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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic,comp.theory
Subject: The philosophy of computation reformulates existing ideas on a new
 basis ---
Date: Sun, 27 Oct 2024 09:17:19 -0500
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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.

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.

> That means that the Halting Problem isn't a problem.
> 
>>
>>> and in a way that is potentially undetectable.
>>>
>>
>> I really don't think so it only seems that way.
> 
> Of course it is.
> 
> The method of assigning meaning to the symbols can be done is a meta- 
> system that the system doesn't know about, and thus its meaning is 
> unknowable to the logic system.
> 

When the only way that you learn is to memorize things from books
you make huge mistakes. It is the typical convention to assign
meaning in a way that the systems is unaware of. This is not the
only possible way. It is a ridiculously stupid way that causes
all kinds of undetectable semantic errors.

>>
>>> You don't seem to understand that fact, but the fundamental nature of 
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