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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: A computable function that reports on the behavior of its actual
 self is not allowed
Date: Mon, 13 May 2024 20:30:32 -0400
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On 5/13/24 10:10 AM, olcott wrote:
> On 5/13/2024 8:55 AM, Fred. Zwarts wrote:
>> Op 13.mei.2024 om 15:39 schreef olcott:
>>> On 5/13/2024 4:34 AM, Fred. Zwarts wrote:
>>>> Op 12.mei.2024 om 21:27 schreef olcott:
>>>>> Computable functions are the basic objects of study in computability
>>>>> theory. Computable functions are the formalized analogue of the
>>>>> intuitive notion of algorithms, in the sense that a function is
>>>>> computable if there exists an algorithm that can do the job of the
>>>>> function, i.e. given an input of the function domain it can return the
>>>>> corresponding output. 
>>>>> https://en.wikipedia.org/wiki/Computable_function
>>>>>
>>>>> A computable function that reports on the behavior of its actual
>>>>> self (or reports on the behavior of its caller) is not allowed.
>>>>
>>>> So, olcott uses his authority to create a new problem. Why would 
>>>> anybody be interested in such limitation?
>>>>
>>>
>>> The definition of computable function is an axiomatic basis
>>> not any mere authority.
>>
>> I was referring to the "is not allowed". If olcott uses his authority 
>> to introduce a new axiom with this sentence, a new problem is created. 
>> Who is interested in a system with this new limitation?
>>
> 
> No decider can take an actual Turing Machine as its input.
> 

But the HALTING function that it is trying to compute DOES, thus the 
Turing Machine takes some from of representation / description / 
specification of that input.

Like MOST inputs to Turing Machines trying to compute some Function.

The only Functions that don't need this are the (relatively few) 
Functions whose input IS a finite string, and even then, often the 
Turing Machine will need to answer with a representation unless that 
output was also a finite string.