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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic,comp.theory
Subject: Re: The philosophy of computation reformulates existing ideas on a
 new basis ---
Date: Sun, 27 Oct 2024 13:48:55 -0400
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On 10/27/24 10:17 AM, olcott wrote:
> I am keeping this post in both sci.logic and comp.theory
> because it focuses on a similar idea to the Curry/Howard
> correspondence between formal systems and computation.
> 
> Computation and all of the mathematical and logical operations
> of mathematical logic can be construed as finite string
> transformation rules applied to finite strings.
> 
> The semantics associated with finite string tokens can
> be directly accessible to expression in the formal language.
> It is basically an enriched type hierarchy called a knowledge
> ontology.
> 
> A computation can be construed as the tape input to a
> Turing machine and its tape output. All of the cases
> where the output was construed as a set of final machine
> states can be written to the tape.
> 
> I am not sure but I think that this may broaden the scope
> of a computable function, or not.

Except that nothing you described related to what a "computabe function" 
is at all, as a "Computable Function" is just a Function (which is just 
a specific, but arbitrary, mapping of an input space to an output space) 
that can have a computation built that computes that mapping based on 
representations of items in the input space to representations of items 
in the output space.

> 
> The operations of formal systems can thus be directly
> performed by a TM. to make things more interesting the
> tape alphabet is UTM-32 of a TM equivalent RASP machine.


> 
> On 10/27/2024 6:38 AM, Richard Damon wrote:
>> On 10/26/24 9:22 PM, olcott wrote:
>>> On 10/26/2024 8:04 PM, Richard Damon wrote:
>>>> On 10/26/24 5:57 PM, olcott wrote:
>>>>> On 10/26/2024 10:48 AM, Richard Damon wrote:
>>>>>> On 10/26/24 8:59 AM, olcott wrote:
>>>>>>> On 10/26/2024 2:52 AM, Mikko wrote:
>>>>>>>> On 2024-10-25 14:37:19 +0000, olcott said:
>>>>>>>>
>>>>>>>>> On 10/25/2024 3:14 AM, Mikko wrote:
>>>>>>>>>> On 2024-10-24 16:07:03 +0000, olcott said:
>>>>>>>>>>
>>>>>>>>>>> On 10/24/2024 9:06 AM, Mikko wrote:
>>>>>>>>>>>> On 2024-10-22 15:04:37 +0000, olcott said:
>>>>>>>>>>>>
>>>>>>>>>>>>> On 10/22/2024 2:39 AM, Mikko wrote:
>>>>>>>>>>>>>> On 2024-10-22 02:04:14 +0000, olcott said:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> On 10/16/2024 11:37 AM, Mikko wrote:
>>>>>>>>>>>>>>>> On 2024-10-16 14:27:09 +0000, olcott said:
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> The whole notion of undecidability is anchored in 
>>>>>>>>>>>>>>>>> ignoring the fact that
>>>>>>>>>>>>>>>>> some expressions of language are simply not truth bearers.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> A formal theory is undecidable if there is no Turing 
>>>>>>>>>>>>>>>> machine that
>>>>>>>>>>>>>>>> determines whether a formula of that theory is a theorem 
>>>>>>>>>>>>>>>> of that
>>>>>>>>>>>>>>>> theory or not. Whether an expression is a truth bearer 
>>>>>>>>>>>>>>>> is not
>>>>>>>>>>>>>>>> relevant. Either there is a valid proof of that formula 
>>>>>>>>>>>>>>>> or there
>>>>>>>>>>>>>>>> is not. No third possibility.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> After being continually interrupted by emergencies
>>>>>>>>>>>>>>> interrupting other emergencies...
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> If the answer to the question: Is X a formula of theory Y
>>>>>>>>>>>>>>> cannot be determined to be yes or no then the question
>>>>>>>>>>>>>>> itself is somehow incorrect.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> There are several possibilities.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> A theory may be intentionally incomplete. For example, 
>>>>>>>>>>>>>> group theory
>>>>>>>>>>>>>> leaves several important question unanswered. There are 
>>>>>>>>>>>>>> infinitely
>>>>>>>>>>>>>> may different groups and group axioms must be true in 
>>>>>>>>>>>>>> every group.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Another possibility is that a theory is poorly 
>>>>>>>>>>>>>> constructed: the
>>>>>>>>>>>>>> author just failed to include an important postulate.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Then there is the possibility that the purpose of the 
>>>>>>>>>>>>>> theory is
>>>>>>>>>>>>>> incompatible with decidability, for example arithmetic.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> An incorrect question is an expression of language that
>>>>>>>>>>>>>>> is not a truth bearer translated into question form.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> When "X a formula of theory Y" is neither true nor false
>>>>>>>>>>>>>>> then "X a formula of theory Y" is not a truth bearer.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Whether AB = BA is not answered by group theory but is alwasy
>>>>>>>>>>>>>> true or false about specific A and B and universally true in
>>>>>>>>>>>>>> some groups but not all.
>>>>>>>>>>>>>
>>>>>>>>>>>>> See my most recent reply to Richard it sums up
>>>>>>>>>>>>> my position most succinctly.
>>>>>>>>>>>>
>>>>>>>>>>>> We already know that your position is uninteresting.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Don't want to bother to look at it (AKA uninteresting) is not at
>>>>>>>>>>> all the same thing as the corrected foundation to computability
>>>>>>>>>>> does not eliminate undecidability.
>>>>>>>>>>
>>>>>>>>>> No, but we already know that you don't offer anything interesting
>>>>>>>>>> about foundations to computability or undecidabilty.
>>>>>>>>>
>>>>>>>>> In the same way that ZFC eliminated RP True_Olcott(L,x)
>>>>>>>>> eliminates undecidability. Not bothering to pay attention
>>>>>>>>> is less than no rebuttal what-so-ever.
>>>>>>>>
>>>>>>>> No, not in the same way. 
>>>>>>>
>>>>>>> Pathological self reference causes an issue in both cases.
>>>>>>> This issue is resolved by disallowing it in both cases.
>>>>>>
>>>>>> Nope, because is set theory, the "self-reference" 
>>>>>
>>>>> does exist and is problematic in its several other instances.
>>>>> Abolishing it in each case DOES ELIMINATE THE FREAKING PROBLEM.
>>>>>
>>>>
>>>> Yes, IN SET THEORY, the "self-reference" can be banned, by the 
>>>> nature of the contstruction.
>>>>
>>>
>>> That seems to be the best way.
>>
>> It works for sets, but not for Computations, due to the way things are 
>> defined.
>>
>>>
>>>> In Computation Theory it can not, without making the system less 
>>>> than Turing Complete, as the structure of the Computations 
>>>> fundamentally allow for it, 
>>>
>>> Sure.
>>
>> So, you ADMIT that your computation system you are trying to advocate 
>> is less than Turing Complete?
>>
> 
> I never said that.

Sure you do.

You have said that D isn't allowed to make its own copy of H.

YOu have said that some inputs are just not allowed to be given.

In a Turing Complete system, ANY program can have a copy of it made and 
be encorporated within the code of another totally independent program.

And a Turing Complete decider can take *ANY* input and decide on it.

> 
>> That means that the Halting Problem isn't a problem.
>>
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