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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 19:58:56 -0500
Organization: i2pn2 (i2pn.org)
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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.

It is derived from the base system, and the meta part can talk about the 
system, but it still has ALL the contents of the base system, so it can 
"talk" that system, and not just "about" the system.

You are stuck on the "Liar Paradox", because you think it is your way 
out, except for the fact that you don't understand what was done with 
it, so the "error" you charge never happened.

Sorry, you are just proving your stupidity,