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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis ---
Date: Fri, 8 Nov 2024 18:39:34 -0600
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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.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer