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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 15:17:28 -0600
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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.

> The Formal System is PA. that defines the basic axioms that are to be 
> used to establish the truth of the statement and where to attempt the 
> proof of it.
> 
> The Meta-Math, is an EXTENSION to PA, where we add a number of 
> additional axioms, none that contradict any of the axions of PA, but in 
> particular, assign each axiom and needed proven statement in PA to a 
> prime number. These provide the additional semantics in the Meta-Math to 
> understand the new meaning that a number could have, and with that 
> semantics, using just the mathematics of PA, the PRR is derived that 
> with the semantics of the MM becomes a proof-checker.
> 
> Note, the Meta-Math is carefully constructed so that there is a 
> correlation of truth, such that anything true in PA is true in MM, and 
> anything statement shown in MM to be true, that doesn't use the 
> additional terms defined, is also true in PA.
> 
> There is no equivocation in that, as nothing changed meaning, only some 
> things that didn't have a semantic meaning (like a number) now does.
> 
> If you want to try to show an actual error or equivocation, go ahead and 
> try, but so far, all you have done is shown that you don't even seem to 
> understand what a Formal System is, since you keep on wanting to "re- 
> invent them" but just repeat the basic definition of them.


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