>>>
>>> *Execution Trace*
>>> Line 11: main() invokes H(D,D);
>>>
>>> *keeps repeating* (unless aborted)
>>> Line 03: simulated D(D) invokes simulated H(D,D) that simulates D(D)
>>>
>>> *Simulation invariant*
>>> D correctly simulated by H cannot possibly reach past its own line
>>> 03.
>>>
>>> D correctly simulated by H cannot possibly reach its simulated final
>>> state in 1 to ∞ steps of correct simulation.
>>>
>>> I translated it into C so that it would be as simple as
>>> possible to see every single detail of exactly what is
>>> really going on. *People insist on denying reality anyway*
>>
>> This is right. But why you insist on something people can't see it?
>
> It does seem to solve the halting problem correctly.
> People don't see it only because they care about disagreement
> much more than they care about truth.
>

On 1/22/24 10:58 PM, olcott wrote:
> On 1/22/2024 9:45 PM, Richard Damon wrote:
>> On 1/22/24 9:05 PM, olcott wrote:
>>> On 1/22/2024 7:44 PM, wij wrote:
>>>> On Mon, 2024-01-22 at 19:19 -0600, olcott wrote:
>>>>> On 1/22/2024 6:57 PM, wij wrote:
>>>>>> On Mon, 2024-01-22 at 18:39 -0600, olcott wrote:
>>>>>>> On 1/22/2024 6:09 PM, wij wrote:
>>>>>>>> On Mon, 2024-01-22 at 10:28 +0200, Mikko wrote:
>>>>>>>>> On 2024-01-21 19:22:22 +0000, wij said:
>>>>>>>>>
>>>>>>>>>> I just found an article about the Halting Problem.
>>>>>>>>>> https://arxiv.org/pdf/1906.05340.pdf
>>>>>>>>>>
>>>>>>>>>> In the conclusion section:
>>>>>>>>>> The idea of a universal halting test seems reasonable, but
>>>>>>>>>> cannot
>>>>>>>>>> be
>>>>>>>>>> for-
>>>>>>>>>> malised as a consistent specification. It has no model and
>>>>>>>>>> does
>>>>>>>>>> not
>>>>>>>>>> exist as
>>>>>>>>>> a conceptual object. Assuming its conceptual existence
>>>>>>>>>> leads to
>>>>>>>>>> a
>>>>>>>>>> paradox.
>>>>>>>>>> The halting problem is universally used in university
>>>>>>>>>> courses
>>>>>>>>>> on
>>>>>>>>>> Computer
>>>>>>>>>> Science to illustrate the limits of computation. Hehner
>>>>>>>>>> claims
>>>>>>>>>> the
>>>>>>>>>> halting
>>>>>>>>>> problem is misconceived......
>>>>>>>>>>
>>>>>>>>>> It looks like what olcott now is claiming. Am I missing
>>>>>>>>>> something?
>>>>>>>>>
>>>>>>>>> The error in the article is the claim that an "inconsistent"
>>>>>>>>> specification
>>>>>>>>> is somehow invalid. But it is not.
>>>>>>>>>
>>>>>>>>> A problem is a request to find at least one thing that
>>>>>>>>> satisfies
>>>>>>>>> the
>>>>>>>>> requirements of the problem or to prove that no such thing
>>>>>>>>> can be
>>>>>>>>> found.
>>>>>>>>> The problem is well posed if for every thing it is possible
>>>>>>>>> to
>>>>>>>>> check
>>>>>>>>> whether it satisfies all requirements.
>>>>>>>>>
>>>>>>>>> The halting problem is solved: a proof that no Turing machine
>>>>>>>>> satisfies
>>>>>>>>> the requirements is known (and nothing else satisfies the
>>>>>>>>> requirement
>>>>>>>>> that it must be a Turing machine).
>>>>>>>>>
>>>>>>>>> It is a matter of opinion whether the usual presentation of
>>>>>>>>> the
>>>>>>>>> halting theorem is the best one. If one does not like the
>>>>>>>>> usual
>>>>>>>>> statement one may instead use:
>>>>>>>>>      For every universal Turing machine U and every Turing
>>>>>>>>> machine
>>>>>>>>> H
>>>>>>>>>      there is an input string S so that
>>>>>>>>>      either T(S) halts but H(S) does not accept
>>>>>>>>>      or T(S) does not halt but H(S) accepts.
>>>>>>>>>
>>>>>>>>> This formulation has the disadvantage that it uses the
>>>>>>>>> concept of
>>>>>>>>> "univesal Turing machine", and therefore depends on the
>>>>>>>>> existence
>>>>>>>>> of one.
>>>>>>>>>
>>>>>>>>> Mikko
>>>>>>>>>
>>>>>>>>
>>>>>>>> Thanks for the explanation.
>>>>>>>> It looked to me it is the statement of Halting Problem proved
>>>>>>>> neither
>>>>>>>> T nor F bugged these people (including olcott).
>>>>>>>> There is also a status of proposition called contingency,
>>>>>>>> https://en.wikipedia.org/wiki/Contingency_(philosophy)
>>>>>>>
>>>>>>> Ultimately all these things boil down to the fact that
>>>>>>> self-contradictory questions must be rejected as incorrect
>>>>>>> questions. Hehner's paper explains this the best:
>>>>>>> https://www.cs.toronto.edu/~hehner/OSS.pdf
>>>>>>>
>>>>>>> The key part that non-technical people can understand is
>>>>>>> Carol's question:
>>>>>>> Can Carol correctly answer “no” to this [yes/no] question?
>>>>>>>
>>>>>>> That question is self-contradictory when posed to Carol
>>>>>>> and has the correct answer of "no" when posed to anyone else.
>>>>>>>
>>>>>>> Carol's question actually originates from my own conversation:
>>>>>>>
>>>>>>> On 6/25/2004 6:30 PM, Daryl McCullough wrote:  (USENET sci.logic)
>>>>>>>    > You ask someone (we'll call him "Jack") to give a truthful
>>>>>>>    > yes/no answer to the following question:
>>>>>>>    >
>>>>>>>    >  Will Jack's answer to this question be no?
>>>>>>>
>>>>>>> was addressed to me in 2004.
>>>>>>> Hehner had no way of knowing this I repeated this
>>>>>>> same question as Bill's question hundreds of times
>>>>>>> until I tracked down the original author.
>>>>>>>
>>>>>>
>>>>>> The HP is asking (equivalent) for A PROGRAM that takes another
>>>>>> program
>>>>>> as its argument and decides whether or not that given program
>>>>>> will terminate.
>>>>>>
>>>>>> The HP is not asking the evaluation of "HP Theorem" (the
>>>>>> conclusion)
>>>>>> to be true or false!!!
>>>>
>>>>> The HP uses a counter-example D that does the opposite
>>>>> of whatever value that H returns, thus making the question
>>>>> Does D halt? a self-contradictory question for H.
>>>>
>>>> It seems you took it as:
>>>> Proposition P="A program that decides whether another program halts or
>>>> not is undecidable".
>>>>
>>>
>>> I have gone over these details many many thousands of times since 2004.
>>> That actual question for H is this:
>>>
>>> "What correct Boolean value does H return when D is defined to do the
>>>   opposite of whatever value that H returns?"
>>
>> So, you are just admitting that you have been working on a false
>> premsis for 20 years
>
> I merely put the full context of the question posed to H directly in the
> question the same way that immibis did for the Barber Paradox.

But it isn't the same question.

The actual question is INDEPENDENT of who you ask it to.

As you have pointed out, making the question refer to who you ask it to
can make it an invalid question.

>
> The question superficially seems to be: Does the barber shave himself?
> This is NOT the actual question. immibis poses the actual question
> with its full context directly in the question.

Right, because that question doesn't specify which Barber you are
talking about.

On 1/22/24 10:53 PM, olcott wrote:
> On 1/22/2024 9:43 PM, Richard Damon wrote:
>> On 1/22/24 1:59 PM, olcott wrote:
>>> On 1/22/2024 6:23 AM, Richard Damon wrote:
>>>> On 1/21/24 11:37 PM, olcott wrote:
>>>>> On 1/21/2024 10:06 PM, Richard Damon wrote:
>>>>>> On 1/21/24 11:01 PM, olcott wrote:
>>>>>>> On 1/21/2024 9:39 PM, Richard Damon wrote:
>>>>>>>> On 1/21/24 10:30 PM, olcott wrote:
>>>>>>>>> On 1/21/2024 9:28 PM, Richard Damon wrote:
>>>>>>>>>> On 1/21/24 10:22 PM, olcott wrote:
>>>>>>>>>>> On 1/21/2024 9:19 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/21/24 9:55 PM, olcott wrote:
>>>>>>>>>>>>> On 1/21/2024 8:28 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/21/24 9:18 PM, olcott wrote:
>>>>>>>>>>>>>>> On 1/21/2024 8:07 PM, immibis wrote:
>>>>>>>>>>>>>>>> On 1/22/24 02:43, olcott wrote:
>>>>>>>>>>>>>>>>> On 1/21/2024 7:38 PM, immibis wrote:
>>>>>>>>>>>>>>>>>> On 1/22/24 02:04, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 1/21/2024 6:58 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 1/21/24 7:54 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 1/21/2024 6:50 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>> On 1/22/24 01:37, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 1/21/2024 6:27 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 1/22/24 01:13, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 1/21/2024 6:04 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 1/21/24 23:56, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> Tarski didn't understand that the correct
>>>>>>>>>>>>>>>>>>>>>>>>>>> evaluation of the Liar Paradox requires
>>>>>>>>>>>>>>>>>>>>>>>>>>> an infinite cycle in the directed graph
>>>>>>>>>>>>>>>>>>>>>>>>>>> of its evaluation sequence.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand the difference between
>>>>>>>>>>>>>>>>>>>>>>>>>> diagonalization and infinite recursion.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Do you think the real numbers are countable?
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Diagonalization is a process by which we know that
>>>>>>>>>>>>>>>>>>>>>>>>> x is unprovable in L that makes sure to ignore the
>>>>>>>>>>>>>>>>>>>>>>>>> reason why x is unprovable in L.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> So are the real numbers countable? Isn't
>>>>>>>>>>>>>>>>>>>>>>>> Cantor's number pathologically self-referential,
>>>>>>>>>>>>>>>>>>>>>>>> making his argument invalid?
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> unify_with_occurs_check(LP, not(true(LP))).
>>>>>>>>>>>>>>>>>>>>>>>>> correctly determines that LP is unprovable
>>>>>>>>>>>>>>>>>>>>>>>>> BECAUSE the directed graph of its evaluation
>>>>>>>>>>>>>>>>>>>>>>>>> sequence contains an infinite cycle.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Provability doesn't give a flying fuck about
>>>>>>>>>>>>>>>>>>>>>>>> evaluation cycles, whatever those are.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> It sure does in Prolog.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Then Prolog is wrong.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> That Prolog pays attention to details that other
>>>>>>>>>>>>>>>>>>>>> systems
>>>>>>>>>>>>>>>>>>>>> ignore make it wrong is like saying that ignorance is
>>>>>>>>>>>>>>>>>>>>> knowledge and knowledge is incorrect.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Prolog handles SIMPLE logic system and problems. It
>>>>>>>>>>>>>>>>>>>> rejects ALL cycles, even if they don't cause logical
>>>>>>>>>>>>>>>>>>>> issues (as I understand it)
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> As you fail to understand it.
>>>>>>>>>>>>>>>>>>> I took 18 months creating Minimal Type Theory that
>>>>>>>>>>>>>>>>>>> automatically generated the directed graph of the
>>>>>>>>>>>>>>>>>>> evaluation sequence of any of its expressions.
>>>>>>>>>>>>>>>>>>> It sued syntax similar to FOL yet is as expressive
>>>>>>>>>>>>>>>>>>> as HOL. I encode a SOL expression in MTT.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> You are rebutting the infinite formulas such as
>>>>>>>>>>>>>>>>>> ¬True(¬True(¬True(...)))
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> But this is already in the standard theory. Infinite
>>>>>>>>>>>>>>>>>> formulas such as ¬True(¬True(¬True(...))) are already
>>>>>>>>>>>>>>>>>> not valid.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Olcott doesn't understand that diagonalization is not
>>>>>>>>>>>>>>>>>> the same as infinite recursion.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Finally a reply that is not nonsense.
>>>>>>>>>>>>>>>>> Diagonalization only knows that for some reason or another
>>>>>>>>>>>>>>>>> x is unprovable in L.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I dispute the notion of "reasons". It's just a fact that
>>>>>>>>>>>>>>>> it's unprovable. There are different ways to find out
>>>>>>>>>>>>>>>> that it's unprovable, or different ways to understand
>>>>>>>>>>>>>>>> that it's unprovable, but not reasons why it's unprovable.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> If the reason that x is unprovable in L is that x
>>>>>>>>>>>>>>> is semantically incorrect in L then instead of saying
>>>>>>>>>>>>>>> that x is undecidable in L the decider rejects x
>>>>>>>>>>>>>>> as invalid input.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> This what Tarski should have done.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> But there are x that are unprovable in L because the chain
>>>>>>>>>>>>>> to them is infinitely long, which makes them true but
>>>>>>>>>>>>>> unprovale.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> (1) x ∉ Provable if and only if p
>>>>>>>>>>>>> (2) x ∈ True if and only if p
>>>>>>>>>>>>> (3) x ∉ Provable if and only if x ∈ True.
>>>>>>>>>>>>>
>>>>>>>>>>>>> When we correct the erroneous line (1) then line (3) becomes
>>>>>>>>>>>>> (3) x ∈ Provable if and only if x ∈ True.
>>>>>>>>>>>>> Thus making your (infinite chain) x simply untrue.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> WHy is it "erroneous", it is a simple statement previously
>>>>>>>>>>>> proven.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> He proved that there are some things that we know
>>>>>>>>>>> are true yet have no way what-so-ever to know that
>>>>>>>>>>> they are true?
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> No, he proved that there are some things that ARE true that we
>>>>>>>>>> can not prove to be true.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> How the Hell is he going to do that on his basis
>>>>>>>>> of the Liar Paradox?
>>>>>>>>>
>>>>>>>>
>>>>>>>> Read his proof. And it isn't "based' on the Liar's paradox,
>>>>>>>
>>>>>>> *It sure as Hell is anchored in the Liar Paradox*
>>>>>>> He get his line (1) directly from the Liar Paradox
>>>>>>>
>>>>>>> Below he shows how he transforms the Liar Paradox
>>>>>>> x ∉ True if and only if p
>>>>>>>
>>>>>>> into his line (1) by replacing "Tr" (for True)
>>>>>>> with 'Pr" (for provable) Here is his line
>>>>>>> (1) x ∉ Provable if and only if p
>>>>>>>
>>>>>>> <page 275>
>>>>>>>     In accordance with the first
>>>>>>>     part of Th. I we can obtain the negation of one of the sentences
>>>>>>>     in condition (α) of convention T of § 3 as a consequence of the
>>>>>>>     definition of the symbol 'Pr' (provided we replace 'Tr' in this
>>>>>>>     convention by 'Pr'). https://liarparadox.org/Tarski_275_276.pdf
>>>>>>> </page 275>
>>>>>>>
>>>>>>> <page 248> Liar Paradox
>>>>>>>     Should we succeed in constructing in the metalanguage
>>>>>>>     a correct definition of truth, then
>>>>>>>
>>>>>>>     It would
>>>>>>>     then be possible to reconstruct the antinomy of the liar in the
>>>>>>>     metalanguage, by forming in the language itself a sentence x
>>>>>>>     such that the sentence of the metalanguage which is correlated
>>>>>>>     with x asserts that x is not a true sentence.
>>>>>>>     https://liarparadox.org/Tarski_247_248.pdf
>>>>>>> </page 248>
>>>>>>>
>>>>>>> Many people today are simply too stupid to understand
>>>>>>> that the Liar Paradox is simply not a truth bearer
>>>>>>> thus must be rejected by any correct True(L, x) predicate.
>>>>>>>
>>>>>>> When Tarski assumes the Liar Paradox as a premise
>>>>>>> this must be rejected and over-ruled.
>>>>>>
>>>>>> Where does he assume it as a premise?
>>>>>>
>>>>>
>>>>> His line (1) is a premise.
>>>>
>>>> Then why does he say, "In other words, we can construct ... " just
>>>> above it.
>>>>
>>>> (1) is a CONCLUSION from the previous paragraph.
>>>>
>>>> you clearly don't know much about logic.
>>>>
>>>>>
>>>>>>>
>>>>>>> (1) x ∉ Provable if and only if p
>>>>>>> must be corrected to say
>>>>>>> (1) x ∈ Provable if and only if p
>>>>>>>
>>>>>>
>>>>>> What was actually wrong with (1). You haven't shown the error in
>>>>>> logic.
>>>>>
>>>>> His line (1) <is> an adapted form of the actual Liar
>>>>> Paradox as I have shown by the quotes above.
>>>>
>>>> NO, the liar paradox says NOTHING about "Provable".
>>>
>>> Tarski says that he takes the Liar Paradox:
>>> x ∉ True if and only if p
>>> and changes it to this
>>> (1) x ∉ Provable if and only if p
>>> on page <275> quoted above.
>>>
>>> It is <page 248> quoted above where he says
>>> that he is using the actual Liar Paradox.
>>>
>>> You have to carefully study what I say before
>>> providing a rebuttal. It took me a half hour
>>> to compose the Tarski quotes.
>>>
>>>
>>
>> Note, page 247 doesn't say "start with the Liar's Paradox" he points
>> out that IT WOULD BE POSSIBLE TO RECONSTRUCT THE LIAR, ie, show that the
> Carefully study every single word of my quotes from
> <page 248> and <page 275> again and again until you
> see that what I say is true.
>
> I had to study these four pages hundreds and hundreds
> of times before I could see that his line (1) was
> adapted from:
> *x ∉ True if and only if p*
> which <is> his version of the Liar Paradox.
>