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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis ---
Date: Fri, 8 Nov 2024 20:17:11 -0500
Organization: i2pn2 (i2pn.org)
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On 11/8/24 8:03 PM, olcott wrote:
> On 11/8/2024 6:58 PM, Richard Damon wrote:
>> On 11/8/24 7:39 PM, olcott wrote:
>>> On 11/8/2024 6:33 PM, Richard Damon wrote:
>>>> On 11/8/24 6:36 PM, olcott wrote:
>>>>> On 11/8/2024 3:59 PM, Richard Damon wrote:
>>>>>> On 11/8/24 4:17 PM, olcott wrote:
>>>>>>> On 11/8/2024 12:31 PM, Richard Damon wrote:
>>>>>>>> On 11/8/24 1:08 PM, olcott wrote:
>>>>>>>>> On 11/8/2024 12:02 PM, Richard Damon wrote:
>>>>>>>>>> On 11/8/24 12:25 PM, olcott wrote:
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> That formal systems that only apply truth preserving
>>>>>>>>>>> operations to expressions of their formal language
>>>>>>>>>>> that have been stipulated to be true cannot possibly
>>>>>>>>>>> be undecidable is proven to be over-your-head on the
>>>>>>>>>>> basis that you have no actual reasoning as a rebuttal.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> No, all you have done is shown that you don't undertstand what 
>>>>>>>>>> you are talking about.
>>>>>>>>>>
>>>>>>>>>> Godel PROVED that the FORMAL SYSTEM that his proof started in, 
>>>>>>>>>> is unable to PROVE that the statement G, being "that no 
>>>>>>>>>> Natural Number g, that satifies a particularly designed 
>>>>>>>>>> Primitive Recursive Relationship" is true, but also shows 
>>>>>>>>>> (using the Meta- Mathematics that derived the PRR for the 
>>>>>>>>>> original Formal System) that no such number can exist.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> The equivocation of switching formal systems from PA to meta-math.
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> No, it just shows you don't understand how meta-systems work.
>>>>>>>>
>>>>>>>
>>>>>>> IT SHOWS THAT I KNOW IT IS STUPID TO
>>>>>>> CONSTRUE TRUE IN META-MATH AS TRUE IN PA.
>>>>>>> THAT YOU DON'T UNDERSTAND THIS IS STUPID IS YOUR ERROR.
>>>>>>
>>>>>> But, as I pointed out, the way Meta-Math is derived from PA, 
>>>>>
>>>>> Meta-math <IS NOT> PA.
>>>>> Meta-math <IS NOT> PA.
>>>>> Meta-math <IS NOT> PA.
>>>>> Meta-math <IS NOT> PA.
>>>>>
>>>>> True in meta-math <IS NOT> True in PA.
>>>>> True in meta-math <IS NOT> True in PA.
>>>>> True in meta-math <IS NOT> True in PA.
>>>>> True in meta-math <IS NOT> True in PA.
>>>>>
>>>>> This sentence is not true: "This sentence is not true"
>>>>> is only true because the inner sentence is bullshit gibberish.
>>>>>
>>>>>
>>>>
>>>> But MM has exactly the same axioms and rules as PA, so anything 
>>>> established by that set of axioms and rules in MM is established in 
>>>> PA too.
>>>>
>>>> There are additional axioms in MM, but the rules are built specifically 
>>>
>>> One single level of indirect reference CHANGES EVERYTHING.
>>> PA speaks PA. Meta-math speaks ABOUT PA.
>>>
>>> The liar paradox is nonsense gibberish except when applied
>>> to itself, then it becomes true.
>>>
>>
>> No, Meta-Math speaks PA, because is includes ALL the axioms and rules 
>> of PA, so it can speak PA.
>>
>> You just don't understand what a meta-system is.
>>
> 
> In C we can have a pointer to a character string
> and a pointer to a pointer to a character string.
> 

But we are not talking about C.

> The pointer to pointer is one level of indirect
> reference away form the pointer to the character string.

But the meta-math is not restricted to nust talking about PA, it can 
talk in the language of PA.

> 
> I know exactly what a meta-system is. It is a system that
> refers to the underlying system by one level of indirect
> reference. PA talks PA meta-math talks ABOUT PA.
> 

Nope, you THINK you know about what a meta-system is, but you don't.

You are using a definition from another context which isn't applicable.

The "meta" systems, are system that FULLY INHERET the base system, and 
then ADD information about that system, in a way they can still talk the 
original language.

Sorry, you are just proving your ignorance.

Read the papers and where they talk about how the meta-systems are built.