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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Two computer science professors agree with Flibble
Date: Sun, 4 May 2025 23:40:34 -0400
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In-Reply-To: <vv9bli$3ifj7$2@dont-email.me>

On 5/4/2025 11:35 PM, olcott wrote:
> On 5/4/2025 10:18 PM, dbush wrote:
>> On 5/4/2025 11:10 PM, olcott wrote:
>>> On 5/4/2025 10:00 PM, dbush wrote:
>>>> On 5/4/2025 9:38 PM, olcott wrote:
>>>>> On 5/4/2025 8:13 PM, Ben Bacarisse wrote:
>>>>>> Richard Heathfield <rjh@cpax.org.uk> writes:
>>>>>>
>>>>>>> On 04/05/2025 23:34, Mr Flibble wrote:
>>>>>>>> The function is neither computable nor incomputable because 
>>>>>>>> there is no
>>>>>>>> function at all, just a category error.
>>>>>>>
>>>>>>> It's a point of view.
>>>>>>
>>>>>> It's a point of view only in the sense that there is no opinion so 
>>>>>> daft
>>>>>> that it's not someone's point of view.  The technical-sounding waffle
>>>>>> about it being a "category error" is simply addressed by asking where
>>>>>> the supposed category error is in other perfectly straightforward
>>>>>> undecidable problems.  For example, whether or not a context-free
>>>>>> grammar is ambiguous or not, or the very simple to pose Post
>>>>>> correspondence problem.
>>>>>>
>>>>>
>>>>> Flibble IS CORRECT when the halting problem is defined
>>>>> to be isomorphic (AKA analogous) to the Liar Paradox:
>>>>> "This sentence is not true".
>>>>>
>>>>> When the Halting Problem is defined as an input that
>>>>> does the opposite of whatever its decider reports
>>>>> then both Boolean return values are incorrect 
>>>>
>>>> False.  One value is correct and one is incorrect.
>>>>
>>>
>>> Both Boolean RETURN VALUES FROM H *ARE* INCORRECT,
>> Category error.  Algorithms do one thing and one thing only.  And the 
>> algorithm that is the fixed code of the function H and everything it 
>> calls gives the wrong answer, and the opposing answer is the right 
>> answer.
> 
> Look at the paper from the PhD computer science
> professor.
> 
> Halting misconceived?
> Bill Stoddart
> August 25, 2017
> 
> *the halting function, as described, cannot be implemented*,
> *because its specication is inconsistent*...
> 
> *Context*
> That halting is not in general computable has been
> proved in many text books and taught on many computer
> science courses, and is supposed to illustrate the
> limits of computation. However, there is a dissenting
> view that these proofs are misconceived.
> 
> In this paper we look at what is perhaps the simplest
> such proof, based on a program that interrogates its own
> halting behaviour and then decides to thwart it. This
> leads to a contradiction that is generally held to show
> that a halting function cannot be implemented.
> 
> The dissenting view agrees with the conclusion that
> *the halting function, as described, cannot be implemented*,
> but suggests that this is *because its specication is inconsistent*
> https://www.complang.tuwien.ac.at/anton/euroforth/ef17/papers/stoddart.pdf
> 

The only way for the specification to be inconsistent if there was an 
algorithm, i.e. a fixed immutable sequence of instructions, that neither 
halts nor not halts when executed directly.

That no such algorithm exists is proof that the specification is not 
inconsistent.